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It’s Not What Machines Can Learn, It’s What We Cannot Teach | null | Can deep neural networks learn to solve any task, and in particular problems of high complexity? This question attracts a lot of interest, with recent works tackling computationally hard tasks such as the traveling salesman problem and satisfiability. In this work we offer a different perspective on this question. Given the common assumption that NP != coNP we prove that any polynomial-time sample generator for an NP-hard problem samples, in fact, from an easier sub-problem. We empirically explore a case study, Conjunctive Query Containment, and show how common data generation techniques generate biased data-sets that lead practitioners to over-estimate model accuracy. Our results suggest that machine learning approaches that require training on a dense uniform sampling from the target distribution cannot be used to solve computationally hard problems, the reason being the difficulty of generating sufficiently large and unbiased training sets. | Gal Yehuda, Moshe Gabel, Assaf Schuster | null | null | 2,020 | icml |
Graphical Models Meet Bandits: A Variational Thompson Sampling Approach | null | We propose a novel framework for structured bandits, which we call an influence diagram bandit. Our framework uses a graphical model to capture complex statistical dependencies between actions, latent variables, and observations; and thus unifies and extends many existing models, such as combinatorial semi-bandits, cascading bandits, and low-rank bandits. We develop novel online learning algorithms that learn to act efficiently in our models. The key idea is to track a structured posterior distribution of model parameters, either exactly or approximately. To act, we sample model parameters from their posterior and then use the structure of the influence diagram to find the most optimistic action under the sampled parameters. We empirically evaluate our algorithms in three structured bandit problems, and show that they perform as well as or better than problem-specific state-of-the-art baselines. | Tong Yu, Branislav Kveton, Zheng Wen, Ruiyi Zhang, Ole J. Mengshoel | null | null | 2,020 | icml |
Learning the Valuations of a $k$-demand Agent | null | We study problems where a learner aims to learn the valuations of an agent by observing which goods he buys under varying price vectors. More specifically, we consider the case of a $k$-demand agent, whose valuation over the goods is additive when receiving up to $k$ goods, but who has no interest in receiving more than $k$ goods. We settle the query complexity for the active-learning (preference elicitation) version, where the learner chooses the prices to post, by giving a \emph{biased binary search} algorithm, generalizing the classical binary search procedure. We complement our query complexity upper bounds by lower bounds that match up to lower-order terms. We also study the passive-learning version in which the learner does not control the prices, and instead they are sampled from some distribution. We show that in the PAC model for passive learning, any \emph{empirical risk minimizer} has a sample complexity that is optimal up to a factor of $\widetilde{O}(k)$. | Hanrui Zhang, Vincent Conitzer | null | null | 2,020 | icml |
Scaling up Hybrid Probabilistic Inference with Logical and Arithmetic Constraints via Message Passing | null | Weighted model integration (WMI) is an appealing framework for probabilistic inference: it allows for expressing the complex dependencies in real-world problems, where variables are both continuous and discrete, via the language of Satisfiability Modulo Theories (SMT), as well as to compute probabilistic queries with complex logical and arithmetic constraints. Yet, existing WMI solvers are not ready to scale to these problems. They either ignore the intrinsic dependency structure of the problem entirely, or they are limited to overly restrictive structures. To narrow this gap, we derive a factorized WMI computation enabling us to devise a scalable WMI solver based on message passing, called MP-WMI. Namely, MP-WMI is the first WMI solver that can (i) perform exact inference on the full class of tree-structured WMI problems, and (ii) perform inter-query amortization, e.g., to compute all marginal densities simultaneously. Experimental results show that our solver dramatically outperforms the existingWMI solvers on a large set of benchmarks. | Zhe Zeng, Paolo Morettin, Fanqi Yan, Antonio Vergari, Guy Van Den Broeck | null | null | 2,020 | icml |
Graph Random Neural Features for Distance-Preserving Graph Representations | null | We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. The embedding naturally deals with graph isomorphism and preserves the metric structure of the graph domain, in probability. In addition to being an explicit embedding method, it also allows us to efficiently and effectively approximate graph metric distances (as well as complete kernel functions); a criterion to select the embedding dimension trading off the approximation accuracy with the computational cost is also provided. GRNF can be used within traditional processing methods or as a training-free input layer of a graph neural network. The theoretical guarantees that accompany GRNF ensure that the considered graph distance is metric, hence allowing to distinguish any pair of non-isomorphic graphs. | Daniele Zambon, Cesare Alippi, Lorenzo Livi | null | null | 2,020 | icml |
Robustness to Programmable String Transformations via Augmented Abstract Training | null | Deep neural networks for natural language processing tasks are vulnerable to adversarial input perturbations. In this paper, we present a versatile language for programmatically specifying string transformations—e.g., insertions, deletions, substitutions, swaps, etc.—that are relevant to the task at hand. We then present an approach to adversarially training models that are robust to such user-defined string transformations. Our approach combines the advantages of search-based techniques for adversarial training with abstraction-based techniques. Specifically, we show how to decompose a set of user-defined string transformations into two component specifications, one that benefits from search and another from abstraction. We use our technique to train models on the AG and SST2 datasets and show that the resulting models are robust to combinations of user-defined transformations mimicking spelling mistakes and other meaning-preserving transformations. | Yuhao Zhang, Aws Albarghouthi, Loris D’Antoni | null | null | 2,020 | icml |
Generative Adversarial Imitation Learning with Neural Network Parameterization: Global Optimality and Convergence Rate | null | Generative adversarial imitation learning (GAIL) demonstrates tremendous success in practice, especially when combined with neural networks. Different from reinforcement learning, GAIL learns both policy and reward function from expert (human) demonstration. Despite its empirical success, it remains unclear whether GAIL with neural networks converges to the globally optimal solution. The major difficulty comes from the nonconvex-nonconcave minimax optimization structure. To bridge the gap between practice and theory, we analyze a gradient-based algorithm with alternating updates and establish its sublinear convergence to the globally optimal solution. To the best of our knowledge, our analysis establishes the global optimality and convergence rate of GAIL with neural networks for the first time. | Yufeng Zhang, Qi Cai, Zhuoran Yang, Zhaoran Wang | null | null | 2,020 | icml |
Converging to Team-Maxmin Equilibria in Zero-Sum Multiplayer Games | null | Efficiently computing equilibria for multiplayer games is still an open challenge in computational game theory. This paper focuses on computing Team-Maxmin Equilibria (TMEs), which is an important solution concept for zero-sum multiplayer games where players in a team having the same utility function play against an adversary independently. Existing algorithms are inefficient to compute TMEs in large games, especially when the strategy space is too large to be represented due to limited memory. In two-player games, the Incremental Strategy Generation (ISG) algorithm is an efficient approach to avoid enumerating all pure strategies. However, the study of ISG for computing TMEs is completely unexplored. To fill this gap, we first study the properties of ISG for multiplayer games, showing that ISG converges to a Nash Equilibrium (NE) but may not converge to a TME. Second, we design an ISG variant for TMEs (ISGT) by exploiting that a TME is an NE maximizing the team’s utility and show that ISGT converges to a TME and the impossibility of relaxing conditions in ISGT. Third, to further improve the scalability, we design an ISGT variant (CISGT) by using the strategy space for computing an equilibrium that is close to a TME but is easier to be computed as the initial strategy space of ISGT. Finally, extensive experimental results show that CISGT is orders of magnitude faster than ISGT and the state-of-the-art algorithm to compute TMEs in large games. | Youzhi Zhang, Bo An | null | null | 2,020 | icml |
A Tree-Structured Decoder for Image-to-Markup Generation | null | Recent encoder-decoder approaches typically employ string decoders to convert images into serialized strings for image-to-markup. However, for tree-structured representational markup, string representations can hardly cope with the structural complexity. In this work, we first show via a set of toy problems that string decoders struggle to decode tree structures, especially as structural complexity increases, we then propose a tree-structured decoder that specifically aims at generating a tree-structured markup. Our decoders works sequentially, where at each step a child node and its parent node are simultaneously generated to form a sub-tree. This sub-tree is consequently used to construct the final tree structure in a recurrent manner. Key to the success of our tree decoder is twofold, (i) it strictly respects the parent-child relationship of trees, and (ii) it explicitly outputs trees as oppose to a linear string. Evaluated on both math formula recognition and chemical formula recognition, the proposed tree decoder is shown to greatly outperform strong string decoder baselines. | Jianshu Zhang, Jun Du, Yongxin Yang, Yi-Zhe Song, Si Wei, Lirong Dai | null | null | 2,020 | icml |
Designing Optimal Dynamic Treatment Regimes: A Causal Reinforcement Learning Approach | null | A dynamic treatment regime (DTR) consists of a sequence of decision rules, one per stage of intervention, that dictates how to determine the treatment assignment to patients based on evolving treatments and covariates’ history. These regimes are particularly effective for managing chronic disorders and is arguably one of the critical ingredients underlying more personalized decision-making systems. All reinforcement learning algorithms for finding the optimal DTR in online settings will suffer O(\sqrt{|D_{X, S}|T}) regret on some environments, where T is the number of experiments, and D_{X, S} is the domains of treatments X and covariates S. This implies T = O (|D_{X, S}|) trials to generate an optimal DTR. In many applications, domains of X and S could be so enormous that the time required to ensure appropriate learning may be unattainable. We show that, if the causal diagram of the underlying environment is provided, one could achieve regret that is exponentially smaller than D_{X, S}. In particular, we develop two online algorithms that satisfy such regret bounds by exploiting the causal structure underlying the DTR; one is based on the principle of optimism in the face of uncertainty (OFU-DTR), and the other uses the posterior sampling learning (PS-DTR). Finally, we introduce efficient methods to accelerate these online learning procedures by leveraging the abundant, yet biased observational (non-experimental) data. | Junzhe Zhang | null | null | 2,020 | icml |
Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization | null | Single-objective black box optimization (also known as zeroth-order optimization) is the process of minimizing a scalar objective $f(x)$, given evaluations at adaptively chosen inputs $x$. In this paper, we consider multi-objective optimization, where $f(x)$ outputs a vector of possibly competing objectives and the goal is to converge to the Pareto frontier. Quantitatively, we wish to maximize the standard \emph{hypervolume indicator} metric, which measures the dominated hypervolume of the entire set of chosen inputs. In this paper, we introduce a novel scalarization function, which we term the \emph{hypervolume scalarization}, and show that drawing random scalarizations from an appropriately chosen distribution can be used to efficiently approximate the \emph{hypervolume indicator} metric. We utilize this connection to show that Bayesian optimization with our scalarization via common acquisition functions, such as Thompson Sampling or Upper Confidence Bound, provably converges to the whole Pareto frontier by deriving tight \emph{hypervolume regret} bounds on the order of $\widetilde{O}(\sqrt{T})$. Furthermore, we highlight the general utility of our scalarization framework by showing that any provably convergent single-objective optimization process can be converted to a multi-objective optimization process with provable convergence guarantees. | Richard Zhang, Daniel Golovin | null | null | 2,020 | icml |
Mix-n-Match : Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning | null | This paper studies the problem of post-hoc calibration of machine learning classifiers. We introduce the following desiderata for uncertainty calibration: (a) accuracy-preserving, (b) data-efficient, and (c) high expressive power. We show that none of the existing methods satisfy all three requirements, and demonstrate how Mix-n-Match calibration strategies (i.e., ensemble and composition) can help achieve remarkably better data-efficiency and expressive power while provably maintaining the classification accuracy of the original classifier. Mix-n-Match strategies are generic in the sense that they can be used to improve the performance of any off-the-shelf calibrator. We also reveal potential issues in standard evaluation practices. Popular approaches (e.g., histogram-based expected calibration error (ECE)) may provide misleading results especially in small-data regime. Therefore, we propose an alternative data-efficient kernel density-based estimator for a reliable evaluation of the calibration performance and prove its asymptotically unbiasedness and consistency. Our approaches outperform state-of-the-art solutions on both the calibration as well as the evaluation tasks in most of the experimental settings. Our codes are available at https://github.com/zhang64- llnl/Mix-n-Match-Calibration. | Jize Zhang, Bhavya Kailkhura, T. Yong-Jin Han | null | null | 2,020 | icml |
Optimal Estimator for Unlabeled Linear Regression | null | Unlabeled linear regression, or “linear regression with an unknown permutation”, has attracted increasing attentions due to its applications in (e.g.,) linkage record and de-anonymization. However, the computation of unlabeled linear regression proves to be cumbersome and existing algorithms typically require considerable time, especially in the high dimensional regime. In this paper, we propose a one-step estimator which is optimal from both the computational and the statistical aspects. From the computational perspective, our estimator exhibits the same order of computational complexity as that of the oracle case (which means the regression coefficients are known in advance and only the permutation needs recovery). From the statistical perspective, when comparing with the necessary conditions for permutation recovery, our requirement on the \emph{signal-to-noise ratio} ($\mathsf{SNR}$) agrees up to merely $\Omega\left(\log \log n\right)$ difference when the stable rank of the regression coefficients $\ensuremath{\mathbf{B}}^{\natural}$ is much less than $\log n/\log \log n$. | Hang Zhang, Ping Li | null | null | 2,020 | icml |
Cautious Adaptation For Reinforcement Learning in Safety-Critical Settings | null | Reinforcement learning (RL) in real-world safety-critical target settings like urban driving is hazardous, imperiling the RL agent, other agents, and the environment. To overcome this difficulty, we propose a "safety-critical adaptation" task setting: an agent first trains in non-safety-critical "source" environments such as in a simulator, before it adapts to the target environment where failures carry heavy costs. We propose a solution approach, CARL, that builds on the intuition that prior experience in diverse environments equips an agent to estimate risk, which in turn enables relative safety through risk-averse, cautious adaptation. CARL first employs model-based RL to train a probabilistic model to capture uncertainty about transition dynamics and catastrophic states across varied source environments. Then, when exploring a new safety-critical environment with unknown dynamics, the CARL agent plans to avoid actions that could lead to catastrophic states. In experiments on car driving, cartpole balancing, and half-cheetah locomotion, CARL successfully acquires cautious exploration behaviors, yielding higher rewards with fewer failures than strong RL adaptation baselines. | Jesse Zhang, Brian Cheung, Chelsea Finn, Sergey Levine, Dinesh Jayaraman | null | null | 2,020 | icml |
Self-Attentive Hawkes Process | null | Capturing the occurrence dynamics is crucial to predicting which type of events will happen next and when. A common method to do this is through Hawkes processes. To enhance their capacity, recurrent neural networks (RNNs) have been incorporated due to RNNs’ successes in processing sequential data such as languages. Recent evidence suggests that self-attention is more competent than RNNs in dealing with languages. However, we are unaware of the effectiveness of self-attention in the context of Hawkes processes. This study aims to fill the gap by designing a self-attentive Hawkes process (SAHP). SAHP employs self-attention to summarise the influence of history events and compute the probability of the next event. One deficit of the conventional self-attention when applied to event sequences is that its positional encoding only considers the order of a sequence ignoring the time intervals between events. To overcome this deficit, we modify its encoding by translating time intervals into phase shifts of sinusoidal functions. Experiments on goodness-of-fit and prediction tasks show the improved capability of SAHP. Furthermore, SAHP is more interpretable than RNN-based counterparts because the learnt attention weights reveal contributions of one event type to the happening of another type. To the best of our knowledge, this is the first work that studies the effectiveness of self-attention in Hawkes processes. | Qiang Zhang, Aldo Lipani, Omer Kirnap, Emine Yilmaz | null | null | 2,020 | icml |
Provably Convergent Two-Timescale Off-Policy Actor-Critic with Function Approximation | null | We present the first provably convergent two-timescale off-policy actor-critic algorithm (COF-PAC) with function approximation. Key to COF-PAC is the introduction of a new critic, the emphasis critic, which is trained via Gradient Emphasis Learning (GEM), a novel combination of the key ideas of Gradient Temporal Difference Learning and Emphatic Temporal Difference Learning. With the help of the emphasis critic and the canonical value function critic, we show convergence for COF-PAC, where the critics are linear and the actor can be nonlinear. | Shangtong Zhang, Bo Liu, Hengshuai Yao, Shimon Whiteson | null | null | 2,020 | icml |
Approximation Capabilities of Neural ODEs and Invertible Residual Networks | null | Recent interest in invertible models and normalizing flows has resulted in new architectures that ensure invertibility of the network model. Neural ODEs and i-ResNets are two recent techniques for constructing models that are invertible, but it is unclear if they can be used to approximate any continuous invertible mapping. Here, we show that out of the box, both of these architectures are limited in their approximation capabilities. We then show how to overcome this limitation: we prove that any homeomorphism on a $p$-dimensional Euclidean space can be approximated by a Neural ODE or an i-ResNet operating on a $2p$-dimensional Euclidean space. We conclude by showing that capping a Neural ODE or an i-ResNet with a single linear layer is sufficient to turn the model into a universal approximator for non-invertible continuous functions. | Han Zhang, Xi Gao, Jacob Unterman, Tom Arodz | null | null | 2,020 | icml |
Learning Structured Latent Factors from Dependent Data:A Generative Model Framework from Information-Theoretic Perspective | null | Learning controllable and generalizable representation of multivariate data with desired structural properties remains a fundamental problem in machine learning. In this paper, we present a novel framework for learning generative models with various underlying structures in the latent space. Learning controllable and generalizable representation of multivariate data with desired structural properties remains a fundamental problem in machine learning. In this paper, we present a novel framework for learning generative models with various underlying structures in the latent space. We represent the inductive bias in the form of mask variables to model the dependency structure in the graphical model and extend the theory of multivariate information bottleneck (Friedman et al., 2001) to enforce it. Our model provides a principled approach to learn a set of semantically meaningful latent factors that reflect various types of desired structures like capturing correlation or encoding invariance, while also offering the flexibility to automatically estimate the dependency structure from data. We show that our framework unifies many existing generative models and can be applied to a variety of tasks, including multimodal data modeling, algorithmic fairness, and out-of-distribution generalization. | Ruixiang Zhang, Masanori Koyama, Katsuhiko Ishiguro | null | null | 2,020 | icml |
Dual-Path Distillation: A Unified Framework to Improve Black-Box Attacks | null | We study the problem of constructing black-box adversarial attacks, where no model information is revealed except for the feedback knowledge of the given inputs. To obtain sufficient knowledge for crafting adversarial examples, previous methods query the target model with inputs that are perturbed with different searching directions. However, these methods suffer from poor query efficiency since the employed searching directions are sampled randomly. To mitigate this issue, we formulate the goal of mounting efficient attacks as an optimization problem in which the adversary tries to fool the target model with a limited number of queries. Under such settings, the adversary has to select appropriate searching directions to reduce the number of model queries. By solving the efficient-attack problem, we find that we need to distill the knowledge in both the path of the adversarial examples and the path of the searching directions. Therefore, we propose a novel framework, dual-path distillation, that utilizes the feedback knowledge not only to craft adversarial examples but also to alter the searching directions to achieve efficient attacks. Experimental results suggest that our framework can significantly increase the query efficiency. | Yonggang Zhang, Ya Li, Tongliang Liu, Xinmei Tian | null | null | 2,020 | icml |
Complexity of Finding Stationary Points of Nonconvex Nonsmooth Functions | null | We provide the first non-asymptotic analysis for finding stationary points of nonsmooth, nonconvex functions. In particular, we study the class of Hadamard semi-differentiable functions, perhaps the largest class of nonsmooth functions for which the chain rule of calculus holds. This class contains important examples such as ReLU neural networks and others with non-differentiable activation functions. First, we show that finding an epsilon-stationary point with first-order methods is impossible in finite time. Therefore, we introduce the notion of (delta, epsilon)-stationarity, a generalization that allows for a point to be within distance delta of an epsilon-stationary point and reduces to epsilon-stationarity for smooth functions. We propose a series of randomized first-order methods and analyze their complexity of finding a (delta, epsilon)-stationary point. Furthermore, we provide a lower bound and show that our stochastic algorithm has min-max optimal dependence on delta. Empirically, our methods perform well for training ReLU neural networks. | Jingzhao Zhang, Hongzhou Lin, Stefanie Jegelka, Suvrit Sra, Ali Jadbabaie | null | null | 2,020 | icml |
GradientDICE: Rethinking Generalized Offline Estimation of Stationary Values | null | We present GradientDICE for estimating the density ratio between the state distribution of the target policy and the sampling distribution in off-policy reinforcement learning. GradientDICE fixes several problems of GenDICE (Zhang et al., 2020), the current state-of-the-art for estimating such density ratios. Namely, the optimization problem in GenDICE is not a convex-concave saddle-point problem once nonlinearity in optimization variable parameterization is introduced to ensure positivity, so primal-dual algorithms are not guaranteed to find the desired solution. However, such nonlinearity is essential to ensure the consistency of GenDICE even with a tabular representation. This is a fundamental contradiction, resulting from GenDICE’s original formulation of the optimization problem. In GradientDICE, we optimize a different objective from GenDICE by using the Perron-Frobenius theorem and eliminating GenDICE’s use of divergence, such that nonlinearity in parameterization is not necessary for GradientDICE, which is provably convergent under linear function approximation. | Shangtong Zhang, Bo Liu, Shimon Whiteson | null | null | 2,020 | icml |
CAUSE: Learning Granger Causality from Event Sequences using Attribution Methods | null | We study the problem of learning Granger causality between event types from asynchronous, interdependent, multi-type event sequences. Existing work suffers from either limited model flexibility or poor model explainability and thus fails to uncover Granger causality across a wide variety of event sequences with diverse event interdependency. To address these weaknesses, we propose CAUSE (Causality from AttribUtions on Sequence of Events), a novel framework for the studied task. The key idea of CAUSE is to first implicitly capture the underlying event interdependency by fitting a neural point process, and then extract from the process a Granger causality statistic using an axiomatic attribution method. Across multiple datasets riddled with diverse event interdependency, we demonstrate that CAUSE achieves superior performance on correctly inferring the inter-type Granger causality over a range of state-of-the-art methods. | Wei Zhang, Thomas Panum, Somesh Jha, Prasad Chalasani, David Page | null | null | 2,020 | icml |
Fast Learning of Graph Neural Networks with Guaranteed Generalizability: One-hidden-layer Case | null | Although graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice, their theoretical guarantee on generalizability remains elusive in the literature. In this paper, we provide a theoretically-grounded generalizability analysis of GNNs with one hidden layer for both regression and binary classification problems. Under the assumption that there exists a ground-truth GNN model (with zero generalization error), the objective of GNN learning is to estimate the ground-truth GNN parameters from the training data. To achieve this objective, we propose a learning algorithm that is built on tensor initialization and accelerated gradient descent. We then show that the proposed learning algorithm converges to the ground-truth GNN model for the regression problem, and to a model sufficiently close to the ground-truth for the binary classification problem. Moreover, for both cases, the convergence rate of the proposed learning algorithm is proven to be linear and faster than the vanilla gradient descent algorithm. We further explore the relationship between the sample complexity of GNNs and their underlying graph properties. Lastly, we provide numerical experiments to demonstrate the validity of our analysis and the effectiveness of the proposed learning algorithm for GNNs. | Shuai Zhang, Meng Wang, Sijia Liu, Pin-Yu Chen, Jinjun Xiong | null | null | 2,020 | icml |
A Flexible Latent Space Model for Multilayer Networks | null | Entities often interact with each other through multiple types of relations, which are often represented as multilayer networks. Multilayer networks among the same set of nodes usually share common structures, while each layer can possess its distinct node connecting behaviors. This paper proposes a flexible latent space model for multilayer networks for the purpose of capturing such characteristics. Specifically, the proposed model embeds each node with a latent vector shared among layers and a layer-specific effect for each layer; both elements together with a layer-specific connectivity matrix determine edge formations. To fit the model, we develop a projected gradient descent algorithm for efficient parameter estimation. We also establish theoretical properties of the maximum likelihood estimators and show that the upper bound of the common latent structure’s estimation error is inversely proportional to the number of layers under mild conditions. The superior performance of the proposed model is demonstrated through simulation studies and applications to two real-world data examples. | Xuefei Zhang, Songkai Xue, Ji Zhu | null | null | 2,020 | icml |
Learning with Feature and Distribution Evolvable Streams | null | In many real-world applications, data are collected in the form of a stream, whose feature space can evolve over time. For instance, in the environmental monitoring task, features can be dynamically vanished or augmented due to the existence of expired old sensors and deployed new sensors. Furthermore, besides the evolvable feature space, the data distribution is usually changing in the streaming scenario. When both feature space and data distribution are evolvable, it is quite challenging to design algorithms with guarantees, particularly theoretical understandings of generalization ability. To address this difficulty, we propose a novel discrepancy measure for data with evolving feature space and data distribution, named the \emph{evolving discrepancy}. Based on that, we present the generalization error analysis, and the theory motivates the design of a learning algorithm which is further implemented by deep neural networks. Empirical studies on synthetic data verify the rationale of our proposed discrepancy measure, and extensive experiments on real-world tasks validate the effectiveness of our algorithm. | Zhen-Yu Zhang, Peng Zhao, Yuan Jiang, Zhi-Hua Zhou | null | null | 2,020 | icml |
On Learning Language-Invariant Representations for Universal Machine Translation | null | The goal of universal machine translation is to learn to translate between any pair of languages. Despite impressive empirical results and an increasing interest in massively multilingual models, theoretical analysis on translation errors made by such universal machine translation models is only nascent. In this paper, we formally prove certain impossibilities of this endeavour in general, as well as prove positive results in the presence of additional (but natural) structure of data. For the former, we derive a lower bound on the translation error in the many-to-many translation setting, which shows that any algorithm aiming to learn shared sentence representations among multiple language pairs has to make a large translation error on at least one of the translation tasks, if no assumption on the structure of the languages is made. For the latter, we show that if the paired documents in the corpus follow a natural \emph{encoder-decoder} generative process, we can expect a natural notion of “generalization”: a linear number of language pairs, rather than quadratic, suffices to learn a good representation. Our theory also explains what kinds of connection graphs between pairs of languages are better suited: ones with longer paths result in worse sample complexity. We believe our theoretical insights and implications contribute to the future algorithmic design of universal machine translation. | Han Zhao, Junjie Hu, Andrej Risteski | null | null | 2,020 | icml |
PEGASUS: Pre-training with Extracted Gap-sentences for Abstractive Summarization | null | Recent work pre-training Transformers with self-supervised objectives on large text corpora has shown great success when fine-tuned on downstream NLP tasks including text summarization. However, pre-training objectives tailored for abstractive text summarization have not been explored. Furthermore there is a lack of systematic evaluation across diverse domains. In this work, we propose pre-training large Transformer-based encoder-decoder models on massive text corpora with a new self-supervised objective. In PEGASUS, important sentences are removed/masked from an input document and are generated together as one output sequence from the remaining sentences, similar to an extractive summary. We evaluated our best PEGASUS model on 12 downstream summarization tasks spanning news, science, stories, instructions, emails, patents, and legislative bills. Experiments demonstrate it achieves state-of-the-art performance on all 12 downstream datasets measured by ROUGE scores. Our model also shows surprising performance on low-resource summarization, surpassing previous state-of-the-art results on 6 datasets with only 1000 examples. Finally we validated our results using human evaluation and show that our model summaries achieve human performance on multiple datasets. | Jingqing Zhang, Yao Zhao, Mohammad Saleh, Peter Liu | null | null | 2,020 | icml |
Sharp Composition Bounds for Gaussian Differential Privacy via Edgeworth Expansion | null | Datasets containing sensitive information are often sequentially analyzed by many algorithms and, accordingly, a fundamental question in differential privacy is concerned with how the overall privacy bound degrades under composition. To address this question, we introduce a family of analytical and sharp privacy bounds under composition using the Edgeworth expansion in the framework of the recently proposed $f$-differential privacy. In short, whereas the existing composition theorem, for example, relies on the central limit theorem, our new privacy bounds under composition gain improved tightness by leveraging the refined approximation accuracy of the Edgeworth expansion. Our approach is easy to implement and computationally efficient for any number of compositions. The superiority of these new bounds is confirmed by an asymptotic error analysis and an application to quantifying the overall privacy guarantees of noisy stochastic gradient descent used in training private deep neural networks. | Qinqing Zheng, Jinshuo Dong, Qi Long, Weijie Su | null | null | 2,020 | icml |
Smaller, more accurate regression forests using tree alternating optimization | null | Regression forests, based on ensemble approaches such as bagging or boosting, have long been recognized as the leading off-the-shelf method for regression. However, forests rely on a greedy top-down procedure such as CART to learn each tree. We extend a recent algorithm for learning classification trees, Tree Alternating Optimization (TAO), to the regression case, and use it with bagging to construct regression forests of oblique trees, having hyperplane splits at the decision nodes. In a wide range of datasets, we show that the resulting forests exceed the accuracy of state-of-the-art algorithms such as random forests, AdaBoost or gradient boosting, often considerably, while yielding forests that have usually fewer and shallower trees and hence fewer parameters and faster inference overall. This result has an immense practical impact and advocates for the power of optimization in ensemble learning. | Arman Zharmagambetov, Miguel Carreira-Perpinan | null | null | 2,020 | icml |
Robust Graph Representation Learning via Neural Sparsification | null | Graph representation learning serves as the core of important prediction tasks, ranging from product recommendation to fraud detection. Real-life graphs usually have complex information in the local neighborhood, where each node is described by a rich set of features and connects to dozens or even hundreds of neighbors. Despite the success of neighborhood aggregation in graph neural networks, task-irrelevant information is mixed into nodes’ neighborhood, making learned models suffer from sub-optimal generalization performance. In this paper, we present NeuralSparse, a supervised graph sparsification technique that improves generalization power by learning to remove potentially task-irrelevant edges from input graphs. Our method takes both structural and non-structural information as input, utilizes deep neural networks to parameterize sparsification processes, and optimizes the parameters by feedback signals from downstream tasks. Under the NeuralSparse framework, supervised graph sparsification could seamlessly connect with existing graph neural networks for more robust performance. Experimental results on both benchmark and private datasets show that NeuralSparse can yield up to 7.2% improvement in testing accuracy when working with existing graph neural networks on node classification tasks. | Cheng Zheng, Bo Zong, Wei Cheng, Dongjin Song, Jingchao Ni, Wenchao Yu, Haifeng Chen, Wei Wang | null | null | 2,020 | icml |
Hybrid Stochastic-Deterministic Minibatch Proximal Gradient: Less-Than-Single-Pass Optimization with Nearly Optimal Generalization | null | Stochastic variance-reduced gradient (SVRG) algorithms have been shown to work favorably in solving large-scale learning problems. Despite the remarkable success, the stochastic gradient complexity of SVRG-type algorithms usually scales linearly with data size and thus could still be expensive for huge data. To address this deficiency, we propose a hybrid stochastic-deterministic minibatch proximal gradient (\HSDAN) algorithm for strongly-convex problems that enjoys provably improved data-size-independent complexity guarantees. More precisely, for quadratic loss $F(\wm)$ of $n$ components, we prove that \HSDAN can attain an $\epsilon$-optimization-error $\EE[F(\wm)-F(\wms)] \leq \epsilon$ within $\mathcal{O}\Big(\frac{\kappa^{1.5}\epsilon^{0.75} \log^{1.5}(\frac{1}{\epsilon}) + 1}{\epsilon} \wedge \Big(\kappa \sqrt{n} \log^{1.5}\big(\frac{1}{\epsilon}\big) + n \log \big(\frac{1}{\epsilon}\big) \Big) \Big)$ stochastic gradient evaluations, where $\kappa$ is condition number. For generic strongly convex loss functions, we prove a nearly identical complexity bound though at the cost of slightly increased logarithmic factors. For large-scale learning problems, our complexity bounds are superior to those of the prior state-of-the-art SVRG algorithms with or without dependence on data size. Particularly, in the case of $\epsilon\!=\!\mathcal{O}\big(1/\sqrt{n}\big)$ which is at the order of intrinsic excess error bound of a learning model and thus sufficient for generalization, the stochastic gradient complexity bounds of \HSDAN for quadratic and generic loss functions are respectively $\mathcal{O} (n^{0.875}\log^{1.5}(n))$ and $\mathcal{O} (n^{0.875}\log^{2.25}(n))$, which to our best knowledge, for the first time achieve optimal generalization in less than a single pass over data. Extensive numerical results demonstrate the computational advantages of our algorithm over the prior ones. | Pan Zhou, Xiao-Tong Yuan | null | null | 2,020 | icml |
Best Arm Identification for Cascading Bandits in the Fixed Confidence Setting | null | We design and analyze CascadeBAI, an algorithm for finding the best set of K items, also called an arm, within the framework of cascading bandits. An upper bound on the time complexity of CascadeBAI is derived by overcoming a crucial analytical challenge, namely, that of probabilistically estimating the amount of available feedback at each step. To do so, we define a new class of random variables (r.v.’s) which we term as left-sided sub-Gaussian r.v.’s; this class is a relaxed version of the sub-Gaussian r.v.’s. This enables the application of a sufficiently tight Bernstein-type concentration inequality. We show, through the derivation of a lower bound on the time complexity, that the performance of CascadeBAI is optimal in some practical regimes. Finally, extensive numerical simulations corroborate the efficacy of CascadeBAI as well as the tightness of our upper bound on its time complexity. | Zixin Zhong, Wang Chi Cheung, Vincent Tan | null | null | 2,020 | icml |
Bisection-Based Pricing for Repeated Contextual Auctions against Strategic Buyer | null | We are interested in learning algorithms that optimize revenue in repeated contextual posted-price auctions where a single seller faces a single strategic buyer. In our setting, the buyer maximizes his expected cumulative discounted surplus, and his valuation of a good is assumed to be a fixed function of a $d$-dimensional context (feature) vector. We introduce a novel deterministic learning algorithm that is based on ideas of the Bisection method and has strategic regret upper bound of $O(\log^2 T)$. Unlike previous works, our algorithm does not require any assumption on the distribution of context information, and the regret guarantee holds for any realization of feature vectors (adversarial upper bound). To construct our algorithm we non-trivially adopted techniques of integral geometry to act against buyer strategicness and improved the penalization trick to work in contextual auctions. | Anton Zhiyanov, Alexey Drutsa | null | null | 2,020 | icml |
Time-Consistent Self-Supervision for Semi-Supervised Learning | null | Semi-supervised learning (SSL) leverages unlabeled data when training a model with insufficient labeled data. A common strategy for SSL is to enforce the consistency of model outputs between similar samples, e.g., neighbors or data augmentations of the same sample. However, model outputs can vary dramatically on unlabeled data over different training stages, e.g., when using large learning rates. This can introduce harmful noises and inconsistent objectives over time that may lead to concept drift and catastrophic forgetting. In this paper, we study the dynamics of neural net outputs in SSL and show that selecting and using first the unlabeled samples with more consistent outputs over the course of training (i.e., "time-consistency") can improve the final test accuracy and save computation. Under the time-consistent data selection, we design an SSL objective composed of two self-supervised losses, i.e., a consistency loss between a sample and its augmentation, and a contrastive loss encouraging different samples to have different outputs. Our approach achieves SOTA on several SSL benchmarks with much fewer computations. | Tianyi Zhou, Shengjie Wang, Jeff Bilmes | null | null | 2,020 | icml |
Divide, Conquer, and Combine: a New Inference Strategy for Probabilistic Programs with Stochastic Support | null | Universal probabilistic programming systems (PPSs) provide a powerful framework for specifying rich probabilistic models. They further attempt to automate the process of drawing inferences from these models, but doing this successfully is severely hampered by the wide range of non–standard models they can express. As a result, although one can specify complex models in a universal PPS, the provided inference engines often fall far short of what is required. In particular, we show that they produce surprisingly unsatisfactory performance for models where the support varies between executions, often doing no better than importance sampling from the prior. To address this, we introduce a new inference framework: Divide, Conquer, and Combine, which remains efficient for such models, and show how it can be implemented as an automated and generic PPS inference engine. We empirically demonstrate substantial performance improvements over existing approaches on three examples. | Yuan Zhou, Hongseok Yang, Yee Whye Teh, Tom Rainforth | null | null | 2,020 | icml |
Causal Effect Estimation and Optimal Dose Suggestions in Mobile Health | null | In this article, we propose novel structural nested models to estimate causal effects of continuous treatments based on mobile health data. To find the treatment regime which optimizes the short-term outcomes for the patients, we define the weighted lag K advantage. The optimal treatment regime is then defined to be the one which maximizes this advantage. This method imposes minimal assumptions on the data generating process. Statistical inference can also be provided for the estimated parameters. Simulation studies and an application to the Ohio type 1 diabetes dataset show that our method could provide meaningful insights for dose suggestions with mobile health data. | Liangyu Zhu, Wenbin Lu, Rui Song | null | null | 2,020 | icml |
Influenza Forecasting Framework based on Gaussian Processes | null | The seasonal epidemic of influenza costs thousands of lives each year in the US. While influenza epidemics occur every year, timing and size of the epidemic vary strongly from season to season. This complicates the public health efforts to adequately respond to such epidemics. Forecasting techniques to predict the development of seasonal epidemics such as influenza, are of great help to public health decision making. Therefore, the US Center for Disease Control and Prevention (CDC) has initiated a yearly challenge to forecast influenza-like illness. Here, we propose a new framework based on Gaussian process (GP) for seasonal epidemics forecasting and demonstrate its capability on the CDC reference data on influenza like illness: our framework leads to accurate forecasts with small but reliable uncertainty estimation. We compare our framework to several state of the art benchmarks and show competitive performance. We, therefore, believe that our GP based framework for seasonal epidemics forecasting will play a key role for future influenza forecasting and, lead to further research in the area. | Christoph Zimmer, Reza Yaesoubi | null | null | 2,020 | icml |
Linear Convergence of Randomized Primal-Dual Coordinate Method for Large-scale Linear Constrained Convex Programming | null | Linear constrained convex programming has many practical applications, including support vector machine and machine learning portfolio problems. We propose the randomized primal-dual coordinate (RPDC) method, a randomized coordinate extension of the first-order primal-dual method by Cohen and Zhu, 1984 and Zhao and Zhu, 2019, to solve linear constrained convex programming. We randomly choose a block of variables based on a uniform distribution, linearize, and apply a Bregman-like function (core function) to the selected block to obtain simple parallel primal-dual decomposition. We then establish almost surely convergence and expected O(1/t) convergence rate, and expected linear convergence under global strong metric subregularity. Finally, we discuss implementation details for the randomized primal-dual coordinate approach and present numerical experiments on support vector machine and machine learning portfolio problems to verify the linear convergence. | Daoli Zhu, Lei Zhao | null | null | 2,020 | icml |
Learning Optimal Tree Models under Beam Search | null | Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable node-wise scorers, have attracted a lot of interests in tackling this challenge due to their logarithmic computational complexity in both training and testing. Tree-based deep models (TDMs) and probabilistic label trees (PLTs) are two representative kinds of them. Though achieving many practical successes, existing tree models suffer from the training-testing discrepancy, where the retrieval performance deterioration caused by beam search in testing is not considered in training. This leads to an intrinsic gap between the most relevant targets and those retrieved by beam search with even the optimally trained node-wise scorers. We take a first step towards understanding and analyzing this problem theoretically, and develop the concept of Bayes optimality under beam search and calibration under beam search as general analyzing tools for this purpose. Moreover, to eliminate the discrepancy, we propose a novel algorithm for learning optimal tree models under beam search. Experiments on both synthetic and real data verify the rationality of our theoretical analysis and demonstrate the superiority of our algorithm compared to state-of-the-art methods. | Jingwei Zhuo, Ziru Xu, Wei Dai, Han Zhu, Han Li, Jian Xu, Kun Gai | null | null | 2,020 | icml |
Variance Reduction and Quasi-Newton for Particle-Based Variational Inference | null | Particle-based Variational Inference methods (ParVIs), like Stein Variational Gradient Descent, are nonparametric variational inference methods that optimize a set of particles to best approximate a target distribution. ParVIs have been proposed as efficient approximate inference algorithms and as potential alternatives to MCMC methods. However, to our knowledge, the quality of the posterior approximation of particles from ParVIs has not been examined before for large-scale Bayesian inference problems. We conduct this analysis and evaluate the sample quality of particles produced by ParVIs, and we find that existing ParVI approaches using stochastic gradients converge insufficiently fast under sample quality metrics. We propose a novel variance reduction and quasi-Newton preconditioning framework for ParVIs, by leveraging the Riemannian structure of the Wasserstein space and advanced Riemannian optimization algorithms. Experimental results demonstrate the accelerated convergence of variance reduction and quasi-Newton methods for ParVIs for accurate posterior inference in large-scale and ill-conditioned problems. | Michael Zhu, Chang Liu, Jun Zhu | null | null | 2,020 | icml |
Learning Adversarially Robust Representations via Worst-Case Mutual Information Maximization | null | Training machine learning models that are robust against adversarial inputs poses seemingly insurmountable challenges. To better understand adversarial robustness, we consider the underlying problem of learning robust representations. We develop a notion of representation vulnerability that captures the maximum change of mutual information between the input and output distributions, under the worst-case input perturbation. Then, we prove a theorem that establishes a lower bound on the minimum adversarial risk that can be achieved for any downstream classifier based on its representation vulnerability. We propose an unsupervised learning method for obtaining intrinsically robust representations by maximizing the worst-case mutual information between the input and output distributions. Experiments on downstream classification tasks support the robustness of the representations found using unsupervised learning with our training principle. | Sicheng Zhu, Xiao Zhang, David Evans | null | null | 2,020 | icml |
A general recurrent state space framework for modeling neural dynamics during decision-making | null | An open question in systems and computational neuroscience is how neural circuits accumulate evidence towards a decision. Fitting models of decision-making theory to neural activity helps answer this question, but current approaches limit the number of these models that we can fit to neural data. Here we propose a general framework for modeling neural activity during decision-making. The framework includes the canonical drift-diffusion model and enables extensions such as multi-dimensional accumulators, variable and collapsing boundaries, and discrete jumps. Our framework is based on constraining the parameters of recurrent state space models, for which we introduce a scalable variational Laplace EM inference algorithm. We applied the modeling approach to spiking responses recorded from monkey parietal cortex during two decision-making tasks. We found that a two-dimensional accumulator better captured the responses of a set of parietal neurons than a single accumulator model, and we identified a variable lower boundary in the responses of a parietal neuron during a random dot motion task. We expect this framework will be useful for modeling neural dynamics in a variety of decision-making settings. | David Zoltowski, Jonathan Pillow, Scott Linderman | null | null | 2,020 | icml |
A New Representation of Successor Features for Transfer across Dissimilar Environments | null | Transfer in reinforcement learning is usually achieved through generalisation across tasks. Whilst many studies have investigated transferring knowledge when the reward function changes, they have assumed that the dynamics of the environments remain consistent. Many real-world RL problems require transfer among environments with different dynamics. To address this problem, we propose an approach based on successor features in which we model successor feature functions with Gaussian Processes permitting the source successor features to be treated as noisy measurements of the target successor feature function. Our theoretical analysis proves the convergence of this approach as well as the bounded error on modelling successor feature functions with Gaussian Processes in environments with both different dynamics and rewards. We demonstrate our method on benchmark datasets and show that it outperforms current baselines. | Majid Abdolshah, Hung Le, Thommen Karimpanal George, Sunil Gupta, Santu Rana, Svetha Venkatesh | null | null | 2,021 | icml |
When Demands Evolve Larger and Noisier: Learning and Earning in a Growing Environment | null | We consider a single-product dynamic pricing problem under a specific non-stationary setting, where the underlying demand process grows over time in expectation and also possibly in the level of random fluctuation. The decision maker sequentially sets price in each time period and learns the unknown demand model, with the goal of maximizing expected cumulative revenue over a time horizon $T$. We prove matching upper and lower bounds on regret and provide near-optimal pricing policies, showing how the growth rate of random fluctuation over time affects the best achievable regret order and the near-optimal policy design. In the analysis, we show that whether the seller knows the length of time horizon $T$ in advance or not surprisingly render different optimal regret orders. We then extend the demand model such that the optimal price may vary with time and present a novel and near-optimal policy for the extended model. Finally, we consider an analogous non-stationary setting in the canonical multi-armed bandit problem, and points out that knowing or not knowing the length of time horizon $T$ render the same optimal regret order, in contrast to the non-stationary dynamic pricing problem. | Feng Zhu, Zeyu Zheng | null | null | 2,020 | icml |
Massively Parallel and Asynchronous Tsetlin Machine Architecture Supporting Almost Constant-Time Scaling | null | Using logical clauses to represent patterns, Tsetlin Machine (TM) have recently obtained competitive performance in terms of accuracy, memory footprint, energy, and learning speed on several benchmarks. Each TM clause votes for or against a particular class, with classification resolved using a majority vote. While the evaluation of clauses is fast, being based on binary operators, the voting makes it necessary to synchronize the clause evaluation, impeding parallelization. In this paper, we propose a novel scheme for desynchronizing the evaluation of clauses, eliminating the voting bottleneck. In brief, every clause runs in its own thread for massive native parallelism. For each training example, we keep track of the class votes obtained from the clauses in local voting tallies. The local voting tallies allow us to detach the processing of each clause from the rest of the clauses, supporting decentralized learning. This means that the TM most of the time will operate on outdated voting tallies. We evaluated the proposed parallelization across diverse learning tasks and it turns out that our decentralized TM learning algorithm copes well with working on outdated data, resulting in no significant loss in learning accuracy. Furthermore, we show that the approach provides up to 50 times faster learning. Finally, learning time is almost constant for reasonable clause amounts (employing from 20 to 7,000 clauses on a Tesla V100 GPU). For sufficiently large clause numbers, computation time increases approximately proportionally. Our parallel and asynchronous architecture thus allows processing of more massive datasets and operating with more clauses for higher accuracy. | Kuruge Darshana Abeyrathna, Bimal Bhattarai, Morten Goodwin, Saeed Rahimi Gorji, Ole-Christoffer Granmo, Lei Jiao, Rupsa Saha, Rohan K. Yadav | null | null | 2,021 | icml |
Debiasing Model Updates for Improving Personalized Federated Training | null | We propose a novel method for federated learning that is customized specifically to the objective of a given edge device. In our proposed method, a server trains a global meta-model by collaborating with devices without actually sharing data. The trained global meta-model is then personalized locally by each device to meet its specific objective. Different from the conventional federated learning setting, training customized models for each device is hindered by both the inherent data biases of the various devices, as well as the requirements imposed by the federated architecture. We propose gradient correction methods leveraging prior works, and explicitly de-bias the meta-model in the distributed heterogeneous data setting to learn personalized device models. We present convergence guarantees of our method for strongly convex, convex and nonconvex meta objectives. We empirically evaluate the performance of our method on benchmark datasets and demonstrate significant communication savings. | Durmus Alp Emre Acar, Yue Zhao, Ruizhao Zhu, Ramon Matas, Matthew Mattina, Paul Whatmough, Venkatesh Saligrama | null | null | 2,021 | icml |
Slot Machines: Discovering Winning Combinations of Random Weights in Neural Networks | null | In contrast to traditional weight optimization in a continuous space, we demonstrate the existence of effective random networks whose weights are never updated. By selecting a weight among a fixed set of random values for each individual connection, our method uncovers combinations of random weights that match the performance of traditionally-trained networks of the same capacity. We refer to our networks as "slot machines" where each reel (connection) contains a fixed set of symbols (random values). Our backpropagation algorithm "spins" the reels to seek "winning" combinations, i.e., selections of random weight values that minimize the given loss. Quite surprisingly, we find that allocating just a few random values to each connection (e.g., 8 values per connection) yields highly competitive combinations despite being dramatically more constrained compared to traditionally learned weights. Moreover, finetuning these combinations often improves performance over the trained baselines. A randomly initialized VGG-19 with 8 values per connection contains a combination that achieves 91% test accuracy on CIFAR-10. Our method also achieves an impressive performance of 98.2% on MNIST for neural networks containing only random weights. | Maxwell M Aladago, Lorenzo Torresani | null | null | 2,021 | icml |
How Does Loss Function Affect Generalization Performance of Deep Learning? Application to Human Age Estimation | null | Good generalization performance across a wide variety of domains caused by many external and internal factors is the fundamental goal of any machine learning algorithm. This paper theoretically proves that the choice of loss function matters for improving the generalization performance of deep learning-based systems. By deriving the generalization error bound for deep neural models trained by stochastic gradient descent, we pinpoint the characteristics of the loss function that is linked to the generalization error and can therefore be used for guiding the loss function selection process. In summary, our main statement in this paper is: choose a stable loss function, generalize better. Focusing on human age estimation from the face which is a challenging topic in computer vision, we then propose a novel loss function for this learning problem. We theoretically prove that the proposed loss function achieves stronger stability, and consequently a tighter generalization error bound, compared to the other common loss functions for this problem. We have supported our findings theoretically, and demonstrated the merits of the guidance process experimentally, achieving significant improvements. | Ali Akbari, Muhammad Awais, Manijeh Bashar, Josef Kittler | null | null | 2,021 | icml |
Memory Efficient Online Meta Learning | null | We propose a novel algorithm for online meta learning where task instances are sequentially revealed with limited supervision and a learner is expected to meta learn them in each round, so as to allow the learner to customize a task-specific model rapidly with little task-level supervision. A fundamental concern arising in online meta-learning is the scalability of memory as more tasks are viewed over time. Heretofore, prior works have allowed for perfect recall leading to linear increase in memory with time. Different from prior works, in our method, prior task instances are allowed to be deleted. We propose to leverage prior task instances by means of a fixed-size state-vector, which is updated sequentially. Our theoretical analysis demonstrates that our proposed memory efficient online learning (MOML) method suffers sub-linear regret with convex loss functions and sub-linear local regret for nonconvex losses. On benchmark datasets we show that our method can outperform prior works even though they allow for perfect recall. | Durmus Alp Emre Acar, Ruizhao Zhu, Venkatesh Saligrama | null | null | 2,021 | icml |
f-Domain Adversarial Learning: Theory and Algorithms | null | Unsupervised domain adaptation is used in many machine learning applications where, during training, a model has access to unlabeled data in the target domain, and a related labeled dataset. In this paper, we introduce a novel and general domain-adversarial framework. Specifically, we derive a novel generalization bound for domain adaptation that exploits a new measure of discrepancy between distributions based on a variational characterization of f-divergences. It recovers the theoretical results from Ben-David et al. (2010a) as a special case and supports divergences used in practice. Based on this bound, we derive a new algorithmic framework that introduces a key correction in the original adversarial training method of Ganin et al. (2016). We show that many regularizers and ad-hoc objectives introduced over the last years in this framework are then not required to achieve performance comparable to (if not better than) state-of-the-art domain-adversarial methods. Experimental analysis conducted on real-world natural language and computer vision datasets show that our framework outperforms existing baselines, and obtains the best results for f-divergences that were not considered previously in domain-adversarial learning. | David Acuna, Guojun Zhang, Marc T. Law, Sanja Fidler | null | null | 2,021 | icml |
Non-Exponentially Weighted Aggregation: Regret Bounds for Unbounded Loss Functions | null | We tackle the problem of online optimization with a general, possibly unbounded, loss function. It is well known that when the loss is bounded, the exponentially weighted aggregation strategy (EWA) leads to a regret in $\sqrt{T}$ after $T$ steps. In this paper, we study a generalized aggregation strategy, where the weights no longer depend exponentially on the losses. Our strategy is based on Follow The Regularized Leader (FTRL): we minimize the expected losses plus a regularizer, that is here a $\phi$-divergence. When the regularizer is the Kullback-Leibler divergence, we obtain EWA as a special case. Using alternative divergences enables unbounded losses, at the cost of a worst regret bound in some cases. | Pierre Alquier | null | null | 2,021 | icml |
Submodular Maximization subject to a Knapsack Constraint: Combinatorial Algorithms with Near-optimal Adaptive Complexity | null | The growing need to deal with massive instances motivates the design of algorithms balancing the quality of the solution with applicability. For the latter, an important measure is the \emph{adaptive complexity}, capturing the number of sequential rounds of parallel computation needed. In this work we obtain the first \emph{constant factor} approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint with \emph{near-optimal} $O(\log n)$ adaptive complexity. Low adaptivity by itself, however, is not enough: one needs to account for the total number of function evaluations (or value queries) as well. Our algorithm asks $\tilde{O}(n^2)$ value queries, but can be modified to run with only $\tilde{O}(n)$ instead, while retaining a low adaptive complexity of $O(\log^2n)$. Besides the above improvement in adaptivity, this is also the first \emph{combinatorial} approach with sublinear adaptive complexity for the problem and yields algorithms comparable to the state-of-the-art even for the special cases of cardinality constraints or monotone objectives. Finally, we showcase our algorithms’ applicability on real-world datasets. | Georgios Amanatidis, Federico Fusco, Philip Lazos, Stefano Leonardi, Alberto Marchetti-Spaccamela, Rebecca Reiffenhäuser | null | null | 2,021 | icml |
Towards the Unification and Robustness of Perturbation and Gradient Based Explanations | null | As machine learning black boxes are increasingly being deployed in critical domains such as healthcare and criminal justice, there has been a growing emphasis on developing techniques for explaining these black boxes in a post hoc manner. In this work, we analyze two popular post hoc interpretation techniques: SmoothGrad which is a gradient based method, and a variant of LIME which is a perturbation based method. More specifically, we derive explicit closed form expressions for the explanations output by these two methods and show that they both converge to the same explanation in expectation, i.e., when the number of perturbed samples used by these methods is large. We then leverage this connection to establish other desirable properties, such as robustness, for these techniques. We also derive finite sample complexity bounds for the number of perturbations required for these methods to converge to their expected explanation. Finally, we empirically validate our theory using extensive experimentation on both synthetic and real-world datasets. | Sushant Agarwal, Shahin Jabbari, Chirag Agarwal, Sohini Upadhyay, Steven Wu, Himabindu Lakkaraju | null | null | 2,021 | icml |
Robust Pure Exploration in Linear Bandits with Limited Budget | null | We consider the pure exploration problem in the fixed-budget linear bandit setting. We provide a new algorithm that identifies the best arm with high probability while being robust to unknown levels of observation noise as well as to moderate levels of misspecification in the linear model. Our technique combines prior approaches to pure exploration in the multi-armed bandit problem with optimal experimental design algorithms to obtain both problem dependent and problem independent bounds. Our success probability is never worse than that of an algorithm that ignores the linear structure, but seamlessly takes advantage of such structure when possible. Furthermore, we only need the number of samples to scale with the dimension of the problem rather than the number of arms. We complement our theoretical results with empirical validation. | Ayya Alieva, Ashok Cutkosky, Abhimanyu Das | null | null | 2,021 | icml |
Locally Persistent Exploration in Continuous Control Tasks with Sparse Rewards | null | A major challenge in reinforcement learning is the design of exploration strategies, especially for environments with sparse reward structures and continuous state and action spaces. Intuitively, if the reinforcement signal is very scarce, the agent should rely on some form of short-term memory in order to cover its environment efficiently. We propose a new exploration method, based on two intuitions: (1) the choice of the next exploratory action should depend not only on the (Markovian) state of the environment, but also on the agent’s trajectory so far, and (2) the agent should utilize a measure of spread in the state space to avoid getting stuck in a small region. Our method leverages concepts often used in statistical physics to provide explanations for the behavior of simplified (polymer) chains in order to generate persistent (locally self-avoiding) trajectories in state space. We discuss the theoretical properties of locally self-avoiding walks and their ability to provide a kind of short-term memory through a decaying temporal correlation within the trajectory. We provide empirical evaluations of our approach in a simulated 2D navigation task, as well as higher-dimensional MuJoCo continuous control locomotion tasks with sparse rewards. | Susan Amin, Maziar Gomrokchi, Hossein Aboutalebi, Harsh Satija, Doina Precup | null | null | 2,021 | icml |
Communication-Efficient Distributed Optimization with Quantized Preconditioners | null | We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among $n$ different nodes, which can communicate using a limited number of bits. Most previous communication-efficient approaches for this problem are limited to first-order optimization, and therefore have \emph{linear} dependence on the condition number in their communication complexity. We show that this dependence is not inherent: communication-efficient methods can in fact have sublinear dependence on the condition number. For this, we design and analyze the first communication-efficient distributed variants of preconditioned gradient descent for Generalized Linear Models, and for Newton’s method. Our results rely on a new technique for quantizing both the preconditioner and the descent direction at each step of the algorithms, while controlling their convergence rate. We also validate our findings experimentally, showing faster convergence and reduced communication relative to previous methods. | Foivos Alimisis, Peter Davies, Dan Alistarh | null | null | 2,021 | icml |
A large-scale benchmark for few-shot program induction and synthesis | null | A landmark challenge for AI is to learn flexible, powerful representations from small numbers of examples. On an important class of tasks, hypotheses in the form of programs provide extreme generalization capabilities from surprisingly few examples. However, whereas large natural few-shot learning image benchmarks have spurred progress in meta-learning for deep networks, there is no comparably big, natural program-synthesis dataset that can play a similar role. This is because, whereas images are relatively easy to label from internet meta-data or annotated by non-experts, generating meaningful input-output examples for program induction has proven hard to scale. In this work, we propose a new way of leveraging unit tests and natural inputs for small programs as meaningful input-output examples for each sub-program of the overall program. This allows us to create a large-scale naturalistic few-shot program-induction benchmark and propose new challenges in this domain. The evaluation of multiple program induction and synthesis algorithms points to shortcomings of current methods and suggests multiple avenues for future work. | Ferran Alet, Javier Lopez-Contreras, James Koppel, Maxwell Nye, Armando Solar-Lezama, Tomas Lozano-Perez, Leslie Kaelbling, Joshua Tenenbaum | null | null | 2,021 | icml |
On Learnability via Gradient Method for Two-Layer ReLU Neural Networks in Teacher-Student Setting | null | Deep learning empirically achieves high performance in many applications, but its training dynamics has not been fully understood theoretically. In this paper, we explore theoretical analysis on training two-layer ReLU neural networks in a teacher-student regression model, in which a student network learns an unknown teacher network through its outputs. We show that with a specific regularization and sufficient over-parameterization, the student network can identify the parameters of the teacher network with high probability via gradient descent with a norm dependent stepsize even though the objective function is highly non-convex. The key theoretical tool is the measure representation of the neural networks and a novel application of a dual certificate argument for sparse estimation on a measure space. We analyze the global minima and global convergence property in the measure space. | Shunta Akiyama, Taiji Suzuki | null | null | 2,021 | icml |
Unitary Branching Programs: Learnability and Lower Bounds | null | Bounded width branching programs are a formalism that can be used to capture the notion of non-uniform constant-space computation. In this work, we study a generalized version of bounded width branching programs where instructions are defined by unitary matrices of bounded dimension. We introduce a new learning framework for these branching programs that leverages on a combination of local search techniques with gradient descent over Riemannian manifolds. We also show that gapped, read-once branching programs of bounded dimension can be learned with a polynomial number of queries in the presence of a teacher. Finally, we provide explicit near-quadratic size lower-bounds for bounded-dimension unitary branching programs, and exponential size lower-bounds for bounded-dimension read-once gapped unitary branching programs. The first lower bound is proven using a combination of Neciporuk’s lower bound technique with classic results from algebraic geometry. The second lower bound is proven within the framework of communication complexity theory. | Fidel Ernesto Diaz Andino, Maria Kokkou, Mateus De Oliveira Oliveira, Farhad Vadiee | null | null | 2,021 | icml |
Permutation Weighting | null | A commonly applied approach for estimating causal effects from observational data is to apply weights which render treatments independent of observed pre-treatment covariates. Recently emphasis has been placed on deriving balancing weights which explicitly target this independence condition. In this work we introduce permutation weighting, a method for estimating balancing weights using a standard binary classifier (regardless of cardinality of treatment). A large class of probabilistic classifiers may be used in this method; the choice of loss for the classifier implies the particular definition of balance. We bound bias and variance in terms of the excess risk of the classifier, show that these disappear asymptotically, and demonstrate that our classification problem directly minimizes imbalance. Additionally, hyper-parameter tuning and model selection can be performed with standard cross-validation methods. Empirical evaluations indicate that permutation weighting provides favorable performance in comparison to existing methods. | David Arbour, Drew Dimmery, Arjun Sondhi | null | null | 2,021 | icml |
Private Stochastic Convex Optimization: Optimal Rates in L1 Geometry | null | Stochastic convex optimization over an $\ell_1$-bounded domain is ubiquitous in machine learning applications such as LASSO but remains poorly understood when learning with differential privacy. We show that, up to logarithmic factors the optimal excess population loss of any $(\epsilon,\delta)$-differentially private optimizer is $\sqrt{\log(d)/n} + \sqrt{d}/\epsilon n.$ The upper bound is based on a new algorithm that combines the iterative localization approach of Feldman et al. (2020) with a new analysis of private regularized mirror descent. It applies to $\ell_p$ bounded domains for $p\in [1,2]$ and queries at most $n^{3/2}$ gradients improving over the best previously known algorithm for the $\ell_2$ case which needs $n^2$ gradients. Further, we show that when the loss functions satisfy additional smoothness assumptions, the excess loss is upper bounded (up to logarithmic factors) by $\sqrt{\log(d)/n} + (\log(d)/\epsilon n)^{2/3}.$ This bound is achieved by a new variance-reduced version of the Frank-Wolfe algorithm that requires just a single pass over the data. We also show that the lower bound in this case is the minimum of the two rates mentioned above. | Hilal Asi, Vitaly Feldman, Tomer Koren, Kunal Talwar | null | null | 2,021 | icml |
Dichotomous Optimistic Search to Quantify Human Perception | null | In this paper we address a variant of the continuous multi-armed bandits problem, called the threshold estimation problem, which is at the heart of many psychometric experiments. Here, the objective is to estimate the sensitivity threshold for an unknown psychometric function Psi, which is assumed to be non decreasing and continuous. Our algorithm, Dichotomous Optimistic Search (DOS), efficiently solves this task by taking inspiration from hierarchical multi-armed bandits and Black-box optimization. Compared to previous approaches, DOS is model free and only makes minimal assumption on Psi smoothness, while having strong theoretical guarantees that compares favorably to recent methods from both Psychophysics and Global Optimization. We also empirically evaluate DOS and show that it significantly outperforms these methods, both in experiments that mimics the conduct of a psychometric experiment, and in tests with large pulls budgets that illustrate the faster convergence rate. | Julien Audiffren | null | null | 2,021 | icml |
Asynchronous Distributed Learning : Adapting to Gradient Delays without Prior Knowledge | null | We consider stochastic convex optimization problems, where several machines act asynchronously in parallel while sharing a common memory. We propose a robust training method for the constrained setting and derive non asymptotic convergence guarantees that do not depend on prior knowledge of update delays, objective smoothness, and gradient variance. Conversely, existing methods for this setting crucially rely on this prior knowledge, which render them unsuitable for essentially all shared-resources computational environments, such as clouds and data centers. Concretely, existing approaches are unable to accommodate changes in the delays which result from dynamic allocation of the machines, while our method implicitly adapts to such changes. | Rotem Zamir Aviv, Ido Hakimi, Assaf Schuster, Kfir Yehuda Levy | null | null | 2,021 | icml |
Robust Reinforcement Learning using Least Squares Policy Iteration with Provable Performance Guarantees | null | This paper addresses the problem of model-free reinforcement learning for Robust Markov Decision Process (RMDP) with large state spaces. The goal of the RMDPs framework is to find a policy that is robust against the parameter uncertainties due to the mismatch between the simulator model and real-world settings. We first propose the Robust Least Squares Policy Evaluation algorithm, which is a multi-step online model-free learning algorithm for policy evaluation. We prove the convergence of this algorithm using stochastic approximation techniques. We then propose Robust Least Squares Policy Iteration (RLSPI) algorithm for learning the optimal robust policy. We also give a general weighted Euclidean norm bound on the error (closeness to optimality) of the resulting policy. Finally, we demonstrate the performance of our RLSPI algorithm on some benchmark problems from OpenAI Gym. | Kishan Panaganti Badrinath, Dileep Kalathil | null | null | 2,021 | icml |
Federated Learning under Arbitrary Communication Patterns | null | Federated Learning is a distributed learning setting where the goal is to train a centralized model with training data distributed over a large number of heterogeneous clients, each with unreliable and relatively slow network connections. A common optimization approach used in federated learning is based on the idea of local SGD: each client runs some number of SGD steps locally and then the updated local models are averaged to form the updated global model on the coordinating server. In this paper, we investigate the performance of an asynchronous version of local SGD wherein the clients can communicate with the server at arbitrary time intervals. Our main result shows that for smooth strongly convex and smooth nonconvex functions we achieve convergence rates that match the synchronous version that requires all clients to communicate simultaneously. | Dmitrii Avdiukhin, Shiva Kasiviswanathan | null | null | 2,021 | icml |
On the Implicit Bias of Initialization Shape: Beyond Infinitesimal Mirror Descent | null | Recent work has highlighted the role of initialization scale in determining the structure of the solutions that gradient methods converge to. In particular, it was shown that large initialization leads to the neural tangent kernel regime solution, whereas small initialization leads to so called “rich regimes”. However, the initialization structure is richer than the overall scale alone and involves relative magnitudes of different weights and layers in the network. Here we show that these relative scales, which we refer to as initialization shape, play an important role in determining the learned model. We develop a novel technique for deriving the inductive bias of gradient-flow and use it to obtain closed-form implicit regularizers for multiple cases of interest. | Shahar Azulay, Edward Moroshko, Mor Shpigel Nacson, Blake E Woodworth, Nathan Srebro, Amir Globerson, Daniel Soudry | null | null | 2,021 | icml |
On-Off Center-Surround Receptive Fields for Accurate and Robust Image Classification | null | Robustness to variations in lighting conditions is a key objective for any deep vision system. To this end, our paper extends the receptive field of convolutional neural networks with two residual components, ubiquitous in the visual processing system of vertebrates: On-center and off-center pathways, with an excitatory center and inhibitory surround; OOCS for short. The On-center pathway is excited by the presence of a light stimulus in its center, but not in its surround, whereas the Off-center pathway is excited by the absence of a light stimulus in its center, but not in its surround. We design OOCS pathways via a difference of Gaussians, with their variance computed analytically from the size of the receptive fields. OOCS pathways complement each other in their response to light stimuli, ensuring this way a strong edge-detection capability, and as a result an accurate and robust inference under challenging lighting conditions. We provide extensive empirical evidence showing that networks supplied with OOCS pathways gain accuracy and illumination-robustness from the novel edge representation, compared to other baselines. | Zahra Babaiee, Ramin Hasani, Mathias Lechner, Daniela Rus, Radu Grosu | null | null | 2,021 | icml |
Tighter Bounds on the Log Marginal Likelihood of Gaussian Process Regression Using Conjugate Gradients | null | We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model parameters by maximising our lower bound retains many benefits of the sparse variational approach while reducing the bias introduced into hyperparameter learning. The basis of our bound is a more careful analysis of the log-determinant term appearing in the log marginal likelihood, as well as using the method of conjugate gradients to derive tight lower bounds on the term involving a quadratic form. Our approach is a step forward in unifying methods relying on lower bound maximisation (e.g. variational methods) and iterative approaches based on conjugate gradients for training Gaussian processes. In experiments, we show improved predictive performance with our model for a comparable amount of training time compared to other conjugate gradient based approaches. | Artem Artemev, David R. Burt, Mark van der Wilk | null | null | 2,021 | icml |
Skill Discovery for Exploration and Planning using Deep Skill Graphs | null | We introduce a new skill-discovery algorithm that builds a discrete graph representation of large continuous MDPs, where nodes correspond to skill subgoals and the edges to skill policies. The agent constructs this graph during an unsupervised training phase where it interleaves discovering skills and planning using them to gain coverage over ever-increasing portions of the state-space. Given a novel goal at test time, the agent plans with the acquired skill graph to reach a nearby state, then switches to learning to reach the goal. We show that the resulting algorithm, Deep Skill Graphs, outperforms both flat and existing hierarchical reinforcement learning methods on four difficult continuous control tasks. | Akhil Bagaria, Jason K Senthil, George Konidaris | null | null | 2,021 | icml |
Locally Adaptive Label Smoothing Improves Predictive Churn | null | Training modern neural networks is an inherently noisy process that can lead to high \emph{prediction churn}– disagreements between re-trainings of the same model due to factors such as randomization in the parameter initialization and mini-batches– even when the trained models all attain similar accuracies. Such prediction churn can be very undesirable in practice. In this paper, we present several baselines for reducing churn and show that training on soft labels obtained by adaptively smoothing each example’s label based on the example’s neighboring labels often outperforms the baselines on churn while improving accuracy on a variety of benchmark classification tasks and model architectures. | Dara Bahri, Heinrich Jiang | null | null | 2,021 | icml |
Don’t Just Blame Over-parametrization for Over-confidence: Theoretical Analysis of Calibration in Binary Classification | null | Modern machine learning models with high accuracy are often miscalibrated—the predicted top probability does not reflect the actual accuracy, and tends to be \emph{over-confident}. It is commonly believed that such over-confidence is mainly due to \emph{over-parametrization}, in particular when the model is large enough to memorize the training data and maximize the confidence. In this paper, we show theoretically that over-parametrization is not the only reason for over-confidence. We prove that \emph{logistic regression is inherently over-confident}, in the realizable, under-parametrized setting where the data is generated from the logistic model, and the sample size is much larger than the number of parameters. Further, this over-confidence happens for general well-specified binary classification problems as long as the activation is symmetric and concave on the positive part. Perhaps surprisingly, we also show that over-confidence is not always the case—there exists another activation function (and a suitable loss function) under which the learned classifier is \emph{under-confident} at some probability values. Overall, our theory provides a precise characterization of calibration in realizable binary classification, which we verify on simulations and real data experiments. | Yu Bai, Song Mei, Huan Wang, Caiming Xiong | null | null | 2,021 | icml |
Augmented World Models Facilitate Zero-Shot Dynamics Generalization From a Single Offline Environment | null | Reinforcement learning from large-scale offline datasets provides us with the ability to learn policies without potentially unsafe or impractical exploration. Significant progress has been made in the past few years in dealing with the challenge of correcting for differing behavior between the data collection and learned policies. However, little attention has been paid to potentially changing dynamics when transferring a policy to the online setting, where performance can be up to 90% reduced for existing methods. In this paper we address this problem with Augmented World Models (AugWM). We augment a learned dynamics model with simple transformations that seek to capture potential changes in physical properties of the robot, leading to more robust policies. We not only train our policy in this new setting, but also provide it with the sampled augmentation as a context, allowing it to adapt to changes in the environment. At test time we learn the context in a self-supervised fashion by approximating the augmentation which corresponds to the new environment. We rigorously evaluate our approach on over 100 different changed dynamics settings, and show that this simple approach can significantly improve the zero-shot generalization of a recent state-of-the-art baseline, often achieving successful policies where the baseline fails. | Philip J Ball, Cong Lu, Jack Parker-Holder, Stephen Roberts | null | null | 2,021 | icml |
Principled Exploration via Optimistic Bootstrapping and Backward Induction | null | One principled approach for provably efficient exploration is incorporating the upper confidence bound (UCB) into the value function as a bonus. However, UCB is specified to deal with linear and tabular settings and is incompatible with Deep Reinforcement Learning (DRL). In this paper, we propose a principled exploration method for DRL through Optimistic Bootstrapping and Backward Induction (OB2I). OB2I constructs a general-purpose UCB-bonus through non-parametric bootstrap in DRL. The UCB-bonus estimates the epistemic uncertainty of state-action pairs for optimistic exploration. We build theoretical connections between the proposed UCB-bonus and the LSVI-UCB in linear setting. We propagate future uncertainty in a time-consistent manner through episodic backward update, which exploits the theoretical advantage and empirically improves the sample-efficiency. Our experiments in MNIST maze and Atari suit suggest that OB2I outperforms several state-of-the-art exploration approaches. | Chenjia Bai, Lingxiao Wang, Lei Han, Jianye Hao, Animesh Garg, Peng Liu, Zhaoran Wang | null | null | 2,021 | icml |
Approximating a Distribution Using Weight Queries | null | We consider a novel challenge: approximating a distribution without the ability to randomly sample from that distribution. We study how such an approximation can be obtained using *weight queries*. Given some data set of examples, a weight query presents one of the examples to an oracle, which returns the probability, according to the target distribution, of observing examples similar to the presented example. This oracle can represent, for instance, counting queries to a database of the target population, or an interface to a search engine which returns the number of results that match a given search. We propose an interactive algorithm that iteratively selects data set examples and performs corresponding weight queries. The algorithm finds a reweighting of the data set that approximates the weights according to the target distribution, using a limited number of weight queries. We derive an approximation bound on the total variation distance between the reweighting found by the algorithm and the best achievable reweighting. Our algorithm takes inspiration from the UCB approach common in multi-armed bandits problems, and combines it with a new discrepancy estimator and a greedy iterative procedure. In addition to our theoretical guarantees, we demonstrate in experiments the advantages of the proposed algorithm over several baselines. A python implementation of the proposed algorithm and of all the experiments can be found at https://github.com/Nadav-Barak/AWP. | Nadav Barak, Sivan Sabato | null | null | 2,021 | icml |
Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Models | null | This paper presents new estimates of the score function and its gradient with respect to the model parameters in a general energy-based latent variable model (EBLVM). The score function and its gradient can be expressed as combinations of expectation and covariance terms over the (generally intractable) posterior of the latent variables. New estimates are obtained by introducing a variational posterior to approximate the true posterior in these terms. The variational posterior is trained to minimize a certain divergence (e.g., the KL divergence) between itself and the true posterior. Theoretically, the divergence characterizes upper bounds of the bias of the estimates. In principle, our estimates can be applied to a wide range of objectives, including kernelized Stein discrepancy (KSD), score matching (SM)-based methods and exact Fisher divergence with a minimal model assumption. In particular, these estimates applied to SM-based methods outperform existing methods in learning EBLVMs on several image datasets. | Fan Bao, Kun Xu, Chongxuan Li, Lanqing Hong, Jun Zhu, Bo Zhang | null | null | 2,021 | icml |
Training Quantized Neural Networks to Global Optimality via Semidefinite Programming | null | Neural networks (NNs) have been extremely successful across many tasks in machine learning. Quantization of NN weights has become an important topic due to its impact on their energy efficiency, inference time and deployment on hardware. Although post-training quantization is well-studied, training optimal quantized NNs involves combinatorial non-convex optimization problems which appear intractable. In this work, we introduce a convex optimization strategy to train quantized NNs with polynomial activations. Our method leverages hidden convexity in two-layer neural networks from the recent literature, semidefinite lifting, and Grothendieck’s identity. Surprisingly, we show that certain quantized NN problems can be solved to global optimality provably in polynomial time in all relevant parameters via tight semidefinite relaxations. We present numerical examples to illustrate the effectiveness of our method. | Burak Bartan, Mert Pilanci | null | null | 2,021 | icml |
Learning Queueing Policies for Organ Transplantation Allocation using Interpretable Counterfactual Survival Analysis | null | Organ transplantation is often the last resort for treating end-stage illnesses, but managing transplant wait-lists is challenging because of organ scarcity and the complexity of assessing donor-recipient compatibility. In this paper, we develop a data-driven model for (real-time) organ allocation using observational data for transplant outcomes. Our model integrates a queuing-theoretic framework with unsupervised learning to cluster the organs into “organ types”, and then construct priority queues (associated with each organ type) wherein incoming patients are assigned. To reason about organ allocations, the model uses synthetic controls to infer a patient’s survival outcomes under counterfactual allocations to the different organ types{–} the model is trained end-to-end to optimise the trade-off between patient waiting time and expected survival time. The usage of synthetic controls enable patient-level interpretations of allocation decisions that can be presented and understood by clinicians. We test our model on multiple data sets, and show that it outperforms other organ-allocation policies in terms of added life-years, and death count. Furthermore, we introduce a novel organ-allocation simulator to accurately test new policies. | Jeroen Berrevoets, Ahmed Alaa, Zhaozhi Qian, James Jordon, Alexander E. S. Gimson, Mihaela van der Schaar | null | null | 2,021 | icml |
Is Space-Time Attention All You Need for Video Understanding? | null | We present a convolution-free approach to video classification built exclusively on self-attention over space and time. Our method, named “TimeSformer,” adapts the standard Transformer architecture to video by enabling spatiotemporal feature learning directly from a sequence of frame-level patches. Our experimental study compares different self-attention schemes and suggests that “divided attention,” where temporal attention and spatial attention are separately applied within each block, leads to the best video classification accuracy among the design choices considered. Despite the radically new design, TimeSformer achieves state-of-the-art results on several action recognition benchmarks, including the best reported accuracy on Kinetics-400 and Kinetics-600. Finally, compared to 3D convolutional networks, our model is faster to train, it can achieve dramatically higher test efficiency (at a small drop in accuracy), and it can also be applied to much longer video clips (over one minute long). Code and models are available at: https://github.com/facebookresearch/TimeSformer. | Gedas Bertasius, Heng Wang, Lorenzo Torresani | null | null | 2,021 | icml |
Learning from Biased Data: A Semi-Parametric Approach | null | We consider risk minimization problems where the (source) distribution $P_S$ of the training observations $Z_1, \ldots, Z_n$ differs from the (target) distribution $P_T$ involved in the risk that one seeks to minimize. Under the natural assumption that $P_S$ dominates $P_T$, \textit{i.e.} $P_T< \! \!
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BibTeX
@InProceedings{pmlr-v139-bertail21a,
title = {Learning from Biased Data: A Semi-Parametric Approach},
author = {Bertail, Patrice and Cl{\'e}men{\c{c}}on, Stephan and Guyonvarch, Yannick and Noiry, Nathan},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {803--812},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/bertail21a/bertail21a.pdf},
url = {https://proceedings.mlr.press/v139/bertail21a.html},
abstract = {We consider risk minimization problems where the (source) distribution $P_S$ of the training observations $Z_1, \ldots, Z_n$ differs from the (target) distribution $P_T$ involved in the risk that one seeks to minimize. Under the natural assumption that $P_S$ dominates $P_T$, \textit{i.e.} $P_T< \! \!
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%0 Conference Paper
%T Learning from Biased Data: A Semi-Parametric Approach
%A Patrice Bertail
%A Stephan Clémençon
%A Yannick Guyonvarch
%A Nathan Noiry
%B Proceedings of the 38th International Conference on Machine Learning
%C Proceedings of Machine Learning Research
%D 2021
%E Marina Meila
%E Tong Zhang
%F pmlr-v139-bertail21a
%I PMLR
%P 803--812
%U https://proceedings.mlr.press/v139/bertail21a.html
%V 139
%X We consider risk minimization problems where the (source) distribution $P_S$ of the training observations $Z_1, \ldots, Z_n$ differs from the (target) distribution $P_T$ involved in the risk that one seeks to minimize. Under the natural assumption that $P_S$ dominates $P_T$, \textit{i.e.} $P_T< \! \!
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APA
Bertail, P., Clémençon, S., Guyonvarch, Y. & Noiry, N.. (2021). Learning from Biased Data: A Semi-Parametric Approach. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:803-812 Available from https://proceedings.mlr.press/v139/bertail21a.html.
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Supplementary ZIP | Patrice Bertail, Stephan Clémençon, Yannick Guyonvarch, Nathan Noiry | null | null | 2,021 | icml |
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Additive Error Guarantees for Weighted Low Rank Approximation | null | Low-rank approximation is a classic tool in data analysis, where the goal is to approximate a matrix $A$ with a low-rank matrix $L$ so as to minimize the error $\norm{A - L}_F^2$. However in many applications, approximating some entries is more important than others, which leads to the weighted low rank approximation problem. However, the addition of weights makes the low-rank approximation problem intractable. Thus many works have obtained efficient algorithms under additional structural assumptions on the weight matrix (such as low rank, and appropriate block structure). We study a natural greedy algorithm for weighted low rank approximation and develop a simple condition under which it yields bi-criteria approximation up to a small additive factor in the error. The algorithm involves iteratively computing the top singular vector of an appropriately varying matrix, and is thus easy to implement at scale. Our methods also allow us to study the problem of low rank approximation under $\ell_p$ norm error. | Aditya Bhaskara, Aravinda Kanchana Ruwanpathirana, Maheshakya Wijewardena | null | null | 2,021 | icml |
Neural Symbolic Regression that scales | null | Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed strategies that do not improve with experience. In this paper, we introduce the first symbolic regression method that leverages large scale pre-training. We procedurally generate an unbounded set of equations, and simultaneously pre-train a Transformer to predict the symbolic equation from a corresponding set of input-output-pairs. At test time, we query the model on a new set of points and use its output to guide the search for the equation. We show empirically that this approach can re-discover a set of well-known physical equations, and that it improves over time with more data and compute. | Luca Biggio, Tommaso Bendinelli, Alexander Neitz, Aurelien Lucchi, Giambattista Parascandolo | null | null | 2,021 | icml |
Online Learning for Load Balancing of Unknown Monotone Resource Allocation Games | null | Consider N players that each uses a mixture of K resources. Each of the players’ reward functions includes a linear pricing term for each resource that is controlled by the game manager. We assume that the game is strongly monotone, so if each player runs gradient descent, the dynamics converge to a unique Nash equilibrium (NE). Unfortunately, this NE can be inefficient since the total load on a given resource can be very high. In principle, we can control the total loads by tuning the coefficients of the pricing terms. However, finding pricing coefficients that balance the loads requires knowing the players’ reward functions and their action sets. Obtaining this game structure information is infeasible in a large-scale network and violates the users’ privacy. To overcome this, we propose a simple algorithm that learns to shift the NE of the game to meet the total load constraints by adjusting the pricing coefficients in an online manner. Our algorithm only requires the total load per resource as feedback and does not need to know the reward functions or the action sets. We prove that our algorithm guarantees convergence in L2 to a NE that meets target total load constraints. Simulations show the effectiveness of our approach when applied to smart grid demand-side management or power control in wireless networks. | Ilai Bistritz, Nicholas Bambos | null | null | 2,021 | icml |
Beyond $log^2(T)$ regret for decentralized bandits in matching markets | null | We design decentralized algorithms for regret minimization in the two sided matching market with one-sided bandit feedback that significantly improves upon the prior works (Liu et al.\,2020a, Sankararaman et al.\,2020, Liu et al.\,2020b). First, for general markets, for any $\varepsilon > 0$, we design an algorithm that achieves a $O(\log^{1+\varepsilon}(T))$ regret to the agent-optimal stable matching, with unknown time horizon $T$, improving upon the $O(\log^{2}(T))$ regret achieved in (Liu et al.\,2020b). Second, we provide the optimal $\Theta(\log(T))$ agent-optimal regret for markets satisfying {\em uniqueness consistency} – markets where leaving participants don’t alter the original stable matching. Previously, $\Theta(\log(T))$ regret was achievable (Sankararaman et al.\,2020, Liu et al.\,2020b) in the much restricted {\em serial dictatorship} setting, when all arms have the same preference over the agents. We propose a phase based algorithm, where in each phase, besides deleting the globally communicated dominated arms the agents locally delete arms with which they collide often. This \emph{local deletion} is pivotal in breaking deadlocks arising from rank heterogeneity of agents across arms. We further demonstrate superiority of our algorithm over existing works through simulations. | Soumya Basu, Karthik Abinav Sankararaman, Abishek Sankararaman | null | null | 2,021 | icml |
Lower Bounds on Cross-Entropy Loss in the Presence of Test-time Adversaries | null | Understanding the fundamental limits of robust supervised learning has emerged as a problem of immense interest, from both practical and theoretical standpoints. In particular, it is critical to determine classifier-agnostic bounds on the training loss to establish when learning is possible. In this paper, we determine optimal lower bounds on the cross-entropy loss in the presence of test-time adversaries, along with the corresponding optimal classification outputs. Our formulation of the bound as a solution to an optimization problem is general enough to encompass any loss function depending on soft classifier outputs. We also propose and provide a proof of correctness for a bespoke algorithm to compute this lower bound efficiently, allowing us to determine lower bounds for multiple practical datasets of interest. We use our lower bounds as a diagnostic tool to determine the effectiveness of current robust training methods and find a gap from optimality at larger budgets. Finally, we investigate the possibility of using of optimal classification outputs as soft labels to empirically improve robust training. | Arjun Nitin Bhagoji, Daniel Cullina, Vikash Sehwag, Prateek Mittal | null | null | 2,021 | icml |
Low-Precision Reinforcement Learning: Running Soft Actor-Critic in Half Precision | null | Low-precision training has become a popular approach to reduce compute requirements, memory footprint, and energy consumption in supervised learning. In contrast, this promising approach has not yet enjoyed similarly widespread adoption within the reinforcement learning (RL) community, partly because RL agents can be notoriously hard to train even in full precision. In this paper we consider continuous control with the state-of-the-art SAC agent and demonstrate that a naïve adaptation of low-precision methods from supervised learning fails. We propose a set of six modifications, all straightforward to implement, that leaves the underlying agent and its hyperparameters unchanged but improves the numerical stability dramatically. The resulting modified SAC agent has lower memory and compute requirements while matching full-precision rewards, demonstrating that low-precision training can substantially accelerate state-of-the-art RL without parameter tuning. | Johan Björck, Xiangyu Chen, Christopher De Sa, Carla P Gomes, Kilian Weinberger | null | null | 2,021 | icml |
Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks | null | The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive power of such schemes was proven to be limited. To overcome these limitations, we propose Message Passing Simplicial Networks (MPSNs), a class of models that perform message passing on simplicial complexes (SCs). To theoretically analyse the expressivity of our model we introduce a Simplicial Weisfeiler-Lehman (SWL) colouring procedure for distinguishing non-isomorphic SCs. We relate the power of SWL to the problem of distinguishing non-isomorphic graphs and show that SWL and MPSNs are strictly more powerful than the WL test and not less powerful than the 3-WL test. We deepen the analysis by comparing our model with traditional graph neural networks (GNNs) with ReLU activations in terms of the number of linear regions of the functions they can represent. We empirically support our theoretical claims by showing that MPSNs can distinguish challenging strongly regular graphs for which GNNs fail and, when equipped with orientation equivariant layers, they can improve classification accuracy in oriented SCs compared to a GNN baseline. | Cristian Bodnar, Fabrizio Frasca, Yuguang Wang, Nina Otter, Guido F Montufar, Pietro Lió, Michael Bronstein | null | null | 2,021 | icml |
One for One, or All for All: Equilibria and Optimality of Collaboration in Federated Learning | null | In recent years, federated learning has been embraced as an approach for bringing about collaboration across large populations of learning agents. However, little is known about how collaboration protocols should take agents’ incentives into account when allocating individual resources for communal learning in order to maintain such collaborations. Inspired by game theoretic notions, this paper introduces a framework for incentive-aware learning and data sharing in federated learning. Our stable and envy-free equilibria capture notions of collaboration in the presence of agents interested in meeting their learning objectives while keeping their own sample collection burden low. For example, in an envy-free equilibrium, no agent would wish to swap their sampling burden with any other agent and in a stable equilibrium, no agent would wish to unilaterally reduce their sampling burden. In addition to formalizing this framework, our contributions include characterizing the structural properties of such equilibria, proving when they exist, and showing how they can be computed. Furthermore, we compare the sample complexity of incentive-aware collaboration with that of optimal collaboration when one ignores agents’ incentives. | Avrim Blum, Nika Haghtalab, Richard Lanas Phillips, Han Shao | null | null | 2,021 | icml |
Evaluating the Implicit Midpoint Integrator for Riemannian Hamiltonian Monte Carlo | null | Riemannian manifold Hamiltonian Monte Carlo is traditionally carried out using the generalized leapfrog integrator. However, this integrator is not the only choice and other integrators yielding valid Markov chain transition operators may be considered. In this work, we examine the implicit midpoint integrator as an alternative to the generalized leapfrog integrator. We discuss advantages and disadvantages of the implicit midpoint integrator for Hamiltonian Monte Carlo, its theoretical properties, and an empirical assessment of the critical attributes of such an integrator for Hamiltonian Monte Carlo: energy conservation, volume preservation, and reversibility. Empirically, we find that while leapfrog iterations are faster, the implicit midpoint integrator has better energy conservation, leading to higher acceptance rates, as well as better conservation of volume and better reversibility, arguably yielding a more accurate sampling procedure. | James Brofos, Roy R Lederman | null | null | 2,021 | icml |
The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning | null | In this work we develop a quantum field theory formalism for deep learning, where input signals are encoded in Gaussian states, a generalization of Gaussian processes which encode the agent’s uncertainty about the input signal. We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles, dubbed “Hintons”. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing, and provides quantum deformations of neural networks that can be run efficiently on those devices. Finally, we discuss a semi-classical limit of the quantum deformed models which is amenable to classical simulation. | Roberto Bondesan, Max Welling | null | null | 2,021 | icml |
Reinforcement Learning of Implicit and Explicit Control Flow Instructions | null | Learning to flexibly follow task instructions in dynamic environments poses interesting challenges for reinforcement learning agents. We focus here on the problem of learning control flow that deviates from a strict step-by-step execution of instructions{—}that is, control flow that may skip forward over parts of the instructions or return backward to previously completed or skipped steps. Demand for such flexible control arises in two fundamental ways: explicitly when control is specified in the instructions themselves (such as conditional branching and looping) and implicitly when stochastic environment dynamics require re-completion of instructions whose effects have been perturbed, or opportunistic skipping of instructions whose effects are already present. We formulate an attention-based architecture that meets these challenges by learning, from task reward only, to flexibly attend to and condition behavior on an internal encoding of the instructions. We test the architecture’s ability to learn both explicit and implicit control in two illustrative domains—one inspired by Minecraft and the other by StarCraft—and show that the architecture exhibits zero-shot generalization to novel instructions of length greater than those in a training set, at a performance level unmatched by three baseline recurrent architectures and one ablation architecture. | Ethan Brooks, Janarthanan Rajendran, Richard L Lewis, Satinder Singh | null | null | 2,021 | icml |
Narrow Margins: Classification, Margins and Fat Tails | null | It is well-known that, for separable data, the regularised two-class logistic regression or support vector machine re-normalised estimate converges to the maximal margin classifier as the regularisation hyper-parameter $\lambda$ goes to 0. The fact that different loss functions may lead to the same solution is of theoretical and practical relevance as margin maximisation allows more straightforward considerations in terms of generalisation and geometric interpretation. We investigate the case where this convergence property is not guaranteed to hold and show that it can be fully characterised by the distribution of error terms in the latent variable interpretation of linear classifiers. In particular, if errors follow a regularly varying distribution, then the regularised and re-normalised estimate does not converge to the maximal margin classifier. This shows that classification with fat tails has a qualitatively different behaviour, which should be taken into account when considering real-life data. | Francois Buet-Golfouse | null | null | 2,021 | icml |
Disambiguation of Weak Supervision leading to Exponential Convergence rates | null | Machine learning approached through supervised learning requires expensive annotation of data. This motivates weakly supervised learning, where data are annotated with incomplete yet discriminative information. In this paper, we focus on partial labelling, an instance of weak supervision where, from a given input, we are given a set of potential targets. We review a disambiguation principle to recover full supervision from weak supervision, and propose an empirical disambiguation algorithm. We prove exponential convergence rates of our algorithm under classical learnability assumptions, and we illustrate the usefulness of our method on practical examples. | Vivien A Cabannnes, Francis Bach, Alessandro Rudi | null | null | 2,021 | icml |
Model-Free and Model-Based Policy Evaluation when Causality is Uncertain | null | When decision-makers can directly intervene, policy evaluation algorithms give valid causal estimates. In off-policy evaluation (OPE), there may exist unobserved variables that both impact the dynamics and are used by the unknown behavior policy. These “confounders” will introduce spurious correlations and naive estimates for a new policy will be biased. We develop worst-case bounds to assess sensitivity to these unobserved confounders in finite horizons when confounders are drawn iid each period. We demonstrate that a model-based approach with robust MDPs gives sharper lower bounds by exploiting domain knowledge about the dynamics. Finally, we show that when unobserved confounders are persistent over time, OPE is far more difficult and existing techniques produce extremely conservative bounds. | David A Bruns-Smith | null | null | 2,021 | icml |
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