The budgeted information gathering problem - where a robot with a fixed fuel budget is required to maximize the amount of information gathered from the world - appears in practice across a wide range of applications in autonomous exploration and inspection with mobile robots. Although there is an extensive amount of prior work investigating effective approximations of the problem, these methods do not address the fact that their performance is heavily dependent on distribution of objects in the world. In this paper, we attempt to address this issue by proposing a novel data-driven imitation learning framework. We present an efficient algorithm, EXPLORE, that trains a policy on the target distribution to imitate a clairvoyant oracle - an oracle that has full information about the world and computes non-myopic solutions to maximize information gathered. We validate the approach on a spectrum of results on a number of 2D and 3D exploration problems that demonstrates the ability of EXPLORE to adapt to different object distributions. Additionally, our analysis provides theoretical insight into the behavior of EXPLORE. Our approach paves the way forward for efficiently applying data-driven methods to the domain of information gathering.
@cite_18: We consider the Bayesian active learning and experimental design problem, where the goal is to learn the value of some unknown target variable through a sequence of informative, noisy tests. In contrast to prior work, we focus on the challenging, yet practically relevant setting where test outcomes can be conditionally dependent given the hidden target variable. Under such assumptions, common heuristics, such as greedily performing tests that maximize the reduction in uncertainty of the target, often perform poorly. In this paper, we propose ECED, a novel, computationally efficient active learning algorithm, and prove strong theoretical guarantees that hold with correlated, noisy tests. Rather than directly optimizing the prediction error, at each step, ECED picks the test that maximizes the gain in a surrogate objective, which takes into account the dependencies between tests. Our analysis relies on an information-theoretic auxiliary function to track the progress of ECED, and utilizes adaptive submodularity to attain the near-optimal bound. We demonstrate strong empirical performance of ECED on two problem instances, including a Bayesian experimental design task intended to distinguish among economic theories of how people make risky decisions, and an active preference learning task via pairwise comparisons.
@cite_26: Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse AI applications including management of sensing resources, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations.
@cite_22: Many robotic path planning applications, such as search and rescue, involve uncertain environments with complex dynamics that can be only partially observed. When selecting the best subset of observation locations subject to constrained resources (such as limited time or battery capacity) it is an important problem to trade off exploration (gathering information about the environment) and exploitation (using the current knowledge about the environment most effectively) for efficiently observing these environments. Even the nonadaptive setting, where paths are planned before observations are made, is NP-hard, and has been subject to much research. In this paper, we present a novel approach to adaptive informative path planning that addresses this exploration-exploitation tradeoff. Our approach is nonmyopic, i.e. it plans ahead for possible observations that can be made in the future. We quantify the benefit of exploration through the adaptivity gap'' between an adaptive and a nonadaptive algorithm in terms of the uncertainty in the environment. Exploiting the submodularity (a diminishing returns property) and locality properties of the objective function, we develop an algorithm that performs provably near-optimally in settings where the adaptivity gap is small. In case of large gap, we use an objective function that simultaneously optimizes paths for exploration and exploitation. We also provide an algorithm to extend any single robot algorithm for adaptive informative path planning to the multi-robot setting while approximately preserving the theoretical guarantee of the single robot algorithm. We extensively evaluate our approach on a domain and a scientific monitoring problem using a real robotic system.
@cite_10: 
@cite_9: We discuss the problem in which an autonomous vehicle must classify an object based on multiple views. We focus on the active classification setting, where the vehicle controls which views to select to best perform the classification. The problem is formulated as an extension to Bayesian active learning, and we show connections to recent theoretical guarantees in this area. We formally analyze the benefit of acting adaptively as new information becomes available. The analysis leads to a probabilistic algorithm for determining the best views to observe based on information theoretic costs. We validate our approach in two ways, both related to underwater inspection: 3D polyhedra recognition in synthetic depth maps and ship hull inspection with imaging sonar. These tasks encompass both the planning and recognition aspects of the active classification problem. The results demonstrate that actively planning for informative views can reduce the number of necessary views by up to 80 when compared to passive methods.
@cite_21: We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of m possible diseases, each test having a cost, and the a-priori likelihood of the patient having any particular disease, what is a good adaptive strategy to perform these tests to minimize the expected cost to identify the disease? We settle the approximability of this problem by giving a tight O(logm)-approximation algorithm. We also consider a more substantial generalization, the Adaptive TSP problem, which can be used to model switching costs between tests in the optimal decision tree problem. Given an underlying metric space, a random subset S of cities is drawn from a known distribution, but S is initially unknown to us--we get information about whether any city is in S only when we visit the city in question. What is a good adaptive way of visiting all the cities in the random subset S while minimizing the expected distance traveled? For this adaptive TSP problem, we give the first poly-logarithmic approximation, and show that this algorithm is best possible unless we can improve the approximation guarantees for the well-known group Steiner tree problem.
@cite_1: 
@cite_32: 
@cite_6: In contrast to classic geometric motion planning, informative path planning IPP seeks a path for a robot to sense the world and gain information. In adaptive IPP, the robot chooses the next sensing location conditioned on all information acquired so far, and the robot's goal is to minimize the travel cost required for identifying a true hypothesis. Adaptive IPP is NP-hard, because the robot must trade-off information gain and travel cost optimally. In this paper we present Recursive Adaptive Identification RAId, a new polynomial-time approximation algorithm for adaptive IPP. We prove a polylogarithmic approximation bound when the robot travels in a metric space. Furthermore, our experiments suggest that RAId is practical and provides good approximate solutions for two distinct robot planning tasks. Although RAId is designed primarily for noiseless observations, a simple extension allows it to handle some tasks with noisy observations.
@cite_2: Adaptive stochastic optimization (ASO) optimizes an objective function adaptively under uncertainty. It plays a crucial role in planning and learning under uncertainty, but is, unfortunately, computationally intractable in general. This paper introduces two conditions on the objective function, the marginal likelihood rate bound and the marginal likelihood bound, which, together with pointwise submodularity, enable efficient approximate solution of ASO. Several interesting classes of functions satisfy these conditions naturally, e.g., the version space reduction function for hypothesis learning. We describe Recursive Adaptive Coverage, a new ASO algorithm that exploits these conditions, and apply the algorithm to two robot planning tasks under uncertainty. In contrast to the earlier submodular optimization approach, our algorithm applies to ASO over both sets and paths.
@cite_5: 
@cite_13: We tackle the fundamental problem of Bayesian active learning with noise, where we need to adaptively select from a number of expensive tests in order to identify an unknown hypothesis sampled from a known prior distribution. In the case of noise-free observations, a greedy algorithm called generalized binary search (GBS) is known to perform near-optimally. We show that if the observations are noisy, perhaps surprisingly, GBS can perform very poorly. We develop EC2, a novel, greedy active learning algorithm and prove that it is competitive with the optimal policy, thus obtaining the first competitiveness guarantees for Bayesian active learning with noisy observations. Our bounds rely on a recently discovered diminishing returns property called adaptive submodularity, generalizing the classical notion of submodular set functions to adaptive policies. Our results hold even if the tests have non-uniform cost and their noise is correlated. We also propose EffECXtive, a particularly fast approximation of EC2, and evaluate it on a Bayesian experimental design problem involving human subjects, intended to tease apart competing economic theories of how people make decisions under uncertainty.
@cite_20: In this paper, we propose a novel and computationally efficient algorithm for simultaneous exploration and coverage with a vision-guided micro aerial vehicle (MAV) in unknown environments. This algorithm continually plans a path that allows the MAV to fulfil two objectives at the same time while avoiding obstacles: observe as much unexplored space as possible, and observe as much of the surface of the environment as possible given viewing angle and distance constraints. The former and latter objectives are known as the exploration and coverage problems respectively. Our algorithm is particularly useful for automated 3D reconstruction at the street level and in indoor environments where obstacles are omnipresent. By solving the exploration problem, we maximize the size of the reconstructed model. By solving the coverage problem, we maximize the completeness of the model. Our algorithm leverages the state lattice concept such that the planned path adheres to specified motion constraints. Furthermore, our algorithm is computationally efficient and able to run on-board the MAV in real-time. We assume that the MAV is equipped with a forward-looking depth-sensing camera in the form of either a stereo camera or RGB-D camera. We use simulation experiments to validate our algorithm. In addition, we show that our algorithm achieves a significantly higher level of coverage as compared to an exploration-only approach while still allowing the MAV to fully explore the environment.
@cite_11: We consider the problem of next-best view selection for volumetric reconstruction of an object by a mobile robot equipped with a camera. Based on a probabilistic volumetric map that is built in real time, the robot can quantify the expected information gain from a set of discrete candidate views. We propose and evaluate several formulations to quantify this information gain for the volumetric reconstruction task, including visibility likelihood and the likelihood of seeing new parts of the object. These metrics are combined with the cost of robot movement in utility functions. The next best view is selected by optimizing these functions, aiming to maximize the likelihood of discovering new parts of the object. We evaluate the functions with simulated and real world experiments within a modular software system that is adaptable to other robotic platforms and reconstruction problems. We release our implementation open source.
Problem in the absence of the travel cost constraint can be efficiently solved using the framework of adaptive submodularity developed by Golovin al @cite_26 @cite_13 as shown by Javdani al @cite_1 @cite_5 and Chen al @cite_10 @cite_18 . Hollinger al @cite_32 @cite_9 propose a heuristic based approach to select a subset of informative nodes and perform minimum cost tours. Singh al @cite_22 replan every step using a non-adaptive information path planning algorithm. Such methods suffer when the adaptivity gap is large @cite_32 . Inspired by adaptive TSP approaches by Gupta al @cite_21 , Lim al @cite_6 @cite_2 propose recursive coverage algorithms to learn policy trees. However such methods cannot scale well to large state and observation spaces. Heng al @cite_20 make a modular approximation of the objective function. Isler al @cite_11 survey a broad number of myopic information gain based heuristics that work well in practice but have no formal guarantees.