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Global Optimality Beyond Two Layers: Training Deep ReLU Networks via Convex Programs | null | Understanding the fundamental mechanism behind the success of deep neural networks is one of the key challenges in the modern machine learning literature. Despite numerous attempts, a solid theoretical analysis is yet to be developed. In this paper, we develop a novel unified framework to reveal a hidden regularization mechanism through the lens of convex optimization. We first show that the training of multiple three-layer ReLU sub-networks with weight decay regularization can be equivalently cast as a convex optimization problem in a higher dimensional space, where sparsity is enforced via a group $\ell_1$-norm regularization. Consequently, ReLU networks can be interpreted as high dimensional feature selection methods. More importantly, we then prove that the equivalent convex problem can be globally optimized by a standard convex optimization solver with a polynomial-time complexity with respect to the number of samples and data dimension when the width of the network is fixed. Finally, we numerically validate our theoretical results via experiments involving both synthetic and real datasets. | Tolga Ergen, Mert Pilanci | null | null | 2,021 | icml |
Poisson-Randomised DirBN: Large Mutation is Needed in Dirichlet Belief Networks | null | The Dirichlet Belief Network (DirBN) was recently proposed as a promising deep generative model to learn interpretable deep latent distributions for objects. However, its current representation capability is limited since its latent distributions across different layers is prone to form similar patterns and can thus hardly use multi-layer structure to form flexible distributions. In this work, we propose Poisson-randomised Dirichlet Belief Networks (Pois-DirBN), which allows large mutations for the latent distributions across layers to enlarge the representation capability. Based on our key idea of inserting Poisson random variables in the layer-wise connection, Pois-DirBN first introduces a component-wise propagation mechanism to enable latent distributions to have large variations across different layers. Then, we develop a layer-wise Gibbs sampling algorithm to infer the latent distributions, leading to a larger number of effective layers compared to DirBN. In addition, we integrate out latent distributions and form a multi-stochastic deep integer network, which provides an alternative view on Pois-DirBN. We apply Pois-DirBN to relational modelling and validate its effectiveness through improved link prediction performance and more interpretable latent distribution visualisations. The code can be downloaded at https://github.com/xuhuifan/Pois_DirBN. | Xuhui Fan, Bin Li, Yaqiong Li, Scott A. Sisson | null | null | 2,021 | icml |
On Variational Inference in Biclustering Models | null | Biclustering structures exist ubiquitously in data matrices and the biclustering problem was first formalized by John Hartigan (1972) to cluster rows and columns simultaneously. In this paper, we develop a theory for the estimation of general biclustering models, where the data is assumed to follow certain statistical distribution with underlying biclustering structure. Due to the existence of latent variables, directly computing the maximal likelihood estimator is prohibitively difficult in practice and we instead consider the variational inference (VI) approach to solve the parameter estimation problem. Although variational inference method generally has good empirical performance, there are very few theoretical results around VI. In this paper, we obtain the precise estimation bound of variational estimator and show that it matches the minimax rate in terms of estimation error under mild assumptions in biclustering setting. Furthermore, we study the convergence property of the coordinate ascent variational inference algorithm, where both local and global convergence results have been provided. Numerical results validate our new theories. | Guanhua Fang, Ping Li | null | null | 2,021 | icml |
Near-Optimal Entrywise Anomaly Detection for Low-Rank Matrices with Sub-Exponential Noise | null | We study the problem of identifying anomalies in a low-rank matrix observed with sub-exponential noise, motivated by applications in retail and inventory management. State of the art approaches to anomaly detection in low-rank matrices apparently fall short, since they require that non-anomalous entries be observed with vanishingly small noise (which is not the case in our problem, and indeed in many applications). So motivated, we propose a conceptually simple entrywise approach to anomaly detection in low-rank matrices. Our approach accommodates a general class of probabilistic anomaly models. We extend recent work on entrywise error guarantees for matrix completion, establishing such guarantees for sub-exponential matrices, where in addition to missing entries, a fraction of entries are corrupted by (an also unknown) anomaly model. Viewing the anomaly detection as a classification task, to the best of our knowledge, we are the first to achieve the min-max optimal detection rate (up to log factors). Using data from a massive consumer goods retailer, we show that our approach provides significant improvements over incumbent approaches to anomaly detection. | Vivek Farias, Andrew A Li, Tianyi Peng | null | null | 2,021 | icml |
On Estimation in Latent Variable Models | null | Latent variable models have been playing a central role in statistics, econometrics, machine learning with applications to repeated observation study, panel data inference, user behavior analysis, etc. In many modern applications, the inference based on latent variable models involves one or several of the following features: the presence of complex latent structure, the observed and latent variables being continuous or discrete, constraints on parameters, and data size being large. Therefore, solving an estimation problem for general latent variable models is highly non-trivial. In this paper, we consider a gradient based method via using variance reduction technique to accelerate estimation procedure. Theoretically, we show the convergence results for the proposed method under general and mild model assumptions. The algorithm has better computational complexity compared with the classical gradient methods and maintains nice statistical properties. Various numerical results corroborate our theory. | Guanhua Fang, Ping Li | null | null | 2,021 | icml |
Model-based Reinforcement Learning for Continuous Control with Posterior Sampling | null | Balancing exploration and exploitation is crucial in reinforcement learning (RL). In this paper, we study model-based posterior sampling for reinforcement learning (PSRL) in continuous state-action spaces theoretically and empirically. First, we show the first regret bound of PSRL in continuous spaces which is polynomial in the episode length to the best of our knowledge. With the assumption that reward and transition functions can be modeled by Bayesian linear regression, we develop a regret bound of $\tilde{O}(H^{3/2}d\sqrt{T})$, where $H$ is the episode length, $d$ is the dimension of the state-action space, and $T$ indicates the total time steps. This result matches the best-known regret bound of non-PSRL methods in linear MDPs. Our bound can be extended to nonlinear cases as well with feature embedding: using linear kernels on the feature representation $\phi$, the regret bound becomes $\tilde{O}(H^{3/2}d_{\phi}\sqrt{T})$, where $d_\phi$ is the dimension of the representation space. Moreover, we present MPC-PSRL, a model-based posterior sampling algorithm with model predictive control for action selection. To capture the uncertainty in models, we use Bayesian linear regression on the penultimate layer (the feature representation layer $\phi$) of neural networks. Empirical results show that our algorithm achieves the state-of-the-art sample efficiency in benchmark continuous control tasks compared to prior model-based algorithms, and matches the asymptotic performance of model-free algorithms. | Ying Fan, Yifei Ming | null | null | 2,021 | icml |
Train simultaneously, generalize better: Stability of gradient-based minimax learners | null | The success of minimax learning problems of generative adversarial networks (GANs) has been observed to depend on the minimax optimization algorithm used for their training. This dependence is commonly attributed to the convergence speed and robustness properties of the underlying optimization algorithm. In this paper, we show that the optimization algorithm also plays a key role in the generalization performance of the trained minimax model. To this end, we analyze the generalization properties of standard gradient descent ascent (GDA) and proximal point method (PPM) algorithms through the lens of algorithmic stability as defined by Bousquet & Elisseeff, 2002 under both convex-concave and nonconvex-nonconcave minimax settings. While the GDA algorithm is not guaranteed to have a vanishing excess risk in convex-concave problems, we show the PPM algorithm enjoys a bounded excess risk in the same setup. For nonconvex-nonconcave problems, we compare the generalization performance of stochastic GDA and GDmax algorithms where the latter fully solves the maximization subproblem at every iteration. Our generalization analysis suggests the superiority of GDA provided that the minimization and maximization subproblems are solved simultaneously with similar learning rates. We discuss several numerical results indicating the role of optimization algorithms in the generalization of learned minimax models. | Farzan Farnia, Asuman Ozdaglar | null | null | 2,021 | icml |
Weight-covariance alignment for adversarially robust neural networks | null | Stochastic Neural Networks (SNNs) that inject noise into their hidden layers have recently been shown to achieve strong robustness against adversarial attacks. However, existing SNNs are usually heuristically motivated, and often rely on adversarial training, which is computationally costly. We propose a new SNN that achieves state-of-the-art performance without relying on adversarial training, and enjoys solid theoretical justification. Specifically, while existing SNNs inject learned or hand-tuned isotropic noise, our SNN learns an anisotropic noise distribution to optimize a learning-theoretic bound on adversarial robustness. We evaluate our method on a number of popular benchmarks, show that it can be applied to different architectures, and that it provides robustness to a variety of white-box and black-box attacks, while being simple and fast to train compared to existing alternatives. | Panagiotis Eustratiadis, Henry Gouk, Da Li, Timothy Hospedales | null | null | 2,021 | icml |
Streaming Bayesian Deep Tensor Factorization | null | Despite the success of existing tensor factorization methods, most of them conduct a multilinear decomposition, and rarely exploit powerful modeling frameworks, like deep neural networks, to capture a variety of complicated interactions in data. More important, for highly expressive, deep factorization, we lack an effective approach to handle streaming data, which are ubiquitous in real-world applications. To address these issues, we propose SBTD, a Streaming Bayesian Deep Tensor factorization method. We first use Bayesian neural networks (NNs) to build a deep tensor factorization model. We assign a spike-and-slab prior over each NN weight to encourage sparsity and to prevent overfitting. We then use multivariate Delta’s method and moment matching to approximate the posterior of the NN output and calculate the running model evidence, based on which we develop an efficient streaming posterior inference algorithm in the assumed-density-filtering and expectation propagation framework. Our algorithm provides responsive incremental updates for the posterior of the latent factors and NN weights upon receiving newly observed tensor entries, and meanwhile identify and inhibit redundant/useless weights. We show the advantages of our approach in four real-world applications. | Shikai Fang, Zheng Wang, Zhimeng Pan, Ji Liu, Shandian Zhe | null | null | 2,021 | icml |
Risk-Sensitive Reinforcement Learning with Function Approximation: A Debiasing Approach | null | We study function approximation for episodic reinforcement learning with entropic risk measure. We first propose an algorithm with linear function approximation. Compared to existing algorithms, which suffer from improper regularization and regression biases, this algorithm features debiasing transformations in backward induction and regression procedures. We further propose an algorithm with general function approximation, which features implicit debiasing transformations. We prove that both algorithms achieve a sublinear regret and demonstrate a trade-off between generality and efficiency. Our analysis provides a unified framework for function approximation in risk-sensitive reinforcement learning, which leads to the first sublinear regret bounds in the setting. | Yingjie Fei, Zhuoran Yang, Zhaoran Wang | null | null | 2,021 | icml |
Unbalanced minibatch Optimal Transport; applications to Domain Adaptation | null | Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale datasets. Among the possible strategies to alleviate this issue, practitioners can rely on computing estimates of these distances over subsets of data, i.e. minibatches. While computationally appealing, we highlight in this paper some limits of this strategy, arguing it can lead to undesirable smoothing effects. As an alternative, we suggest that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behaviors. We discuss the associated theoretical properties, such as unbiased estimators, existence of gradients and concentration bounds. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines. | Kilian Fatras, Thibault Sejourne, Rémi Flamary, Nicolas Courty | null | null | 2,021 | icml |
Connecting Optimal Ex-Ante Collusion in Teams to Extensive-Form Correlation: Faster Algorithms and Positive Complexity Results | null | We focus on the problem of finding an optimal strategy for a team of players that faces an opponent in an imperfect-information zero-sum extensive-form game. Team members are not allowed to communicate during play but can coordinate before the game. In this setting, it is known that the best the team can do is sample a profile of potentially randomized strategies (one per player) from a joint (a.k.a. correlated) probability distribution at the beginning of the game. In this paper, we first provide new modeling results about computing such an optimal distribution by drawing a connection to a different literature on extensive-form correlation. Second, we provide an algorithm that allows one for capping the number of profiles employed in the solution. This begets an anytime algorithm by increasing the cap. We find that often a handful of well-chosen such profiles suffices to reach optimal utility for the team. This enables team members to reach coordination through a simple and understandable plan. Finally, inspired by this observation and leveraging theoretical concepts that we introduce, we develop an efficient column-generation algorithm for finding an optimal distribution for the team. We evaluate it on a suite of common benchmark games. It is three orders of magnitude faster than the prior state of the art on games that the latter can solve and it can also solve several games that were previously unsolvable. | Gabriele Farina, Andrea Celli, Nicola Gatti, Tuomas Sandholm | null | null | 2,021 | icml |
Reserve Price Optimization for First Price Auctions in Display Advertising | null | The display advertising industry has recently transitioned from second- to first-price auctions as its primary mechanism for ad allocation and pricing. In light of this, publishers need to re-evaluate and optimize their auction parameters, notably reserve prices. In this paper, we propose a gradient-based algorithm to adaptively update and optimize reserve prices based on estimates of bidders’ responsiveness to experimental shocks in reserves. Our key innovation is to draw on the inherent structure of the revenue objective in order to reduce the variance of gradient estimates and improve convergence rates in both theory and practice. We show that revenue in a first-price auction can be usefully decomposed into a \emph{demand} component and a \emph{bidding} component, and introduce techniques to reduce the variance of each component. We characterize the bias-variance trade-offs of these techniques and validate the performance of our proposed algorithm through experiments on synthetic data and real display ad auctions data from a major ad exchange. | Zhe Feng, Sebastien Lahaie, Jon Schneider, Jinchao Ye | null | null | 2,021 | icml |
Dimensionality Reduction for the Sum-of-Distances Metric | null | We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any “shape” that lies in a $k$-dimensional subspace. Here, by “shape” we mean any set of points in $R^d$. Our algorithm takes an input in the form of an $n \times d$ matrix $A$, where each row of $A$ denotes a data point, and outputs a subspace $P$ of dimension $O(k^{3}/\epsilon^6)$ such that the projections of each of the $n$ points onto the subspace $P$ and the distances of each of the points to the subspace $P$ are sufficient to obtain an $\epsilon$-approximation to the sum of distances to any arbitrary shape that lies in a $k$-dimensional subspace of $R^d$. These include important problems such as $k$-median, $k$-subspace approximation, and $(j,l)$ subspace clustering with $j \cdot l \leq k$. Dimensionality reduction reduces the data storage requirement to $(n+d)k^{3}/\epsilon^6$ from nnz$(A)$. Here nnz$(A)$ could potentially be as large as $nd$. Our algorithm runs in time nnz$(A)/\epsilon^2 + (n+d)$poly$(k/\epsilon)$, up to logarithmic factors. For dense matrices, where nnz$(A) \approx nd$, we give a faster algorithm, that runs in time $nd + (n+d)$poly$(k/\epsilon)$ up to logarithmic factors. Our dimensionality reduction algorithm can also be used to obtain poly$(k/\epsilon)$ size coresets for $k$-median and $(k,1)$-subspace approximation problems in polynomial time. | Zhili Feng, Praneeth Kacham, David Woodruff | null | null | 2,021 | icml |
KD3A: Unsupervised Multi-Source Decentralized Domain Adaptation via Knowledge Distillation | null | Conventional unsupervised multi-source domain adaptation (UMDA) methods assume all source domains can be accessed directly. However, this assumption neglects the privacy-preserving policy, where all the data and computations must be kept decentralized. There exist three challenges in this scenario: (1) Minimizing the domain distance requires the pairwise calculation of the data from the source and target domains, while the data on the source domain is not available. (2) The communication cost and privacy security limit the application of existing UMDA methods, such as the domain adversarial training. (3) Since users cannot govern the data quality, the irrelevant or malicious source domains are more likely to appear, which causes negative transfer. To address the above problems, we propose a privacy-preserving UMDA paradigm named Knowledge Distillation based Decentralized Domain Adaptation (KD3A), which performs domain adaptation through the knowledge distillation on models from different source domains. The extensive experiments show that KD3A significantly outperforms state-of-the-art UMDA approaches. Moreover, the KD3A is robust to the negative transfer and brings a 100x reduction of communication cost compared with other decentralized UMDA methods. | Haozhe Feng, Zhaoyang You, Minghao Chen, Tianye Zhang, Minfeng Zhu, Fei Wu, Chao Wu, Wei Chen | null | null | 2,021 | icml |
Uncertainty Principles of Encoding GANs | null | The compelling synthesis results of Generative Adversarial Networks (GANs) demonstrate rich semantic knowledge in their latent codes. To obtain this knowledge for downstream applications, encoding GANs has been proposed to learn encoders, such that real world data can be encoded to latent codes, which can be fed to generators to reconstruct those data. However, despite the theoretical guarantees of precise reconstruction in previous works, current algorithms generally reconstruct inputs with non-negligible deviations from inputs. In this paper we study this predicament of encoding GANs, which is indispensable research for the GAN community. We prove three uncertainty principles of encoding GANs in practice: a) the ‘perfect’ encoder and generator cannot be continuous at the same time, which implies that current framework of encoding GANs is ill-posed and needs rethinking; b) neural networks cannot approximate the underlying encoder and generator precisely at the same time, which explains why we cannot get ‘perfect’ encoders and generators as promised in previous theories; c) neural networks cannot be stable and accurate at the same time, which demonstrates the difficulty of training and trade-off between fidelity and disentanglement encountered in previous works. Our work may eliminate gaps between previous theories and empirical results, promote the understanding of GANs, and guide network designs for follow-up works. | Ruili Feng, Zhouchen Lin, Jiapeng Zhu, Deli Zhao, Jingren Zhou, Zheng-Jun Zha | null | null | 2,021 | icml |
A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups | null | Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation, and permutation groups. In this work we provide a completely general algorithm for solving for the equivariant layers of matrix groups. In addition to recovering solutions from other works as special cases, we construct multilayer perceptrons equivariant to multiple groups that have never been tackled before, including $\mathrm{O}(1,3)$, $\mathrm{O}(5)$, $\mathrm{Sp}(n)$, and the Rubik’s cube group. Our approach outperforms non-equivariant baselines, with applications to particle physics and modeling dynamical systems. We release our software library to enable researchers to construct equivariant layers for arbitrary | Marc Finzi, Max Welling, Andrew Gordon Wilson | null | null | 2,021 | icml |
Few-Shot Conformal Prediction with Auxiliary Tasks | null | We develop a novel approach to conformal prediction when the target task has limited data available for training. Conformal prediction identifies a small set of promising output candidates in place of a single prediction, with guarantees that the set contains the correct answer with high probability. When training data is limited, however, the predicted set can easily become unusably large. In this work, we obtain substantially tighter prediction sets while maintaining desirable marginal guarantees by casting conformal prediction as a meta-learning paradigm over exchangeable collections of auxiliary tasks. Our conformalization algorithm is simple, fast, and agnostic to the choice of underlying model, learning algorithm, or dataset. We demonstrate the effectiveness of this approach across a number of few-shot classification and regression tasks in natural language processing, computer vision, and computational chemistry for drug discovery. | Adam Fisch, Tal Schuster, Tommi Jaakkola, Dr.Regina Barzilay | null | null | 2,021 | icml |
Understanding Noise Injection in GANs | null | Noise injection is an effective way of circumventing overfitting and enhancing generalization in machine learning, the rationale of which has been validated in deep learning as well. Recently, noise injection exhibits surprising effectiveness when generating high-fidelity images in Generative Adversarial Networks (GANs) (e.g. StyleGAN). Despite its successful applications in GANs, the mechanism of its validity is still unclear. In this paper, we propose a geometric framework to theoretically analyze the role of noise injection in GANs. First, we point out the existence of the adversarial dimension trap inherent in GANs, which leads to the difficulty of learning a proper generator. Second, we successfully model the noise injection framework with exponential maps based on Riemannian geometry. Guided by our theories, we propose a general geometric realization for noise injection. Under our novel framework, the simple noise injection used in StyleGAN reduces to the Euclidean case. The goal of our work is to make theoretical steps towards understanding the underlying mechanism of state-of-the-art GAN algorithms. Experiments on image generation and GAN inversion validate our theory in practice. | Ruili Feng, Deli Zhao, Zheng-Jun Zha | null | null | 2,021 | icml |
What’s in the Box? Exploring the Inner Life of Neural Networks with Robust Rules | null | We propose a novel method for exploring how neurons within neural networks interact. In particular, we consider activation values of a network for given data, and propose to mine noise-robust rules of the form X {\rightarrow} Y , where X and Y are sets of neurons in different layers. We identify the best set of rules by the Minimum Description Length Principle as the rules that together are most descriptive of the activation data. To learn good rule sets in practice, we propose the unsupervised ExplaiNN algorithm. Extensive evaluation shows that the patterns it discovers give clear insight in how networks perceive the world: they identify shared, respectively class-specific traits, compositionality within the network, as well as locality in convolutional layers. Moreover, these patterns are not only easily interpretable, but also supercharge prototyping as they identify which groups of neurons to consider in unison. | Jonas Fischer, Anna Olah, Jilles Vreeken | null | null | 2,021 | icml |
PID Accelerated Value Iteration Algorithm | null | The convergence rate of Value Iteration (VI), a fundamental procedure in dynamic programming and reinforcement learning, for solving MDPs can be slow when the discount factor is close to one. We propose modifications to VI in order to potentially accelerate its convergence behaviour. The key insight is the realization that the evolution of the value function approximations $(V_k)_{k \geq 0}$ in the VI procedure can be seen as a dynamical system. This opens up the possibility of using techniques from \emph{control theory} to modify, and potentially accelerate, this dynamics. We present such modifications based on simple controllers, such as PD (Proportional-Derivative), PI (Proportional-Integral), and PID. We present the error dynamics of these variants of VI, and provably (for certain classes of MDPs) and empirically (for more general classes) show that the convergence rate can be significantly improved. We also propose a gain adaptation mechanism in order to automatically select the controller gains, and empirically show the effectiveness of this procedure. | Amir-Massoud Farahmand, Mohammad Ghavamzadeh | null | null | 2,021 | icml |
SECANT: Self-Expert Cloning for Zero-Shot Generalization of Visual Policies | null | Generalization has been a long-standing challenge for reinforcement learning (RL). Visual RL, in particular, can be easily distracted by irrelevant factors in high-dimensional observation space. In this work, we consider robust policy learning which targets zero-shot generalization to unseen visual environments with large distributional shift. We propose SECANT, a novel self-expert cloning technique that leverages image augmentation in two stages to *decouple* robust representation learning from policy optimization. Specifically, an expert policy is first trained by RL from scratch with weak augmentations. A student network then learns to mimic the expert policy by supervised learning with strong augmentations, making its representation more robust against visual variations compared to the expert. Extensive experiments demonstrate that SECANT significantly advances the state of the art in zero-shot generalization across 4 challenging domains. Our average reward improvements over prior SOTAs are: DeepMind Control (+26.5%), robotic manipulation (+337.8%), vision-based autonomous driving (+47.7%), and indoor object navigation (+15.8%). Code release and video are available at https://linxifan.github.io/secant-site/. | Linxi Fan, Guanzhi Wang, De-An Huang, Zhiding Yu, Li Fei-Fei, Yuke Zhu, Animashree Anandkumar | null | null | 2,021 | icml |
GNNAutoScale: Scalable and Expressive Graph Neural Networks via Historical Embeddings | null | We present GNNAutoScale (GAS), a framework for scaling arbitrary message-passing GNNs to large graphs. GAS prunes entire sub-trees of the computation graph by utilizing historical embeddings from prior training iterations, leading to constant GPU memory consumption in respect to input node size without dropping any data. While existing solutions weaken the expressive power of message passing due to sub-sampling of edges or non-trainable propagations, our approach is provably able to maintain the expressive power of the original GNN. We achieve this by providing approximation error bounds of historical embeddings and show how to tighten them in practice. Empirically, we show that the practical realization of our framework, PyGAS, an easy-to-use extension for PyTorch Geometric, is both fast and memory-efficient, learns expressive node representations, closely resembles the performance of their non-scaling counterparts, and reaches state-of-the-art performance on large-scale graphs. | Matthias Fey, Jan E. Lenssen, Frank Weichert, Jure Leskovec | null | null | 2,021 | icml |
Clustered Sampling: Low-Variance and Improved Representativity for Clients Selection in Federated Learning | null | This work addresses the problem of optimizing communications between server and clients in federated learning (FL). Current sampling approaches in FL are either biased, or non optimal in terms of server-clients communications and training stability. To overcome this issue, we introduce clustered sampling for clients selection. We prove that clustered sampling leads to better clients representatitivity and to reduced variance of the clients stochastic aggregation weights in FL. Compatibly with our theory, we provide two different clustering approaches enabling clients aggregation based on 1) sample size, and 2) models similarity. Through a series of experiments in non-iid and unbalanced scenarios, we demonstrate that model aggregation through clustered sampling consistently leads to better training convergence and variability when compared to standard sampling approaches. Our approach does not require any additional operation on the clients side, and can be seamlessly integrated in standard FL implementations. Finally, clustered sampling is compatible with existing methods and technologies for privacy enhancement, and for communication reduction through model compression. | Yann Fraboni, Richard Vidal, Laetitia Kameni, Marco Lorenzi | null | null | 2,021 | icml |
PsiPhi-Learning: Reinforcement Learning with Demonstrations using Successor Features and Inverse Temporal Difference Learning | null | We study reinforcement learning (RL) with no-reward demonstrations, a setting in which an RL agent has access to additional data from the interaction of other agents with the same environment. However, it has no access to the rewards or goals of these agents, and their objectives and levels of expertise may vary widely. These assumptions are common in multi-agent settings, such as autonomous driving. To effectively use this data, we turn to the framework of successor features. This allows us to disentangle shared features and dynamics of the environment from agent-specific rewards and policies. We propose a multi-task inverse reinforcement learning (IRL) algorithm, called \emph{inverse temporal difference learning} (ITD), that learns shared state features, alongside per-agent successor features and preference vectors, purely from demonstrations without reward labels. We further show how to seamlessly integrate ITD with learning from online environment interactions, arriving at a novel algorithm for reinforcement learning with demonstrations, called $\Psi \Phi$-learning (pronounced ‘Sci-Fi’). We provide empirical evidence for the effectiveness of $\Psi \Phi$-learning as a method for improving RL, IRL, imitation, and few-shot transfer, and derive worst-case bounds for its performance in zero-shot transfer to new tasks. | Angelos Filos, Clare Lyle, Yarin Gal, Sergey Levine, Natasha Jaques, Gregory Farquhar | null | null | 2,021 | icml |
A Deep Reinforcement Learning Approach to Marginalized Importance Sampling with the Successor Representation | null | Marginalized importance sampling (MIS), which measures the density ratio between the state-action occupancy of a target policy and that of a sampling distribution, is a promising approach for off-policy evaluation. However, current state-of-the-art MIS methods rely on complex optimization tricks and succeed mostly on simple toy problems. We bridge the gap between MIS and deep reinforcement learning by observing that the density ratio can be computed from the successor representation of the target policy. The successor representation can be trained through deep reinforcement learning methodology and decouples the reward optimization from the dynamics of the environment, making the resulting algorithm stable and applicable to high-dimensional domains. We evaluate the empirical performance of our approach on a variety of challenging Atari and MuJoCo environments. | Scott Fujimoto, David Meger, Doina Precup | null | null | 2,021 | icml |
Discriminative Complementary-Label Learning with Weighted Loss | null | Complementary-label learning (CLL) deals with the weak supervision scenario where each training instance is associated with one \emph{complementary} label, which specifies the class label that the instance does \emph{not} belong to. Given the training instance ${\bm x}$, existing CLL approaches aim at modeling the \emph{generative} relationship between the complementary label $\bar y$, i.e. $P(\bar y\mid {\bm x})$, and the ground-truth label $y$, i.e. $P(y\mid {\bm x})$. Nonetheless, as the ground-truth label is not directly accessible for complementarily labeled training instance, strong generative assumptions may not hold for real-world CLL tasks. In this paper, we derive a simple and theoretically-sound \emph{discriminative} model towards $P(\bar y\mid {\bm x})$, which naturally leads to a risk estimator with estimation error bound at $\mathcal{O}(1/\sqrt{n})$ convergence rate. Accordingly, a practical CLL approach is proposed by further introducing weighted loss to the empirical risk to maximize the predictive gap between potential ground-truth label and complementary label. Extensive experiments clearly validate the effectiveness of the proposed discriminative complementary-label learning approach. | Yi Gao, Min-Ling Zhang | null | null | 2,021 | icml |
Unsupervised Co-part Segmentation through Assembly | null | Co-part segmentation is an important problem in computer vision for its rich applications. We propose an unsupervised learning approach for co-part segmentation from images. For the training stage, we leverage motion information embedded in videos and explicitly extract latent representations to segment meaningful object parts. More importantly, we introduce a dual procedure of part-assembly to form a closed loop with part-segmentation, enabling an effective self-supervision. We demonstrate the effectiveness of our approach with a host of extensive experiments, ranging from human bodies, hands, quadruped, and robot arms. We show that our approach can achieve meaningful and compact part segmentation, outperforming state-of-the-art approaches on diverse benchmarks. | Qingzhe Gao, Bin Wang, Libin Liu, Baoquan Chen | null | null | 2,021 | icml |
Variational Data Assimilation with a Learned Inverse Observation Operator | null | Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a cornerstone of large scale forecasting applications such as numerical weather prediction. As such, it is implemented in current operational systems of weather forecasting agencies across the globe. However, finding a good initial state poses a difficult optimization problem in part due to the non-invertible relationship between physical states and their corresponding observations. We learn a mapping from observational data to physical states and show how it can be used to improve optimizability. We employ this mapping in two ways: to better initialize the non-convex optimization problem, and to reformulate the objective function in better behaved physics space instead of observation space. Our experimental results for the Lorenz96 model and a two-dimensional turbulent fluid flow demonstrate that this procedure significantly improves forecast quality for chaotic systems. | Thomas Frerix, Dmitrii Kochkov, Jamie Smith, Daniel Cremers, Michael Brenner, Stephan Hoyer | null | null | 2,021 | icml |
Parametric Graph for Unimodal Ranking Bandit | null | We tackle the online ranking problem of assigning $L$ items to $K$ positions on a web page in order to maximize the number of user clicks. We propose an original algorithm, easy to implement and with strong theoretical guarantees to tackle this problem in the Position-Based Model (PBM) setting, well suited for applications where items are displayed on a grid. Besides learning to rank, our algorithm, GRAB (for parametric Graph for unimodal RAnking Bandit), also learns the parameter of a compact graph over permutations of $K$ items among $L$. The logarithmic regret bound of this algorithm is a direct consequence of the unimodality property of the bandit setting with respect to the learned graph. Experiments against state-of-the-art learning algorithms which also tackle the PBM setting, show that our method is more efficient while giving regret performance on par with the best known algorithms on simulated and real life datasets. | Camille-Sovanneary Gauthier, Romaric Gaudel, Elisa Fromont, Boammani Aser Lompo | null | null | 2,021 | icml |
Post-selection inference with HSIC-Lasso | null | Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection inference. Indeed, the selected features can be significantly flawed when the selection procedure is not accounted for. We propose a selective inference procedure using the so-called model-free "HSIC-Lasso" based on the framework of truncated Gaussians combined with the polyhedral lemma. We then develop an algorithm, which allows for low computational costs and provides a selection of the regularisation parameter. The performance of our method is illustrated by both artificial and real-world data based experiments, which emphasise a tight control of the type-I error, even for small sample sizes. | Tobias Freidling, Benjamin Poignard, Héctor Climente-González, Makoto Yamada | null | null | 2,021 | icml |
Auto-NBA: Efficient and Effective Search Over the Joint Space of Networks, Bitwidths, and Accelerators | null | While maximizing deep neural networks’ (DNNs’) acceleration efficiency requires a joint search/design of three different yet highly coupled aspects, including the networks, bitwidths, and accelerators, the challenges associated with such a joint search have not yet been fully understood and addressed. The key challenges include (1) the dilemma of whether to explode the memory consumption due to the huge joint space or achieve sub-optimal designs, (2) the discrete nature of the accelerator design space that is coupled yet different from that of the networks and bitwidths, and (3) the chicken and egg problem associated with network-accelerator co-search, i.e., co-search requires operation-wise hardware cost, which is lacking during search as the optimal accelerator depending on the whole network is still unknown during search. To tackle these daunting challenges towards optimal and fast development of DNN accelerators, we propose a framework dubbed Auto-NBA to enable jointly searching for the Networks, Bitwidths, and Accelerators, by efficiently localizing the optimal design within the huge joint design space for each target dataset and acceleration specification. Our Auto-NBA integrates a heterogeneous sampling strategy to achieve unbiased search with constant memory consumption, and a novel joint-search pipeline equipped with a generic differentiable accelerator search engine. Extensive experiments and ablation studies validate that both Auto-NBA generated networks and accelerators consistently outperform state-of-the-art designs (including co-search/exploration techniques, hardware-aware NAS methods, and DNN accelerators), in terms of search time, task accuracy, and accelerator efficiency. Our codes are available at: https://github.com/RICE-EIC/Auto-NBA. | Yonggan Fu, Yongan Zhang, Yang Zhang, David Cox, Yingyan Lin | null | null | 2,021 | icml |
Provable Generalization of SGD-trained Neural Networks of Any Width in the Presence of Adversarial Label Noise | null | We consider a one-hidden-layer leaky ReLU network of arbitrary width trained by stochastic gradient descent (SGD) following an arbitrary initialization. We prove that SGD produces neural networks that have classification accuracy competitive with that of the best halfspace over the distribution for a broad class of distributions that includes log-concave isotropic and hard margin distributions. Equivalently, such networks can generalize when the data distribution is linearly separable but corrupted with adversarial label noise, despite the capacity to overfit. To the best of our knowledge, this is the first work to show that overparameterized neural networks trained by SGD can generalize when the data is corrupted with adversarial label noise. | Spencer Frei, Yuan Cao, Quanquan Gu | null | null | 2,021 | icml |
On Proximal Policy Optimization’s Heavy-tailed Gradients | null | Modern policy gradient algorithms such as Proximal Policy Optimization (PPO) rely on an arsenal of heuristics, including loss clipping and gradient clipping, to ensure successful learning. These heuristics are reminiscent of techniques from robust statistics, commonly used for estimation in outlier-rich ("heavy-tailed") regimes. In this paper, we present a detailed empirical study to characterize the heavy-tailed nature of the gradients of the PPO surrogate reward function. We demonstrate that the gradients, especially for the actor network, exhibit pronounced heavy-tailedness and that it increases as the agent’s policy diverges from the behavioral policy (i.e., as the agent goes further off policy). Further examination implicates the likelihood ratios and advantages in the surrogate reward as the main sources of the observed heavy-tailedness. We then highlight issues arising due to the heavy-tailed nature of the gradients. In this light, we study the effects of the standard PPO clipping heuristics, demonstrating that these tricks primarily serve to offset heavy-tailedness in gradients. Thus motivated, we propose incorporating GMOM, a high-dimensional robust estimator, into PPO as a substitute for three clipping tricks. Despite requiring less hyperparameter tuning, our method matches the performance of PPO (with all heuristics enabled) on a battery of MuJoCo continuous control tasks. | Saurabh Garg, Joshua Zhanson, Emilio Parisotto, Adarsh Prasad, Zico Kolter, Zachary Lipton, Sivaraman Balakrishnan, Ruslan Salakhutdinov, Pradeep Ravikumar | null | null | 2,021 | icml |
Learn-to-Share: A Hardware-friendly Transfer Learning Framework Exploiting Computation and Parameter Sharing | null | Task-specific fine-tuning on pre-trained transformers has achieved performance breakthroughs in multiple NLP tasks. Yet, as both computation and parameter size grows linearly with the number of sub-tasks, it is increasingly difficult to adopt such methods to the real world due to unrealistic memory and computation overhead on computing devices. Previous works on fine-tuning focus on reducing the growing parameter size to save storage cost by parameter sharing. However, compared to storage, the constraint of computation is a more critical issue with the fine-tuning models in modern computing environments. In this work, we propose LeTS, a framework that leverages both computation and parameter sharing across multiple tasks. Compared to traditional fine-tuning, LeTS proposes a novel neural architecture that contains a fixed pre-trained transformer model, plus learnable additive components for sub-tasks. The learnable components reuse the intermediate activations in the fixed pre-trained model, decoupling computation dependency. Differentiable neural architecture search is used to determine a task-specific computation sharing scheme, and a novel early stage pruning is applied to additive components for sparsity to achieve parameter sharing. Extensive experiments show that with 1.4% of extra parameters per task, LeTS reduces the computation by 49.5% on GLUE benchmarks with only 0.2% accuracy loss compared to full fine-tuning. | Cheng Fu, Hanxian Huang, Xinyun Chen, Yuandong Tian, Jishen Zhao | null | null | 2,021 | icml |
Policy Information Capacity: Information-Theoretic Measure for Task Complexity in Deep Reinforcement Learning | null | Progress in deep reinforcement learning (RL) research is largely enabled by benchmark task environments. However, analyzing the nature of those environments is often overlooked. In particular, we still do not have agreeable ways to measure the difficulty or solvability of a task, given that each has fundamentally different actions, observations, dynamics, rewards, and can be tackled with diverse RL algorithms. In this work, we propose policy information capacity (PIC) – the mutual information between policy parameters and episodic return – and policy-optimal information capacity (POIC) – between policy parameters and episodic optimality – as two environment-agnostic, algorithm-agnostic quantitative metrics for task difficulty. Evaluating our metrics across toy environments as well as continuous control benchmark tasks from OpenAI Gym and DeepMind Control Suite, we empirically demonstrate that these information-theoretic metrics have higher correlations with normalized task solvability scores than a variety of alternatives. Lastly, we show that these metrics can also be used for fast and compute-efficient optimizations of key design parameters such as reward shaping, policy architectures, and MDP properties for better solvability by RL algorithms without ever running full RL experiments. | Hiroki Furuta, Tatsuya Matsushima, Tadashi Kozuno, Yutaka Matsuo, Sergey Levine, Ofir Nachum, Shixiang Shane Gu | null | null | 2,021 | icml |
Double-Win Quant: Aggressively Winning Robustness of Quantized Deep Neural Networks via Random Precision Training and Inference | null | Quantization is promising in enabling powerful yet complex deep neural networks (DNNs) to be deployed into resource constrained platforms. However, quantized DNNs are vulnerable to adversarial attacks unless being equipped with sophisticated techniques, leading to a dilemma of struggling between DNNs’ efficiency and robustness. In this work, we demonstrate a new perspective regarding quantization’s role in DNNs’ robustness, advocating that quantization can be leveraged to largely boost DNNs’ robustness, and propose a framework dubbed Double-Win Quant that can boost the robustness of quantized DNNs over their full precision counterparts by a large margin. Specifically, we for the first time identify that when an adversarially trained model is quantized to different precisions in a post-training manner, the associated adversarial attacks transfer poorly between different precisions. Leveraging this intriguing observation, we further develop Double-Win Quant integrating random precision inference and training to further reduce and utilize the poor adversarial transferability, enabling an aggressive “win-win" in terms of DNNs’ robustness and efficiency. Extensive experiments and ablation studies consistently validate Double-Win Quant’s effectiveness and advantages over state-of-the-art (SOTA) adversarial training methods across various attacks/models/datasets. Our codes are available at: https://github.com/RICE-EIC/Double-Win-Quant. | Yonggan Fu, Qixuan Yu, Meng Li, Vikas Chandra, Yingyan Lin | null | null | 2,021 | icml |
On the difficulty of unbiased alpha divergence minimization | null | Several approximate inference algorithms have been proposed to minimize an alpha-divergence between an approximating distribution and a target distribution. Many of these algorithms introduce bias, the magnitude of which becomes problematic in high dimensions. Other algorithms are unbiased. These often seem to suffer from high variance, but little is rigorously known. In this work we study unbiased methods for alpha-divergence minimization through the Signal-to-Noise Ratio (SNR) of the gradient estimator. We study several representative scenarios where strong analytical results are possible, such as fully-factorized or Gaussian distributions. We find that when alpha is not zero, the SNR worsens exponentially in the dimensionality of the problem. This casts doubt on the practicality of these methods. We empirically confirm these theoretical results. | Tomas Geffner, Justin Domke | null | null | 2,021 | icml |
The Power of Adaptivity for Stochastic Submodular Cover | null | In the stochastic submodular cover problem, the goal is to select a subset of stochastic items of minimum expected cost to cover a submodular function. Solutions in this setting correspond to a sequential decision process that selects items one by one “adaptively” (depending on prior observations). While such adaptive solutions achieve the best objective, the inherently sequential nature makes them undesirable in many applications. We ask: \emph{how well can solutions with only a few adaptive rounds approximate fully-adaptive solutions?} We consider both cases where the stochastic items are independent, and where they are correlated. For both situations, we obtain nearly tight answers, establishing smooth tradeoffs between the number of adaptive rounds and the solution quality, relative to fully adaptive solutions. Experiments on synthetic and real datasets validate the practical performance of our algorithms, showing qualitative improvements in the solutions as we allow more rounds of adaptivity; in practice, solutions using just a few rounds of adaptivity are nearly as good as fully adaptive solutions. | Rohan Ghuge, Anupam Gupta, Viswanath Nagarajan | null | null | 2,021 | icml |
How and Why to Use Experimental Data to Evaluate Methods for Observational Causal Inference | null | Methods that infer causal dependence from observational data are central to many areas of science, including medicine, economics, and the social sciences. A variety of theoretical properties of these methods have been proven, but empirical evaluation remains a challenge, largely due to the lack of observational data sets for which treatment effect is known. We describe and analyze observational sampling from randomized controlled trials (OSRCT), a method for evaluating causal inference methods using data from randomized controlled trials (RCTs). This method can be used to create constructed observational data sets with corresponding unbiased estimates of treatment effect, substantially increasing the number of data sets available for evaluating causal inference methods. We show that, in expectation, OSRCT creates data sets that are equivalent to those produced by randomly sampling from empirical data sets in which all potential outcomes are available. We then perform a large-scale evaluation of seven causal inference methods over 37 data sets, drawn from RCTs, as well as simulators, real-world computational systems, and observational data sets augmented with a synthetic response variable. We find notable performance differences when comparing across data from different sources, demonstrating the importance of using data from a variety of sources when evaluating any causal inference method. | Amanda M Gentzel, Purva Pruthi, David Jensen | null | null | 2,021 | icml |
Query Complexity of Adversarial Attacks | null | There are two main attack models considered in the adversarial robustness literature: black-box and white-box. We consider these threat models as two ends of a fine-grained spectrum, indexed by the number of queries the adversary can ask. Using this point of view we investigate how many queries the adversary needs to make to design an attack that is comparable to the best possible attack in the white-box model. We give a lower bound on that number of queries in terms of entropy of decision boundaries of the classifier. Using this result we analyze two classical learning algorithms on two synthetic tasks for which we prove meaningful security guarantees. The obtained bounds suggest that some learning algorithms are inherently more robust against query-bounded adversaries than others. | Grzegorz Gluch, Rüdiger Urbanke | null | null | 2,021 | icml |
Differentially Private Aggregation in the Shuffle Model: Almost Central Accuracy in Almost a Single Message | null | The shuffle model of differential privacy has attracted attention in the literature due to it being a middle ground between the well-studied central and local models. In this work, we study the problem of summing (aggregating) real numbers or integers, a basic primitive in numerous machine learning tasks, in the shuffle model. We give a protocol achieving error arbitrarily close to that of the (Discrete) Laplace mechanism in central differential privacy, while each user only sends 1 + o(1) short messages in expectation. | Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Rasmus Pagh, Amer Sinha | null | null | 2,021 | icml |
Let’s Agree to Degree: Comparing Graph Convolutional Networks in the Message-Passing Framework | null | In this paper we cast neural networks defined on graphs as message-passing neural networks (MPNNs) to study the distinguishing power of different classes of such models. We are interested in when certain architectures are able to tell vertices apart based on the feature labels given as input with the graph. We consider two variants of MPNNS: anonymous MPNNs whose message functions depend only on the labels of vertices involved; and degree-aware MPNNs whose message functions can additionally use information regarding the degree of vertices. The former class covers popular graph neural network (GNN) formalisms for which the distinguished power is known. The latter covers graph convolutional networks (GCNs), introduced by Kipf and Welling, for which the distinguishing power was unknown. We obtain lower and upper bounds on the distinguishing power of (anonymous and degree-aware) MPNNs in terms of the distinguishing power of the Weisfeiler-Lehman (WL) algorithm. Our main results imply that (i) the distinguishing power of GCNs is bounded by the WL algorithm, but they may be one step ahead; (ii) the WL algorithm cannot be simulated by “plain vanilla” GCNs but the addition of a trade-off parameter between features of the vertex and those of its neighbours (as proposed by Kipf and Welling) resolves this problem. | Floris Geerts, Filip Mazowiecki, Guillermo Perez | null | null | 2,021 | icml |
EMaQ: Expected-Max Q-Learning Operator for Simple Yet Effective Offline and Online RL | null | Off-policy reinforcement learning (RL) holds the promise of sample-efficient learning of decision-making policies by leveraging past experience. However, in the offline RL setting – where a fixed collection of interactions are provided and no further interactions are allowed – it has been shown that standard off-policy RL methods can significantly underperform. In this work, we closely investigate an important simplification of BCQ (Fujimoto et al., 2018) – a prior approach for offline RL – removing a heuristic design choice. Importantly, in contrast to their original theoretical considerations, we derive this simplified algorithm through the introduction of a novel backup operator, Expected-Max Q-Learning (EMaQ), which is more closely related to the resulting practical algorithm. Specifically, in addition to the distribution support, EMaQ explicitly considers the number of samples and the proposal distribution, allowing us to derive new sub-optimality bounds. In the offline RL setting – the main focus of this work – EMaQ matches and outperforms prior state-of-the-art in the D4RL benchmarks (Fu et al., 2020). In the online RL setting, we demonstrate that EMaQ is competitive with Soft Actor Critic (SAC). The key contributions of our empirical findings are demonstrating the importance of careful generative model design for estimating behavior policies, and an intuitive notion of complexity for offline RL problems. With its simple interpretation and fewer moving parts, such as no explicit function approximator representing the policy, EMaQ serves as a strong yet easy to implement baseline for future work. | Seyed Kamyar Seyed Ghasemipour, Dale Schuurmans, Shixiang Shane Gu | null | null | 2,021 | icml |
AutoAttend: Automated Attention Representation Search | null | Self-attention mechanisms have been widely adopted in many machine learning areas, including Natural Language Processing (NLP) and Graph Representation Learning (GRL), etc. However, existing works heavily rely on hand-crafted design to obtain customized attention mechanisms. In this paper, we automate Key, Query and Value representation design, which is one of the most important steps to obtain effective self-attentions. We propose an automated self-attention representation model, AutoAttend, which can automatically search powerful attention representations for downstream tasks leveraging Neural Architecture Search (NAS). In particular, we design a tailored search space for attention representation automation, which is flexible to produce effective attention representation designs. Based on the design prior obtained from attention representations in previous works, we further regularize our search space to reduce the space complexity without the loss of expressivity. Moreover, we propose a novel context-aware parameter sharing mechanism considering special characteristics of each sub-architecture to provide more accurate architecture estimations when conducting parameter sharing in our tailored search space. Experiments show the superiority of our proposed AutoAttend model over previous state-of-the-arts on eight text classification tasks in NLP and four node classification tasks in GRL. | Chaoyu Guan, Xin Wang, Wenwu Zhu | null | null | 2,021 | icml |
12-Lead ECG Reconstruction via Koopman Operators | null | 32% of all global deaths in the world are caused by cardiovascular diseases. Early detection, especially for patients with ischemia or cardiac arrhythmia, is crucial. To reduce the time between symptoms onset and treatment, wearable ECG sensors were developed to allow for the recording of the full 12-lead ECG signal at home. However, if even a single lead is not correctly positioned on the body that lead becomes corrupted, making automatic diagnosis on the basis of the full signal impossible. In this work, we present a methodology to reconstruct missing or noisy leads using the theory of Koopman Operators. Given a dataset consisting of full 12-lead ECGs, we learn a dynamical system describing the evolution of the 12 individual signals together in time. The Koopman theory indicates that there exists a high-dimensional embedding space in which the operator which propagates from one time instant to the next is linear. We therefore learn both the mapping to this embedding space, as well as the corresponding linear operator. Armed with this representation, we are able to impute missing leads by solving a least squares system in the embedding space, which can be achieved efficiently due to the sparse structure of the system. We perform an empirical evaluation using 12-lead ECG signals from thousands of patients, and show that we are able to reconstruct the signals in such way that enables accurate clinical diagnosis. | Tomer Golany, Kira Radinsky, Daniel Freedman, Saar Minha | null | null | 2,021 | icml |
On a Combination of Alternating Minimization and Nesterov’s Momentum | null | Alternating minimization (AM) procedures are practically efficient in many applications for solving convex and non-convex optimization problems. On the other hand, Nesterov’s accelerated gradient is theoretically optimal first-order method for convex optimization. In this paper we combine AM and Nesterov’s acceleration to propose an accelerated alternating minimization algorithm. We prove $1/k^2$ convergence rate in terms of the objective for convex problems and $1/k$ in terms of the squared gradient norm for non-convex problems, where $k$ is the iteration counter. Our method does not require any knowledge of neither convexity of the problem nor function parameters such as Lipschitz constant of the gradient, i.e. it is adaptive to convexity and smoothness and is uniformly optimal for smooth convex and non-convex problems. Further, we develop its primal-dual modification for strongly convex problems with linear constraints and prove the same $1/k^2$ for the primal objective residual and constraints feasibility. | Sergey Guminov, Pavel Dvurechensky, Nazarii Tupitsa, Alexander Gasnikov | null | null | 2,021 | icml |
UneVEn: Universal Value Exploration for Multi-Agent Reinforcement Learning | null | VDN and QMIX are two popular value-based algorithms for cooperative MARL that learn a centralized action value function as a monotonic mixing of per-agent utilities. While this enables easy decentralization of the learned policy, the restricted joint action value function can prevent them from solving tasks that require significant coordination between agents at a given timestep. We show that this problem can be overcome by improving the joint exploration of all agents during training. Specifically, we propose a novel MARL approach called Universal Value Exploration (UneVEn) that learns a set of related tasks simultaneously with a linear decomposition of universal successor features. With the policies of already solved related tasks, the joint exploration process of all agents can be improved to help them achieve better coordination. Empirical results on a set of exploration games, challenging cooperative predator-prey tasks requiring significant coordination among agents, and StarCraft II micromanagement benchmarks show that UneVEn can solve tasks where other state-of-the-art MARL methods fail. | Tarun Gupta, Anuj Mahajan, Bei Peng, Wendelin Boehmer, Shimon Whiteson | null | null | 2,021 | icml |
Adversarial Policy Learning in Two-player Competitive Games | null | In a two-player deep reinforcement learning task, recent work shows an attacker could learn an adversarial policy that triggers a target agent to perform poorly and even react in an undesired way. However, its efficacy heavily relies upon the zero-sum assumption made in the two-player game. In this work, we propose a new adversarial learning algorithm. It addresses the problem by resetting the optimization goal in the learning process and designing a new surrogate optimization function. Our experiments show that our method significantly improves adversarial agents’ exploitability compared with the state-of-art attack. Besides, we also discover that our method could augment an agent with the ability to abuse the target game’s unfairness. Finally, we show that agents adversarially re-trained against our adversarial agents could obtain stronger adversary-resistance. | Wenbo Guo, Xian Wu, Sui Huang, Xinyu Xing | null | null | 2,021 | icml |
Diversity Actor-Critic: Sample-Aware Entropy Regularization for Sample-Efficient Exploration | null | In this paper, sample-aware policy entropy regularization is proposed to enhance the conventional policy entropy regularization for better exploration. Exploiting the sample distribution obtainable from the replay buffer, the proposed sample-aware entropy regularization maximizes the entropy of the weighted sum of the policy action distribution and the sample action distribution from the replay buffer for sample-efficient exploration. A practical algorithm named diversity actor-critic (DAC) is developed by applying policy iteration to the objective function with the proposed sample-aware entropy regularization. Numerical results show that DAC significantly outperforms existing recent algorithms for reinforcement learning. | Seungyul Han, Youngchul Sung | null | null | 2,021 | icml |
Soft then Hard: Rethinking the Quantization in Neural Image Compression | null | Quantization is one of the core components in lossy image compression. For neural image compression, end-to-end optimization requires differentiable approximations of quantization, which can generally be grouped into three categories: additive uniform noise, straight-through estimator and soft-to-hard annealing. Training with additive uniform noise approximates the quantization error variationally but suffers from the train-test mismatch. The other two methods do not encounter this mismatch but, as shown in this paper, hurt the rate-distortion performance since the latent representation ability is weakened. We thus propose a novel soft-then-hard quantization strategy for neural image compression that first learns an expressive latent space softly, then closes the train-test mismatch with hard quantization. In addition, beyond the fixed integer-quantization, we apply scaled additive uniform noise to adaptively control the quantization granularity by deriving a new variational upper bound on actual rate. Experiments demonstrate that our proposed methods are easy to adopt, stable to train, and highly effective especially on complex compression models. | Zongyu Guo, Zhizheng Zhang, Runsen Feng, Zhibo Chen | null | null | 2,021 | icml |
Decentralized Single-Timescale Actor-Critic on Zero-Sum Two-Player Stochastic Games | null | We study the global convergence and global optimality of the actor-critic algorithm applied for the zero-sum two-player stochastic games in a decentralized manner. We focus on the single-timescale setting where the critic is updated by applying the Bellman operator only once and the actor is updated by policy gradient with the information from the critic. Our algorithm is in a decentralized manner, as we assume that each player has no access to the actions of the other one, which, in a way, protects the privacy of both players. Moreover, we consider linear function approximations for both actor and critic, and we prove that the sequence of joint policy generated by our decentralized linear algorithm converges to the minimax equilibrium at a sublinear rate \(\cO(\sqrt{K})\), where \(K\){is} the number of iterations. To the best of our knowledge, we establish the global optimality and convergence of decentralized actor-critic algorithm on zero-sum two-player stochastic games with linear function approximations for the first time. | Hongyi Guo, Zuyue Fu, Zhuoran Yang, Zhaoran Wang | null | null | 2,021 | icml |
Sparse Feature Selection Makes Batch Reinforcement Learning More Sample Efficient | null | This paper provides a statistical analysis of high-dimensional batch reinforcement learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that sparsity-aware methods can make batch RL more sample efficient. We first consider the off-policy policy evaluation problem. To evaluate a new target policy, we analyze a Lasso fitted Q-evaluation method and establish a finite-sample error bound that has no polynomial dependence on the ambient dimension. To reduce the Lasso bias, we further propose a post model-selection estimator that applies fitted Q-evaluation to the features selected via group Lasso. Under an additional signal strength assumption, we derive a sharper instance-dependent error bound that depends on a divergence function measuring the distribution mismatch between the data distribution and occupancy measure of the target policy. Further, we study the Lasso fitted Q-iteration for batch policy optimization and establish a finite-sample error bound depending on the ratio between the number of relevant features and restricted minimal eigenvalue of the data’s covariance. In the end, we complement the results with minimax lower bounds for batch-data policy evaluation/optimization that nearly match our upper bounds. The results suggest that having well-conditioned data is crucial for sparse batch policy learning. | Botao Hao, Yaqi Duan, Tor Lattimore, Csaba Szepesvari, Mengdi Wang | null | null | 2,021 | icml |
Regret Minimization in Stochastic Non-Convex Learning via a Proximal-Gradient Approach | null | This paper develops a methodology for regret minimization with stochastic first-order oracle feedback in online, constrained, non-smooth, non-convex problems. In this setting, the minimization of external regret is beyond reach for first-order methods, and there are no gradient-based algorithmic frameworks capable of providing a solution. On that account, we propose a conceptual approach that leverages non-convex optimality measures, leading to a suitable generalization of the learner’s local regret. We focus on a local regret measure defined via a proximal-gradient mapping, that also encompasses the original notion proposed by Hazan et al. (2017). To achieve no local regret in this setting, we develop a proximal-gradient method based on stochastic first-order feedback, and a simpler method for when access to a perfect first-order oracle is possible. Both methods are order-optimal (in the min-max sense), and we also establish a bound on the number of proximal-gradient queries these methods require. As an important application of our results, we also obtain a link between online and offline non-convex stochastic optimization manifested as a new proximal-gradient scheme with complexity guarantees matching those obtained via variance reduction techniques. | Nadav Hallak, Panayotis Mertikopoulos, Volkan Cevher | null | null | 2,021 | icml |
Systematic Analysis of Cluster Similarity Indices: How to Validate Validation Measures | null | Many cluster similarity indices are used to evaluate clustering algorithms, and choosing the best one for a particular task remains an open problem. We demonstrate that this problem is crucial: there are many disagreements among the indices, these disagreements do affect which algorithms are preferred in applications, and this can lead to degraded performance in real-world systems. We propose a theoretical framework to tackle this problem: we develop a list of desirable properties and conduct an extensive theoretical analysis to verify which indices satisfy them. This allows for making an informed choice: given a particular application, one can first select properties that are desirable for the task and then identify indices satisfying these. Our work unifies and considerably extends existing attempts at analyzing cluster similarity indices: we introduce new properties, formalize existing ones, and mathematically prove or disprove each property for an extensive list of validation indices. This broader and more rigorous approach leads to recommendations that considerably differ from how validation indices are currently being chosen by practitioners. Some of the most popular indices are even shown to be dominated by previously overlooked ones. | Martijn M Gösgens, Alexey Tikhonov, Liudmila Prokhorenkova | null | null | 2,021 | icml |
Spectral Normalisation for Deep Reinforcement Learning: An Optimisation Perspective | null | Most of the recent deep reinforcement learning advances take an RL-centric perspective and focus on refinements of the training objective. We diverge from this view and show we can recover the performance of these developments not by changing the objective, but by regularising the value-function estimator. Constraining the Lipschitz constant of a single layer using spectral normalisation is sufficient to elevate the performance of a Categorical-DQN agent to that of a more elaborated agent on the challenging Atari domain. We conduct ablation studies to disentangle the various effects normalisation has on the learning dynamics and show that is sufficient to modulate the parameter updates to recover most of the performance of spectral normalisation. These findings hint towards the need to also focus on the neural component and its learning dynamics to tackle the peculiarities of Deep Reinforcement Learning. | Florin Gogianu, Tudor Berariu, Mihaela C Rosca, Claudia Clopath, Lucian Busoniu, Razvan Pascanu | null | null | 2,021 | icml |
Revisiting Point Cloud Shape Classification with a Simple and Effective Baseline | null | Processing point cloud data is an important component of many real-world systems. As such, a wide variety of point-based approaches have been proposed, reporting steady benchmark improvements over time. We study the key ingredients of this progress and uncover two critical results. First, we find that auxiliary factors like different evaluation schemes, data augmentation strategies, and loss functions, which are independent of the model architecture, make a large difference in performance. The differences are large enough that they obscure the effect of architecture. When these factors are controlled for, PointNet++, a relatively older network, performs competitively with recent methods. Second, a very simple projection-based method, which we refer to as SimpleView, performs surprisingly well. It achieves on par or better results than sophisticated state-of-the-art methods on ModelNet40 while being half the size of PointNet++. It also outperforms state-of-the-art methods on ScanObjectNN, a real-world point cloud benchmark, and demonstrates better cross-dataset generalization. Code is available at https://github.com/princeton-vl/SimpleView. | Ankit Goyal, Hei Law, Bowei Liu, Alejandro Newell, Jia Deng | null | null | 2,021 | icml |
Crystallization Learning with the Delaunay Triangulation | null | Based on the Delaunay triangulation, we propose the crystallization learning to estimate the conditional expectation function in the framework of nonparametric regression. By conducting the crystallization search for the Delaunay simplices closest to the target point in a hierarchical way, the crystallization learning estimates the conditional expectation of the response by fitting a local linear model to the data points of the constructed Delaunay simplices. Instead of conducting the Delaunay triangulation for the entire feature space which would encounter enormous computational difficulty, our approach focuses only on the neighborhood of the target point and thus greatly expedites the estimation for high-dimensional cases. Because the volumes of Delaunay simplices are adaptive to the density of feature data points, our method selects neighbor data points uniformly in all directions and thus is more robust to the local geometric structure of the data than existing nonparametric regression methods. We develop the asymptotic properties of the crystallization learning and conduct numerical experiments on both synthetic and real data to demonstrate the advantages of our method in estimation of the conditional expectation function and prediction of the response. | Jiaqi Gu, Guosheng Yin | null | null | 2,021 | icml |
Grounding Language to Entities and Dynamics for Generalization in Reinforcement Learning | null | We investigate the use of natural language to drive the generalization of control policies and introduce the new multi-task environment Messenger with free-form text manuals describing the environment dynamics. Unlike previous work, Messenger does not assume prior knowledge connecting text and state observations {—} the control policy must simultaneously ground the game manual to entity symbols and dynamics in the environment. We develop a new model, EMMA (Entity Mapper with Multi-modal Attention) which uses an entity-conditioned attention module that allows for selective focus over relevant descriptions in the manual for each entity in the environment. EMMA is end-to-end differentiable and learns a latent grounding of entities and dynamics from text to observations using only environment rewards. EMMA achieves successful zero-shot generalization to unseen games with new dynamics, obtaining a 40% higher win rate compared to multiple baselines. However, win rate on the hardest stage of Messenger remains low (10%), demonstrating the need for additional work in this direction. | Austin W. Hanjie, Victor Y Zhong, Karthik Narasimhan | null | null | 2,021 | icml |
Distribution-Free Calibration Guarantees for Histogram Binning without Sample Splitting | null | We prove calibration guarantees for the popular histogram binning (also called uniform-mass binning) method of Zadrozny and Elkan (2001). Histogram binning has displayed strong practical performance, but theoretical guarantees have only been shown for sample split versions that avoid ’double dipping’ the data. We demonstrate that the statistical cost of sample splitting is practically significant on a credit default dataset. We then prove calibration guarantees for the original method that double dips the data, using a certain Markov property of order statistics. Based on our results, we make practical recommendations for choosing the number of bins in histogram binning. In our illustrative simulations, we propose a new tool for assessing calibration—validity plots—which provide more information than an ECE estimate. | Chirag Gupta, Aaditya Ramdas | null | null | 2,021 | icml |
Knowledge Enhanced Machine Learning Pipeline against Diverse Adversarial Attacks | null | Despite the great successes achieved by deep neural networks (DNNs), recent studies show that they are vulnerable against adversarial examples, which aim to mislead DNNs by adding small adversarial perturbations. Several defenses have been proposed against such attacks, while many of them have been adaptively attacked. In this work, we aim to enhance the ML robustness from a different perspective by leveraging domain knowledge: We propose a Knowledge Enhanced Machine Learning Pipeline (KEMLP) to integrate domain knowledge (i.e., logic relationships among different predictions) into a probabilistic graphical model via first-order logic rules. In particular, we develop KEMLP by integrating a diverse set of weak auxiliary models based on their logical relationships to the main DNN model that performs the target task. Theoretically, we provide convergence results and prove that, under mild conditions, the prediction of KEMLP is more robust than that of the main DNN model. Empirically, we take road sign recognition as an example and leverage the relationships between road signs and their shapes and contents as domain knowledge. We show that compared with adversarial training and other baselines, KEMLP achieves higher robustness against physical attacks, $\mathcal{L}_p$ bounded attacks, unforeseen attacks, and natural corruptions under both whitebox and blackbox settings, while still maintaining high clean accuracy. | Nezihe Merve Gürel, Xiangyu Qi, Luka Rimanic, Ce Zhang, Bo Li | null | null | 2,021 | icml |
Compressed Maximum Likelihood | null | Maximum likelihood (ML) is one of the most fundamental and general statistical estimation techniques. Inspired by recent advances in estimating distribution functionals, we propose $\textit{compressed maximum likelihood}$ (CML) that applies ML to the compressed samples. We then show that CML is sample-efficient for several essential learning tasks over both discrete and continuous domains, including learning densities with structures, estimating probability multisets, and inferring symmetric distribution functionals. | Yi Hao, Alon Orlitsky | null | null | 2,021 | icml |
Adversarial Combinatorial Bandits with General Non-linear Reward Functions | null | In this paper we study the adversarial combinatorial bandit with a known non-linear reward function, extending existing work on adversarial linear combinatorial bandit. {The adversarial combinatorial bandit with general non-linear reward is an important open problem in bandit literature, and it is still unclear whether there is a significant gap from the case of linear reward, stochastic bandit, or semi-bandit feedback.} We show that, with $N$ arms and subsets of $K$ arms being chosen at each of $T$ time periods, the minimax optimal regret is $\widetilde\Theta_{d}(\sqrt{N^d T})$ if the reward function is a $d$-degree polynomial with $d< K$, and $\Theta_K(\sqrt{N^K T})$ if the reward function is not a low-degree polynomial. {Both bounds are significantly different from the bound $O(\sqrt{\mathrm{poly}(N,K)T})$ for the linear case, which suggests that there is a fundamental gap between the linear and non-linear reward structures.} Our result also finds applications to adversarial assortment optimization problem in online recommendation. We show that in the worst-case of adversarial assortment problem, the optimal algorithm must treat each individual $\binom{N}{K}$ assortment as independent. | Yanjun Han, Yining Wang, Xi Chen | null | null | 2,021 | icml |
A Collective Learning Framework to Boost GNN Expressiveness for Node Classification | null | Collective Inference (CI) is a procedure designed to boost weak relational classifiers, specially for node classification tasks. Graph Neural Networks (GNNs) are strong classifiers that have been used with great success. Unfortunately, most existing practical GNNs are not most-expressive (universal). Thus, it is an open question whether one can improve strong relational node classifiers, such as GNNs, with CI. In this work, we investigate this question and propose {\em collective learning} for GNNs —a general collective classification approach for node representation learning that increases their representation power. We show that previous attempts to incorporate CI into GNNs fail to boost their expressiveness because they do not adapt CI’s Monte Carlo sampling to representation learning. We evaluate our proposed framework with a variety of state-of-the-art GNNs. Our experiments show a consistent, significant boost in node classification accuracy —regardless of the choice of underlying GNN— for inductive node classification in partially-labeled graphs, across five real-world network datasets. | Mengyue Hang, Jennifer Neville, Bruno Ribeiro | null | null | 2,021 | icml |
PipeTransformer: Automated Elastic Pipelining for Distributed Training of Large-scale Models | null | The size of Transformer models is growing at an unprecedented rate. It has taken less than one year to reach trillion-level parameters since the release of GPT-3 (175B). Training such models requires both substantial engineering efforts and enormous computing resources, which are luxuries most research teams cannot afford. In this paper, we propose PipeTransformer, which leverages automated elastic pipelining for efficient distributed training of Transformer models. In PipeTransformer, we design an adaptive on the fly freeze algorithm that can identify and freeze some layers gradually during training, and an elastic pipelining system that can dynamically allocate resources to train the remaining active layers. More specifically, PipeTransformer automatically excludes frozen layers from the pipeline, packs active layers into fewer GPUs, and forks more replicas to increase data-parallel width. We evaluate PipeTransformer using Vision Transformer (ViT) on ImageNet and BERT on SQuAD and GLUE datasets. Our results show that compared to the state-of-the-art baseline, PipeTransformer attains up to 2.83-fold speedup without losing accuracy. We also provide various performance analyses for a more comprehensive understanding of our algorithmic and system-wise design. Finally, we have modularized our training system with flexible APIs and made the source code publicly available at https://DistML.ai. | Chaoyang He, Shen Li, Mahdi Soltanolkotabi, Salman Avestimehr | null | null | 2,021 | icml |
SPECTRE: defending against backdoor attacks using robust statistics | null | Modern machine learning increasingly requires training on a large collection of data from multiple sources, not all of which can be trusted. A particularly frightening scenario is when a small fraction of corrupted data changes the behavior of the trained model when triggered by an attacker-specified watermark. Such a compromised model will be deployed unnoticed as the model is accurate otherwise. There has been promising attempts to use the intermediate representations of such a model to separate corrupted examples from clean ones. However, these methods require a significant fraction of the data to be corrupted, in order to have strong enough signal for detection. We propose a novel defense algorithm using robust covariance estimation to amplify the spectral signature of corrupted data. This defense is able to completely remove backdoors whenever the benchmark backdoor attacks are successful, even in regimes where previous methods have no hope for detecting poisoned examples. | Jonathan Hayase, Weihao Kong, Raghav Somani, Sewoong Oh | null | null | 2,021 | icml |
Hierarchical VAEs Know What They Don’t Know | null | Deep generative models have been demonstrated as state-of-the-art density estimators. Yet, recent work has found that they often assign a higher likelihood to data from outside the training distribution. This seemingly paradoxical behavior has caused concerns over the quality of the attained density estimates. In the context of hierarchical variational autoencoders, we provide evidence to explain this behavior by out-of-distribution data having in-distribution low-level features. We argue that this is both expected and desirable behavior. With this insight in hand, we develop a fast, scalable and fully unsupervised likelihood-ratio score for OOD detection that requires data to be in-distribution across all feature-levels. We benchmark the method on a vast set of data and model combinations and achieve state-of-the-art results on out-of-distribution detection. | Jakob D. Havtorn, Jes Frellsen, Søren Hauberg, Lars Maaløe | null | null | 2,021 | icml |
Zeroth-Order Non-Convex Learning via Hierarchical Dual Averaging | null | We propose a hierarchical version of dual averaging for zeroth-order online non-convex optimization {–} i.e., learning processes where, at each stage, the optimizer is facing an unknown non-convex loss function and only receives the incurred loss as feedback. The proposed class of policies relies on the construction of an online model that aggregates loss information as it arrives, and it consists of two principal components: (a) a regularizer adapted to the Fisher information metric (as opposed to the metric norm of the ambient space); and (b) a principled exploration of the problem’s state space based on an adapted hierarchical schedule. This construction enables sharper control of the model’s bias and variance, and allows us to derive tight bounds for both the learner’s static and dynamic regret {–} i.e., the regret incurred against the best dynamic policy in hindsight over the horizon of play. | Amélie Héliou, Matthieu Martin, Panayotis Mertikopoulos, Thibaud Rahier | null | null | 2,021 | icml |
SoundDet: Polyphonic Moving Sound Event Detection and Localization from Raw Waveform | null | We present a new framework SoundDet, which is an end-to-end trainable and light-weight framework, for polyphonic moving sound event detection and localization. Prior methods typically approach this problem by preprocessing raw waveform into time-frequency representations, which is more amenable to process with well-established image processing pipelines. Prior methods also detect in segment-wise manner, leading to incomplete and partial detections. SoundDet takes a novel approach and directly consumes the raw, multichannel waveform and treats the spatio-temporal sound event as a complete “sound-object" to be detected. Specifically, SoundDet consists of a backbone neural network and two parallel heads for temporal detection and spatial localization, respectively. Given the large sampling rate of raw waveform, the backbone network first learns a set of phase-sensitive and frequency-selective bank of filters to explicitly retain direction-of-arrival information, whilst being highly computationally and parametrically efficient than standard 1D/2D convolution. A dense sound event proposal map is then constructed to handle the challenges of predicting events with large varying temporal duration. Accompanying the dense proposal map are a temporal overlapness map and a motion smoothness map that measure a proposal’s confidence to be an event from temporal detection accuracy and movement consistency perspective. Involving the two maps guarantees SoundDet to be trained in a spatio-temporally unified manner. Experimental results on the public DCASE dataset show the advantage of SoundDet on both segment-based evaluation and our newly proposed event-based evaluation system. | Yuhang He, Niki Trigoni, Andrew Markham | null | null | 2,021 | icml |
Logarithmic Regret for Reinforcement Learning with Linear Function Approximation | null | Reinforcement learning (RL) with linear function approximation has received increasing attention recently. However, existing work has focused on obtaining $\sqrt{T}$-type regret bound, where $T$ is the number of interactions with the MDP. In this paper, we show that logarithmic regret is attainable under two recently proposed linear MDP assumptions provided that there exists a positive sub-optimality gap for the optimal action-value function. More specifically, under the linear MDP assumption (Jin et al., 2020), the LSVI-UCB algorithm can achieve $\tilde{O}(d^{3}H^5/\text{gap}_{\text{min}}\cdot \log(T))$regret; and under the linear mixture MDP assumption (Ayoub et al., 2020), the UCRL-VTR algorithm can achieve $\tilde{O}(d^{2}H^5/\text{gap}_{\text{min}}\cdot \log^3(T))$ regret, where $d$ is the dimension of feature mapping, $H$ is the length of episode, $\text{gap}_{\text{min}}$ is the minimal sub-optimality gap, and $\tilde O$ hides all logarithmic terms except $\log(T)$. To the best of our knowledge, these are the first logarithmic regret bounds for RL with linear function approximation. We also establish gap-dependent lower bounds for the two linear MDP models. | Jiafan He, Dongruo Zhou, Quanquan Gu | null | null | 2,021 | icml |
Model Performance Scaling with Multiple Data Sources | null | Real-world machine learning systems are often trained using a mix of data sources with varying cost and quality. Understanding how the size and composition of a training dataset affect model performance is critical for advancing our understanding of generalization, as well as designing more effective data collection policies. We show that there is a simple scaling law that predicts the loss incurred by a model even under varying dataset composition. Our work expands recent observations of scaling laws for log-linear generalization error in the i.i.d setting and uses this to cast model performance prediction as a learning problem. Using the theory of optimal experimental design, we derive a simple rational function approximation to generalization error that can be fitted using a few model training runs. Our approach can achieve highly accurate ($r^2\approx .9$) predictions of model performance under substantial extrapolation in two different standard supervised learning tasks and is accurate ($r^2 \approx .83$) on more challenging machine translation and question answering tasks where many baselines achieve worse-than-random performance. | Tatsunori Hashimoto | null | null | 2,021 | icml |
Improving Molecular Graph Neural Network Explainability with Orthonormalization and Induced Sparsity | null | Rationalizing which parts of a molecule drive the predictions of a molecular graph convolutional neural network (GCNN) can be difficult. To help, we propose two simple regularization techniques to apply during the training of GCNNs: Batch Representation Orthonormalization (BRO) and Gini regularization. BRO, inspired by molecular orbital theory, encourages graph convolution operations to generate orthonormal node embeddings. Gini regularization is applied to the weights of the output layer and constrains the number of dimensions the model can use to make predictions. We show that Gini and BRO regularization can improve the accuracy of state-of-the-art GCNN attribution methods on artificial benchmark datasets. In a real-world setting, we demonstrate that medicinal chemists significantly prefer explanations extracted from regularized models. While we only study these regularizers in the context of GCNNs, both can be applied to other types of neural networks. | Ryan Henderson, Djork-Arné Clevert, Floriane Montanari | null | null | 2,021 | icml |
Federated Learning of User Verification Models Without Sharing Embeddings | null | We consider the problem of training User Verification (UV) models in federated setup, where each user has access to the data of only one class and user embeddings cannot be shared with the server or other users. To address this problem, we propose Federated User Verification (FedUV), a framework in which users jointly learn a set of vectors and maximize the correlation of their instance embeddings with a secret linear combination of those vectors. We show that choosing the linear combinations from the codewords of an error-correcting code allows users to collaboratively train the model without revealing their embedding vectors. We present the experimental results for user verification with voice, face, and handwriting data and show that FedUV is on par with existing approaches, while not sharing the embeddings with other users or the server. | Hossein Hosseini, Hyunsin Park, Sungrack Yun, Christos Louizos, Joseph Soriaga, Max Welling | null | null | 2,021 | icml |
Multiplicative Noise and Heavy Tails in Stochastic Optimization | null | Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modeling stochastic optimization algorithms as discrete random recurrence relations, we show that multiplicative noise, as it commonly arises due to variance in local rates of convergence, results in heavy-tailed stationary behaviour in the parameters. Theoretical results are obtained characterizing this for a large class of (non-linear and even non-convex) models and optimizers (including momentum, Adam, and stochastic Newton), demonstrating that this phenomenon holds generally. We describe dependence on key factors, including step size, batch size, and data variability, all of which exhibit similar qualitative behavior to recent empirical results on state-of-the-art neural network models. Furthermore, we empirically illustrate how multiplicative noise and heavy-tailed structure improve capacity for basin hopping and exploration of non-convex loss surfaces, over commonly-considered stochastic dynamics with only additive noise and light-tailed structure. | Liam Hodgkinson, Michael Mahoney | null | null | 2,021 | icml |
Finding Relevant Information via a Discrete Fourier Expansion | null | A fundamental obstacle in learning information from data is the presence of nonlinear redundancies and dependencies in it. To address this, we propose a Fourier-based approach to extract relevant information in the supervised setting. We first develop a novel Fourier expansion for functions of correlated binary random variables. This expansion is a generalization of the standard Fourier analysis on the Boolean cube beyond product probability spaces. We further extend our Fourier analysis to stochastic mappings. As an important application of this analysis, we investigate learning with feature subset selection. We reformulate this problem in the Fourier domain and introduce a computationally efficient measure for selecting features. Bridging the Bayesian error rate with the Fourier coefficients, we demonstrate that the Fourier expansion provides a powerful tool to characterize nonlinear dependencies in the features-label relation. Via theoretical analysis, we show that our proposed measure finds provably asymptotically optimal feature subsets. Lastly, we present an algorithm based on our measure and verify our findings via numerical experiments on various datasets. | Mohsen Heidari, Jithin Sreedharan, Gil I Shamir, Wojciech Szpankowski | null | null | 2,021 | icml |
The Limits of Min-Max Optimization Algorithms: Convergence to Spurious Non-Critical Sets | null | Compared to minimization, the min-max optimization in machine learning applications is considerably more convoluted because of the existence of cycles and similar phenomena. Such oscillatory behaviors are well-understood in the convex-concave regime, and many algorithms are known to overcome them. In this paper, we go beyond this basic setting and characterize the convergence properties of many popular methods in solving non-convex/non-concave problems. In particular, we show that a wide class of state-of-the-art schemes and heuristics may converge with arbitrarily high probability to attractors that are in no way min-max optimal or even stationary. Our work thus points out a potential pitfall among many existing theoretical frameworks, and we corroborate our theoretical claims by explicitly showcasing spurious attractors in simple two-dimensional problems. | Ya-Ping Hsieh, Panayotis Mertikopoulos, Volkan Cevher | null | null | 2,021 | icml |
A Scalable Deterministic Global Optimization Algorithm for Clustering Problems | null | The minimum sum-of-squares clustering (MSSC) task, which can be treated as a Mixed Integer Second Order Cone Programming (MISOCP) problem, is rarely investigated in the literature through deterministic optimization to find its global optimal value. In this paper, we modelled the MSSC task as a two-stage optimization problem and proposed a tailed reduced-space branch and bound (BB) algorithm. We designed several approaches to construct lower and upper bounds at each node in the BB scheme, including a scenario grouping based Lagrangian decomposition approach. One key advantage of this reduced-space algorithm is that it only needs to perform branching on the centers of clusters to guarantee convergence, and the size of centers is independent of the number of data samples. Moreover, the lower bounds can be computed by solving small-scale sample subproblems, and upper bounds can be obtained trivially. These two properties enable our algorithm easy to be paralleled and can be scalable to the dataset with up to 200,000 samples for finding a global $\epsilon$-optimal solution of the MSSC task. We performed numerical experiments on both synthetic and real-world datasets and compared our proposed algorithms with the off-the-shelf global optimal solvers and classical local optimal algorithms. The results reveal a strong performance and scalability of our algorithm. | Kaixun Hua, Mingfei Shi, Yankai Cao | null | null | 2,021 | icml |
On the Random Conjugate Kernel and Neural Tangent Kernel | null | We investigate the distributions of Conjugate Kernel (CK) and Neural Tangent Kernel (NTK) for ReLU networks with random initialization. We derive the precise distributions and moments of the diagonal elements of these kernels. For a feedforward network, these values converge in law to a log-normal distribution when the network depth $d$ and width $n$ simultaneously tend to infinity and the variance of log diagonal elements is proportional to ${d}/{n}$. For the residual network, in the limit that number of branches $m$ increases to infinity and the width $n$ remains fixed, the diagonal elements of Conjugate Kernel converge in law to a log-normal distribution where the variance of log value is proportional to ${1}/{n}$, and the diagonal elements of NTK converge in law to a log-normal distributed variable times the conjugate kernel of one feedforward network. Our new theoretical analysis results suggest that residual network remains trainable in the limit of infinite branches and fixed network width. The numerical experiments are conducted and all results validate the soundness of our theoretical analysis. | Zhengmian Hu, Heng Huang | null | null | 2,021 | icml |
Trees with Attention for Set Prediction Tasks | null | In many machine learning applications, each record represents a set of items. For example, when making predictions from medical records, the medications prescribed to a patient are a set whose size is not fixed and whose order is arbitrary. However, most machine learning algorithms are not designed to handle set structures and are limited to processing records of fixed size. Set-Tree, presented in this work, extends the support for sets to tree-based models, such as Random-Forest and Gradient-Boosting, by introducing an attention mechanism and set-compatible split criteria. We evaluate the new method empirically on a wide range of problems ranging from making predictions on sub-atomic particle jets to estimating the redshift of galaxies. The new method outperforms existing tree-based methods consistently and significantly. Moreover, it is competitive and often outperforms Deep Learning. We also discuss the theoretical properties of Set-Trees and explain how they enable item-level explainability. | Roy Hirsch, Ran Gilad-Bachrach | null | null | 2,021 | icml |
On Recovering from Modeling Errors Using Testing Bayesian Networks | null | We consider the problem of supervised learning with Bayesian Networks when the used dependency structure is incomplete due to missing edges or missing variable states. These modeling errors induce independence constraints on the learned model that may not hold in the true, data-generating distribution. We provide a unified treatment of these modeling errors as instances of state-space abstractions. We then identify a class of Bayesian Networks and queries which allow one to fully recover from such modeling errors if one can choose Conditional Probability Tables (CPTs) dynamically based on evidence. We show theoretically that the recently proposed Testing Bayesian Networks (TBNs), which can be trained by compiling them into Testing Arithmetic Circuits (TACs), provide a promising construct for emulating this CPT selection mechanism. Finally, we present empirical results that illustrate the promise of TBNs as a tool for recovering from certain modeling errors in the context of supervised learning. | Haiying Huang, Adnan Darwiche | null | null | 2,021 | icml |
Chebyshev Polynomial Codes: Task Entanglement-based Coding for Distributed Matrix Multiplication | null | Distributed computing has been a prominent solution to efficiently process massive datasets in parallel. However, the existence of stragglers is one of the major concerns that slows down the overall speed of distributed computing. To deal with this problem, we consider a distributed matrix multiplication scenario where a master assigns multiple tasks to each worker to exploit stragglers’ computing ability (which is typically wasted in conventional distributed computing). We propose Chebyshev polynomial codes, which can achieve order-wise improvement in encoding complexity at the master and communication load in distributed matrix multiplication using task entanglement. The key idea of task entanglement is to reduce the number of encoded matrices for multiple tasks assigned to each worker by intertwining encoded matrices. We experimentally demonstrate that, in cloud environments, Chebyshev polynomial codes can provide significant reduction in overall processing time in distributed computing for matrix multiplication, which is a key computational component in modern deep learning. | Sangwoo Hong, Heecheol Yang, Youngseok Yoon, Taehyun Cho, Jungwoo Lee | null | null | 2,021 | icml |
Near-Optimal Representation Learning for Linear Bandits and Linear RL | null | This paper studies representation learning for multi-task linear bandits and multi-task episodic RL with linear value function approximation. We first consider the setting where we play $M$ linear bandits with dimension $d$ concurrently, and these bandits share a common $k$-dimensional linear representation so that $k\ll d$ and $k \ll M$. We propose a sample-efficient algorithm, MTLR-OFUL, which leverages the shared representation to achieve $\tilde{O}(M\sqrt{dkT} + d\sqrt{kMT} )$ regret, with $T$ being the number of total steps. Our regret significantly improves upon the baseline $\tilde{O}(Md\sqrt{T})$ achieved by solving each task independently. We further develop a lower bound that shows our regret is near-optimal when $d > M$. Furthermore, we extend the algorithm and analysis to multi-task episodic RL with linear value function approximation under low inherent Bellman error (Zanette et al., 2020a). To the best of our knowledge, this is the first theoretical result that characterize the benefits of multi-task representation learning for exploration in RL with function approximation. | Jiachen Hu, Xiaoyu Chen, Chi Jin, Lihong Li, Liwei Wang | null | null | 2,021 | icml |
FL-NTK: A Neural Tangent Kernel-based Framework for Federated Learning Analysis | null | Federated Learning (FL) is an emerging learning scheme that allows different distributed clients to train deep neural networks together without data sharing. Neural networks have become popular due to their unprecedented success. To the best of our knowledge, the theoretical guarantees of FL concerning neural networks with explicit forms and multi-step updates are unexplored. Nevertheless, training analysis of neural networks in FL is non-trivial for two reasons: first, the objective loss function we are optimizing is non-smooth and non-convex, and second, we are even not updating in the gradient direction. Existing convergence results for gradient descent-based methods heavily rely on the fact that the gradient direction is used for updating. The current paper presents a new class of convergence analysis for FL, Federated Neural Tangent Kernel (FL-NTK), which corresponds to overparamterized ReLU neural networks trained by gradient descent in FL and is inspired by the analysis in Neural Tangent Kernel (NTK). Theoretically, FL-NTK converges to a global-optimal solution at a linear rate with properly tuned learning parameters. Furthermore, with proper distributional assumptions, FL-NTK can also achieve good generalization. The proposed theoretical analysis scheme can be generalized to more complex neural networks. | Baihe Huang, Xiaoxiao Li, Zhao Song, Xin Yang | null | null | 2,021 | icml |
Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processes | null | Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e. stochastic processes whose samples are fields like those occurring in physics and engineering. Considering general transformations such as rotations and reflections, we show that spatial invariance of stochastic fields requires an inference model to be equivariant. Leveraging recent advances from the equivariance literature, we study equivariance in two classes of models. Firstly, we fully characterise equivariant Gaussian processes. Secondly, we introduce Steerable Conditional Neural Processes (SteerCNPs), a new, fully equivariant member of the Neural Process family. In experiments with Gaussian process vector fields, images, and real-world weather data, we observe that SteerCNPs significantly improve the performance of previous models and equivariance leads to improvements in transfer learning tasks. | Peter Holderrieth, Michael J Hutchinson, Yee Whye Teh | null | null | 2,021 | icml |
A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distance | null | The Wasserstein distance has become increasingly important in machine learning and deep learning. Despite its popularity, the Wasserstein distance is hard to approximate because of the curse of dimensionality. A recently proposed approach to alleviate the curse of dimensionality is to project the sampled data from the high dimensional probability distribution onto a lower-dimensional subspace, and then compute the Wasserstein distance between the projected data. However, this approach requires to solve a max-min problem over the Stiefel manifold, which is very challenging in practice. In this paper, we propose a Riemannian block coordinate descent (RBCD) method to solve this problem, which is based on a novel reformulation of the regularized max-min problem over the Stiefel manifold. We show that the complexity of arithmetic operations for RBCD to obtain an $\epsilon$-stationary point is $O(\epsilon^{-3})$, which is significantly better than the complexity of existing methods. Numerical results on both synthetic and real datasets demonstrate that our method is more efficient than existing methods, especially when the number of sampled data is very large. | Minhui Huang, Shiqian Ma, Lifeng Lai | null | null | 2,021 | icml |
Accurate Post Training Quantization With Small Calibration Sets | null | Lately, post-training quantization methods have gained considerable attention, as they are simple to use, and require only a small unlabeled calibration set. This small dataset cannot be used to fine-tune the model without significant over-fitting. Instead, these methods only use the calibration set to set the activations’ dynamic ranges. However, such methods always resulted in significant accuracy degradation, when used below 8-bits (except on small datasets). Here we aim to break the 8-bit barrier. To this end, we minimize the quantization errors of each layer or block separately by optimizing its parameters over the calibration set. We empirically demonstrate that this approach is: (1) much less susceptible to over-fitting than the standard fine-tuning approaches, and can be used even on a very small calibration set; and (2) more powerful than previous methods, which only set the activations’ dynamic ranges. We suggest two flavors for our method, parallel and sequential aim for a fixed and flexible bit-width allocation. For the latter, we demonstrate how to optimally allocate the bit-widths for each layer, while constraining accuracy degradation or model compression by proposing a novel integer programming formulation. Finally, we suggest model global statistics tuning, to correct biases introduced during quantization. Together, these methods yield state-of-the-art results for both vision and text models. For instance, on ResNet50, we obtain less than 1% accuracy degradation — with 4-bit weights and activations in all layers, but first and last. The suggested methods are two orders of magnitude faster than the traditional Quantize Aware Training approach used for lower than 8-bit quantization. We open-sourced our code \textit{https://github.com/papers-submission/CalibTIP}. | Itay Hubara, Yury Nahshan, Yair Hanani, Ron Banner, Daniel Soudry | null | null | 2,021 | icml |
Learning Randomly Perturbed Structured Predictors for Direct Loss Minimization | null | Direct loss minimization is a popular approach for learning predictors over structured label spaces. This approach is computationally appealing as it replaces integration with optimization and allows to propagate gradients in a deep net using loss-perturbed prediction. Recently, this technique was extended to generative models, by introducing a randomized predictor that samples a structure from a randomly perturbed score function. In this work, we interpolate between these techniques by learning the variance of randomized structured predictors as well as their mean, in order to balance between the learned score function and the randomized noise. We demonstrate empirically the effectiveness of learning this balance in structured discrete spaces. | Hedda Cohen Indelman, Tamir Hazan | null | null | 2,021 | icml |
Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning | null | Marginal-likelihood based model-selection, even though promising, is rarely used in deep learning due to estimation difficulties. Instead, most approaches rely on validation data, which may not be readily available. In this work, we present a scalable marginal-likelihood estimation method to select both hyperparameters and network architectures, based on the training data alone. Some hyperparameters can be estimated online during training, simplifying the procedure. Our marginal-likelihood estimate is based on Laplace’s method and Gauss-Newton approximations to the Hessian, and it outperforms cross-validation and manual tuning on standard regression and image classification datasets, especially in terms of calibration and out-of-distribution detection. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable (e.g., in nonstationary settings). | Alexander Immer, Matthias Bauer, Vincent Fortuin, Gunnar Rätsch, Khan Mohammad Emtiyaz | null | null | 2,021 | icml |
Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions | null | Generative adversarial networks (GANs) are often billed as "universal distribution learners", but precisely what distributions they can represent and learn is still an open question. Heavy-tailed distributions are prevalent in many different domains such as financial risk-assessment, physics, and epidemiology. We observe that existing GAN architectures do a poor job of matching the asymptotic behavior of heavy-tailed distributions, a problem that we show stems from their construction. Additionally, common loss functions produce unstable or near-zero gradients when faced with the infinite moments and large distances between outlier points characteristic of heavy-tailed distributions. We address these problems with the Pareto GAN. A Pareto GAN leverages extreme value theory and the functional properties of neural networks to learn a distribution that matches the asymptotic behavior of the marginal distributions of the features. We identify issues with standard loss functions and propose the use of alternative metric spaces that enable stable and efficient learning. Finally, we evaluate our proposed approach on a variety of heavy-tailed datasets. | Todd Huster, Jeremy Cohen, Zinan Lin, Kevin Chan, Charles Kamhoua, Nandi O. Leslie, Cho-Yu Jason Chiang, Vyas Sekar | null | null | 2,021 | icml |
Distributed Second Order Methods with Fast Rates and Compressed Communication | null | We develop several new communication-efficient second-order methods for distributed optimization. Our first method, NEWTON-STAR, is a variant of Newton’s method from which it inherits its fast local quadratic rate. However, unlike Newton’s method, NEWTON-STAR enjoys the same per iteration communication cost as gradient descent. While this method is impractical as it relies on the use of certain unknown parameters characterizing the Hessian of the objective function at the optimum, it serves as the starting point which enables us to design practical variants thereof with strong theoretical guarantees. In particular, we design a stochastic sparsification strategy for learning the unknown parameters in an iterative fashion in a communication efficient manner. Applying this strategy to NEWTON-STAR leads to our next method, NEWTON-LEARN, for which we prove local linear and superlinear rates independent of the condition number. When applicable, this method can have dramatically superior convergence behavior when compared to state-of-the-art methods. Finally, we develop a globalization strategy using cubic regularization which leads to our next method, CUBIC-NEWTON-LEARN, for which we prove global sublinear and linear convergence rates, and a fast superlinear rate. Our results are supported with experimental results on real datasets, and show several orders of magnitude improvement on baseline and state-of-the-art methods in terms of communication complexity. | Rustem Islamov, Xun Qian, Peter Richtarik | null | null | 2,021 | icml |
Randomized Entity-wise Factorization for Multi-Agent Reinforcement Learning | null | Multi-agent settings in the real world often involve tasks with varying types and quantities of agents and non-agent entities; however, common patterns of behavior often emerge among these agents/entities. Our method aims to leverage these commonalities by asking the question: “What is the expected utility of each agent when only considering a randomly selected sub-group of its observed entities?” By posing this counterfactual question, we can recognize state-action trajectories within sub-groups of entities that we may have encountered in another task and use what we learned in that task to inform our prediction in the current one. We then reconstruct a prediction of the full returns as a combination of factors considering these disjoint groups of entities and train this “randomly factorized" value function as an auxiliary objective for value-based multi-agent reinforcement learning. By doing so, our model can recognize and leverage similarities across tasks to improve learning efficiency in a multi-task setting. Our approach, Randomized Entity-wise Factorization for Imagined Learning (REFIL), outperforms all strong baselines by a significant margin in challenging multi-task StarCraft micromanagement settings. | Shariq Iqbal, Christian A Schroeder De Witt, Bei Peng, Wendelin Boehmer, Shimon Whiteson, Fei Sha | null | null | 2,021 | icml |
Active Learning for Distributionally Robust Level-Set Estimation | null | Many cases exist in which a black-box function $f$ with high evaluation cost depends on two types of variables $\bm x$ and $\bm w$, where $\bm x$ is a controllable \emph{design} variable and $\bm w$ are uncontrollable \emph{environmental} variables that have random variation following a certain distribution $P$. In such cases, an important task is to find the range of design variables $\bm x$ such that the function $f(\bm x, \bm w)$ has the desired properties by incorporating the random variation of the environmental variables $\bm w$. A natural measure of robustness is the probability that $f(\bm x, \bm w)$ exceeds a given threshold $h$, which is known as the \emph{probability threshold robustness} (PTR) measure in the literature on robust optimization. However, this robustness measure cannot be correctly evaluated when the distribution $P$ is unknown. In this study, we addressed this problem by considering the \textit{distributionally robust PTR} (DRPTR) measure, which considers the worst-case PTR within given candidate distributions. Specifically, we studied the problem of efficiently identifying a reliable set $H$, which is defined as a region in which the DRPTR measure exceeds a certain desired probability $\alpha$, which can be interpreted as a level set estimation (LSE) problem for DRPTR. We propose a theoretically grounded and computationally efficient active learning method for this problem. We show that the proposed method has theoretical guarantees on convergence and accuracy, and confirmed through numerical experiments that the proposed method outperforms existing methods. | Yu Inatsu, Shogo Iwazaki, Ichiro Takeuchi | null | null | 2,021 | icml |
How to Learn when Data Reacts to Your Model: Performative Gradient Descent | null | Performative distribution shift captures the setting where the choice of which ML model is deployed changes the data distribution. For example, a bank which uses the number of open credit lines to determine a customer’s risk of default on a loan may induce customers to open more credit lines in order to improve their chances of being approved. Because of the interactions between the model and data distribution, finding the optimal model parameters is challenging. Works in this area have focused on finding stable points, which can be far from optimal. Here we introduce \emph{performative gradient descent} (PerfGD), an algorithm for computing performatively optimal points. Under regularity assumptions on the performative loss, PerfGD is the first algorithm which provably converges to an optimal point. PerfGD explicitly captures how changes in the model affects the data distribution and is simple to use. We support our findings with theory and experiments. | Zachary Izzo, Lexing Ying, James Zou | null | null | 2,021 | icml |
Crowdsourcing via Annotator Co-occurrence Imputation and Provable Symmetric Nonnegative Matrix Factorization | null | Unsupervised learning of the Dawid-Skene (D&S) model from noisy, incomplete and crowdsourced annotations has been a long-standing challenge, and is a critical step towards reliably labeling massive data. A recent work takes a coupled nonnegative matrix factorization (CNMF) perspective, and shows appealing features: It ensures the identifiability of the D&S model and enjoys low sample complexity, as only the estimates of the co-occurrences of annotator labels are involved. However, the identifiability holds only when certain somewhat restrictive conditions are met in the context of crowdsourcing. Optimizing the CNMF criterion is also costly—and convergence assurances are elusive. This work recasts the pairwise co-occurrence based D&S model learning problem as a symmetric NMF (SymNMF) problem—which offers enhanced identifiability relative to CNMF. In practice, the SymNMF model is often (largely) incomplete, due to the lack of co-labeled items by some annotators. Two lightweight algorithms are proposed for co-occurrence imputation. Then, a low-complexity shifted rectified linear unit (ReLU)-empowered SymNMF algorithm is proposed to identify the D&S model. Various performance characterizations (e.g., missing co-occurrence recoverability, stability, and convergence) and evaluations are also presented. | Shahana Ibrahim, Xiao Fu | null | null | 2,021 | icml |
LieTransformer: Equivariant Self-Attention for Lie Groups | null | Group equivariant neural networks are used as building blocks of group invariant neural networks, which have been shown to improve generalisation performance and data efficiency through principled parameter sharing. Such works have mostly focused on group equivariant convolutions, building on the result that group equivariant linear maps are necessarily convolutions. In this work, we extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups. We demonstrate the generality of our approach by showing experimental results that are competitive to baseline methods on a wide range of tasks: shape counting on point clouds, molecular property regression and modelling particle trajectories under Hamiltonian dynamics. | Michael J Hutchinson, Charline Le Lan, Sheheryar Zaidi, Emilien Dupont, Yee Whye Teh, Hyunjik Kim | null | null | 2,021 | icml |
Robust Density Estimation from Batches: The Best Things in Life are (Nearly) Free | null | In many applications data are collected in batches, some potentially biased, corrupt, or even adversarial. Learning algorithms for this setting have therefore garnered considerable recent attention. In particular, a sequence of works has shown that all approximately piecewise polynomial distributions—and in particular all Gaussian, Gaussian-mixture, log-concave, low-modal, and monotone-hazard distributions—can be learned robustly in polynomial time. However, these results left open the question, stated explicitly in \cite{chen2020learning}, about the best possible sample complexity of such algorithms. We answer this question, showing that, perhaps surprisingly, up to logarithmic factors, the optimal sample complexity is the same as for genuine, non-adversarial, data! To establish the result, we reduce robust learning of approximately piecewise polynomial distributions to robust learning of the probability of all subsets of size at most $k$ of a larger discrete domain, and learn these probabilities in optimal sample complexity linear in $k$ regardless of the domain size. In simulations, the algorithm runs very quickly and estimates distributions to essentially the accuracy achieved when all adversarial batches are removed. The results also imply the first polynomial-time sample-optimal algorithm for robust interval-based classification based on batched data. | Ayush Jain, Alon Orlitsky | null | null | 2,021 | icml |
Parallel and Flexible Sampling from Autoregressive Models via Langevin Dynamics | null | This paper introduces an alternative approach to sampling from autoregressive models. Autoregressive models are typically sampled sequentially, according to the transition dynamics defined by the model. Instead, we propose a sampling procedure that initializes a sequence with white noise and follows a Markov chain defined by Langevin dynamics on the global log-likelihood of the sequence. This approach parallelizes the sampling process and generalizes to conditional sampling. Using an autoregressive model as a Bayesian prior, we can steer the output of a generative model using a conditional likelihood or constraints. We apply these techniques to autoregressive models in the visual and audio domains, with competitive results for audio source separation, super-resolution, and inpainting. | Vivek Jayaram, John Thickstun | null | null | 2,021 | icml |
Inverse Decision Modeling: Learning Interpretable Representations of Behavior | null | Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent *description* of existing behavior in the first place. In this paper, we develop an expressive, unifying perspective on *inverse decision modeling*: a framework for learning parameterized representations of sequential decision behavior. First, we formalize the *forward* problem (as a normative standard), subsuming common classes of control behavior. Second, we use this to formalize the *inverse* problem (as a descriptive model), generalizing existing work on imitation/reward learning—while opening up a much broader class of research problems in behavior representation. Finally, we instantiate this approach with an example (*inverse bounded rational control*), illustrating how this structure enables learning (interpretable) representations of (bounded) rationality—while naturally capturing intuitive notions of suboptimal actions, biased beliefs, and imperfect knowledge of environments. | Daniel Jarrett, Alihan Hüyük, Mihaela Van Der Schaar | null | null | 2,021 | icml |
Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding | null | We study the problem of learning conditional average treatment effects (CATE) from high-dimensional, observational data with unobserved confounders. Unobserved confounders introduce ignorance—a level of unidentifiability—about an individual’s response to treatment by inducing bias in CATE estimates. We present a new parametric interval estimator suited for high-dimensional data, that estimates a range of possible CATE values when given a predefined bound on the level of hidden confounding. Further, previous interval estimators do not account for ignorance about the CATE associated with samples that may be underrepresented in the original study, or samples that violate the overlap assumption. Our interval estimator also incorporates model uncertainty so that practitioners can be made aware of such out-of-distribution data. We prove that our estimator converges to tight bounds on CATE when there may be unobserved confounding and assess it using semi-synthetic, high-dimensional datasets. | Andrew Jesson, Sören Mindermann, Yarin Gal, Uri Shalit | null | null | 2,021 | icml |
In-Database Regression in Input Sparsity Time | null | Sketching is a powerful dimensionality reduction technique for accelerating algorithms for data analysis. A crucial step in sketching methods is to compute a subspace embedding (SE) for a large matrix $A \in \mathbb{R}^{N \times d}$. SE’s are the primary tool for obtaining extremely efficient solutions for many linear-algebraic tasks, such as least squares regression and low rank approximation. Computing an SE often requires an explicit representation of $A$ and running time proportional to the size of $A$. However, if $A= T_1 \Join T_2 \Join …\Join T_m$ is the result of a database join query on several smaller tables $T_i \in \mathbb{R}^{n_i \times d_i}$, then this running time can be prohibitive, as $A$ itself can have as many as $O(n_1 n_2 \cdots n_m)$ rows. In this work, we design subspace embeddings for database joins which can be computed significantly faster than computing the join. For the case of a two table join $A = T_1 \Join T_2$ we give input-sparsity algorithms for computing subspace embeddings, with running time bounded by the number of non-zero entries in $T_1,T_2$. This results in input-sparsity time algorithms for high accuracy regression, significantly improving upon the running time of prior FAQ-based methods for regression. We extend our results to arbitrary joins for the ridge regression problem, also considerably improving the running time of prior methods. Empirically, we apply our method to real datasets and show that it is significantly faster than existing algorithms. | Rajesh Jayaram, Alireza Samadian, David Woodruff, Peng Ye | null | null | 2,021 | icml |
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