Dealing with Partially Observable Markov Decision Processes is notably a challenging task. We face an average-reward infinite-horizon POMDP setting with an unknown transition model, where we assume the knowledge of the observation model. Under this assumption, we propose the Observation-Aware Spectral (OAS) estimation technique, which enables the POMDP parameters to be learned from samples collected using a belief-based policy. Then, we propose the OAS-UCRL algorithm that implicitly balances the exploration-exploitation trade-off following the $\textit{optimism in the face of uncertainty}$ principle. The algorithm runs through episodes of increasing length. For each episode, the optimal belief-based policy of the estimated POMDP interacts with the environment and collects samples that will be used in the next episode by the OAS estimation procedure to compute a new estimate of the POMDP parameters. Given the estimated model, an optimization oracle computes the new optimal policy. We show the consistency of the OAS procedure, and we prove a regret guarantee of order $\mathcal{O}(\sqrt{T \log(T)})$ for the proposed OAS-UCRL algorithm. We compare against the oracle playing the optimal stochastic belief-based policy and show the efficient scaling of our approach with respect to the dimensionality of the state, action, and observation space. We finally conduct numerical simulations to validate and compare the proposed technique with other baseline approaches.
Microsoft Research（微软研究院）；Imperial College London（伦敦帝国理工学院）
Partially observable Markov decision processes (POMDPs) are a powerful abstraction for tasks that require decision making under uncertainty, and capture a wide range of real world tasks. Today, effective planning approaches exist that generate effective strategies given black-box models of a POMDP task. Yet, an open question is how to acquire accurate models for complex domains. In this paper we propose DELIP, an approach to model learning for POMDPs that utilizes amortized structured variational inference. We empirically show that our model leads to effective control strategies when coupled w…
Predictive state representations (PSRs) are models of controlled non-Markov observation sequences which exhibit the same generative process governing POMDP observations without relying on an underlying latent state. In that respect, a PSR is indistinguishable from the corresponding POMDP. However, PSRs notoriously ignore the notion of rewards, which undermines the general utility of PSR models for control, planning, or reinforcement learning. Therefore, we describe a sufficient and necessary accuracy condition which determines whether a PSR is able to accurately model POMDP rewards, we show th…
This paper presents a new neural architecture that combines a modulated Hebbian network (MOHN) with DQN, which we call modulated Hebbian plus Q network architecture (MOHQA). The hypothesis is that such a combination allows MOHQA to solve difficult partially observable Markov decision process (POMDP) problems which impair temporal difference (TD)-based RL algorithms such as DQN, as the TD error cannot be easily derived from observations. The key idea is to use a Hebbian network with bio-inspired neural traces in order to bridge temporal delays between actions and rewards when confounding observ…
Multi-agent active perception is a task where a team of agents cooperatively gathers observations to compute a joint estimate of a hidden variable. The task is decentralized and the joint estimate can only be computed after the task ends by fusing observations of all agents. The objective is to maximize the accuracy of the estimate. The accuracy is quantified by a centralized prediction reward determined by a centralized decision-maker who perceives the observations gathered by all agents after the task ends. In this paper, we model multi-agent active perception as a decentralized partially ob…
Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学研究所）；UCLA（加州大学洛杉矶分校）
We consider the problem of finding the best memoryless stochastic policy for an infinite-horizon partially observable Markov decision process (POMDP) with finite state and action spaces with respect to either the discounted or mean reward criterion. We show that the (discounted) state-action frequencies and the expected cumulative reward are rational functions of the policy, whereby the degree is determined by the degree of partial observability. We then describe the optimization problem as a linear optimization problem in the space of feasible state-action frequencies subject to polynomial co…
University of California, Irvine（加利福尼亚大学欧文分校）；INRIA, France（法国国家信息与自动化研究所）
We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive) latent variable models such as hidden Markov models, POMDPs are more challenging since the learner interacts with the environment and possibly changes the future observations in the process. We devise a learning algorithm running through epochs, in each epoch we employ spectral techniques to learn the POMDP parameters from a trajectory generated by a fixed p…
University of Oxford（牛津大学）；University of British Columbia（不列颠哥伦比亚大学）；Inverted AI（Inverted AI公司）；Alberta Machine Learning Intelligence Institute (AMII)（阿尔伯塔机器学习智能研究所（AMII））；Montréal Institute for Learning Algorithms (MILA)（蒙特利尔学习算法研究所（MILA））
Policies for partially observed Markov decision processes can be efficiently learned by imitating policies for the corresponding fully observed Markov decision processes. Unfortunately, existing approaches for this kind of imitation learning have a serious flaw: the expert does not know what the trainee cannot see, and so may encourage actions that are sub-optimal, even unsafe, under partial information. We derive an objective to instead train the expert to maximize the expected reward of the imitating agent policy, and use it to construct an efficient algorithm, adaptive asymmetric DAgger (A2…
Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）
Reward optimization in fully observable Markov decision processes is equivalent to a linear program over the polytope of state-action frequencies. Taking a similar perspective in the case of partially observable Markov decision processes with memoryless stochastic policies, the problem was recently formulated as the optimization of a linear objective subject to polynomial constraints. Based on this we present an approach for Reward Optimization in State-Action space (ROSA). We test this approach experimentally in maze navigation tasks. We find that ROSA is computationally efficient and can yie…
The Chinese University of Hong Kong（香港中文大学）；University of Toronto（多伦多大学）
We study the model-based undiscounted reinforcement learning for partially observable Markov decision processes (POMDPs). The oracle we consider is the optimal policy of the POMDP with a known environment in terms of the average reward over an infinite horizon. We propose a learning algorithm for this problem, building on spectral method-of-moments estimations for hidden Markov models, the belief error control in POMDPs and upper-confidence-bound methods for online learning. We establish a regret bound of $O(T^{2/3}\sqrt{\log T})$ for the proposed learning algorithm where $T$ is the learning h…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；The University of Massachusetts: Dartmouth（马萨诸塞大学达特茅斯分校）；United States Army Research Laboratory（美国陆军研究实验室）
In inverse reinforcement learning (IRL), a learning agent infers a reward function encoding the underlying task using demonstrations from experts. However, many existing IRL techniques make the often unrealistic assumption that the agent has access to full information about the environment. We remove this assumption by developing an algorithm for IRL in partially observable Markov decision processes (POMDPs). We address two limitations of existing IRL techniques. First, they require an excessive amount of data due to the information asymmetry between the expert and the learner. Second, most of…
In many practical settings control decisions must be made under partial/imperfect information about the evolution of a relevant state variable. Partially Observable Markov Decision Processes (POMDPs) is a relatively well-developed framework for modeling and analyzing such problems. In this paper we consider the structural estimation of the primitives of a POMDP model based upon the observable history of the process. We analyze the structural properties of POMDP model with random rewards and specify conditions under which the model is identifiable without knowledge of the state dynamics. We con…
The Partially Observable Markov Decision Process (POMDP) is a powerful framework for capturing decision-making problems that involve state and transition uncertainty. However, most current POMDP planners cannot effectively handle high-dimensional image observations prevalent in real world applications, and often require lengthy online training that requires interaction with the environment. In this work, we propose Visual Tree Search (VTS), a compositional learning and planning procedure that combines generative models learned offline with online model-based POMDP planning. The deep generative…
Harvard University（哈佛大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes, where the evaluation policy depends only on observable variables but the behavior policy depends on latent states (Tennenholtz et al. (2020a)). Prior work on this problem uses a causal identification strategy based on one-step observable proxies of the hidden state, which relies on the invertibility of certain one-step moment matrices. In this work, we relax this requirement by using spectral methods and extending one-step proxies both into the past and future. We empirically compare our OPE methods to e…
DeepMind（深度思维）；Princeton University（普林斯顿大学）；Google Research India（谷歌印度研究院）；University of Alberta（阿尔伯塔大学）
This paper introduces a simple efficient learning algorithms for general sequential decision making. The algorithm combines Optimism for exploration with Maximum Likelihood Estimation for model estimation, which is thus named OMLE. We prove that OMLE learns the near-optimal policies of an enormously rich class of sequential decision making problems in a polynomial number of samples. This rich class includes not only a majority of known tractable model-based Reinforcement Learning (RL) problems (such as tabular MDPs, factored MDPs, low witness rank problems, tabular weakly-revealing/observable …
Online solvers for partially observable Markov decision processes have difficulty scaling to problems with large action spaces. This paper proposes a method called PA-POMCPOW to sample a subset of the action space that provides varying mixtures of exploitation and exploration for inclusion in a search tree. The proposed method first evaluates the action space according to a score function that is a linear combination of expected reward and expected information gain. The actions with the highest score are then added to the search tree during tree expansion. Experiments show that PA-POMCPOW is a…
Baylor College of Medicine（贝勒医学院）；Rice University（莱斯大学）；University of Minnesota（明尼苏达大学）
Complex behaviors are often driven by an internal model, which integrates sensory information over time and facilitates long-term planning. Inferring an agent's internal model is a crucial ingredient in social interactions (theory of mind), for imitation learning, and for interpreting neural activities of behaving agents. Here we describe a generic method to model an agent's behavior under an environment with uncertainty, and infer the agent's internal model, reward function, and dynamic beliefs. We apply our method to a simulated agent performing a naturalistic foraging task. We assume the ag…
University of Science and Technology of China（中国科学技术大学）；Hefei Comprehensive National Science Center（合肥综合性国家科学中心）；Texas A&M University（德州农工大学）
Generalization in partially observed markov decision processes (POMDPs) is critical for successful applications of visual reinforcement learning (VRL) in real scenarios. A widely used idea is to learn task-relevant representations that encode task-relevant information of common features in POMDPs, i.e., rewards and transition dynamics. As transition dynamics in the latent state space -- which are task-relevant and invariant to visual distractions -- are unknown to the agents, existing methods alternatively use transition dynamics in the observation space to extract task-relevant information in…
Solving Partially Observable Markov Decision Processes (POMDPs) is hard. Learning optimal controllers for POMDPs when the model is unknown is harder. Online learning of optimal controllers for unknown POMDPs, which requires efficient learning using regret-minimizing algorithms that effectively tradeoff exploration and exploitation, is even harder, and no solution exists currently. In this paper, we consider infinite-horizon average-cost POMDPs with unknown transition model, though a known observation model. We propose a natural posterior sampling-based reinforcement learning algorithm (PSRL-PO…
University of Amsterdam（阿姆斯特丹大学）；University of Oxford（牛津大学）；University of Liverpool（利物浦大学）；Delft University of Technology（代尔夫特理工大学）
In active perception tasks, an agent aims to select sensory actions that reduce its uncertainty about one or more hidden variables. While partially observable Markov decision processes (POMDPs) provide a natural model for such problems, reward functions that directly penalize uncertainty in the agent's belief can remove the piecewise-linear and convex property of the value function required by most POMDP planners. Furthermore, as the number of sensors available to the agent grows, the computational cost of POMDP planning grows exponentially with it, making POMDP planning infeasible with tradit…
Institute of Physics（物理研究所）；Institut de Recherche sur les Phenomènes Hors Équilibre（非平衡现象研究所）；Centrale Marseille（马塞尔中央理工学院）；CNRS（法国国家科学研究中心）；Aix-Marseille Université（艾克斯-马赛大学）
Reinforcement learning is generally difficult for partially observable Markov decision processes (POMDPs), which occurs when the agent's observation is partial or noisy. To seek good performance in POMDPs, one strategy is to endow the agent with a finite memory, whose update is governed by the policy. However, policy optimization is non-convex in that case and can lead to poor training performance for random initialization. The performance can be empirically improved by constraining the memory architecture, then sacrificing optimality to facilitate training. Here we study this trade-off in a t…
C-IDS: Solving Contextual POMDP via Information-Directed Objective
Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida 32608, USA（电气与计算机工程系，佛罗里达大学，盖恩斯维尔，佛罗里达州32608，美国）；Aerospace Engineering, DEVCOM Army Research Laboratory, Adelphi, MD 21001, USA（航空航天工程，DEVCOM陆军研究实验室，阿德里菲，马里兰州21001，美国）
Rapid online adaptation to changing tasks is an important problem in machine learning and, recently, a focus of meta-reinforcement learning. However, reinforcement learning (RL) algorithms struggle in POMDP environments because the state of the system, essential in a RL framework, is not always visible. Additionally, hand-designed meta-RL architectures may not include suitable computational structures for specific learning problems. The evolution of online learning mechanisms, on the contrary, has the ability to incorporate learning strategies into an agent that can (i) evolve memory when requ…
IIT Bombay（印度理工学院孟买分校）；Indian Institute of Science（印度科学学院）
We describe and study a model for an Automated Online Recommendation System (AORS) in which a user's preferences can be time-dependent and can also depend on the history of past recommendations and play-outs. The three key features of the model that makes it more realistic compared to existing models for recommendation systems are (1) user preference is inherently latent, (2) current recommendations can affect future preferences, and (3) it allows for the development of learning algorithms with provable performance guarantees. The problem is cast as an average-cost restless multi-armed bandit …
Function approximation has enabled remarkable advances in applying reinforcement learning (RL) techniques in environments with high-dimensional inputs, such as images, in an end-to-end fashion, mapping such inputs directly to low-level control. Nevertheless, these have proved vulnerable to small adversarial input perturbations. A number of approaches for improving or certifying robustness of end-to-end RL to adversarial perturbations have emerged as a result, focusing on cumulative reward. However, what is often at stake in adversarial scenarios is the violation of fundamental properties, such…
North Carolina State University（北卡罗来纳州立大学）；University of Alberta（阿尔伯塔大学）；University of New Mexico（新墨西哥大学）；University of Michigan（密歇根大学）
We develop an off-policy actor-critic algorithm for learning an optimal policy from a training set composed of data from multiple individuals. This algorithm is developed with a view towards its use in mobile health.
New York University（纽约大学）；New York University Shanghai（上海纽约大学）
We develop theory and algorithms for average-reward on-policy Reinforcement Learning (RL). We first consider bounding the difference of the long-term average reward for two policies. We show that previous work based on the discounted return (Schulman et al., 2015; Achiam et al., 2017) results in a non-meaningful bound in the average-reward setting. By addressing the average-reward criterion directly, we then derive a novel bound which depends on the average divergence between the two policies and Kemeny's constant. Based on this bound, we develop an iterative procedure which produces a sequenc…
Drug dosing is an important application of AI, which can be formulated as a Reinforcement Learning (RL) problem. In this paper, we identify two major challenges of using RL for drug dosing: delayed and prolonged effects of administering medications, which break the Markov assumption of the RL framework. We focus on prolongedness and define PAE-POMDP (Prolonged Action Effect-Partially Observable Markov Decision Process), a subclass of POMDPs in which the Markov assumption does not hold specifically due to prolonged effects of actions. Motivated by the pharmacology literature, we propose a simpl…
We introduce reinforcement learning for heterogeneous teams in which rewards for an agent are additively factored into local costs, stimuli unique to each agent, and global rewards, those shared by all agents in the domain. Motivating domains include coordination of varied robotic platforms, which incur different costs for the same action, but share an overall goal. We present two templates for learning in this setting with factored rewards: a generalization of Perkins' Monte Carlo exploring starts for POMDPs to canonical MPOMDPs, with a single policy mapping joint observations of all agents t…
Explanation through Reward Model Reconciliation using POMDP Tree Search
Department of Aerospace Engineering Sciences, University of Colorado Boulder（科罗拉多大学博尔德分校航空航天工程科学系）；Applied Physics Laboratory, Johns Hopkins University（约翰霍普金斯大学应用物理实验室）
University of California, Los Angeles（加州大学洛杉矶分校）；University of Michigan（密歇根大学）
In this paper we consider the problem of learning the optimal policy for uncontrolled restless bandit problems. In an uncontrolled restless bandit problem, there is a finite set of arms, each of which when pulled yields a positive reward. There is a player who sequentially selects one of the arms at each time step. The goal of the player is to maximize its undiscounted reward over a time horizon T. The reward process of each arm is a finite state Markov chain, whose transition probabilities are unknown by the player. State transitions of each arm is independent of the selection of the player. …
University of Toronto（多伦多大学）；Vector Institute（矢量研究所）；Schwartz Reisman Institute for Technology and Society（施瓦茨·赖斯曼技术与社会研究所）；Pontificia Universidad Católica de Chile（智利天主教大学）；Centro Nacional de Inteligencia Artificial（国家人工智能中心）
Natural and formal languages provide an effective mechanism for humans to specify instructions and reward functions. We investigate how to generate policies via RL when reward functions are specified in a symbolic language captured by Reward Machines, an increasingly popular automaton-inspired structure. We are interested in the case where the mapping of environment state to a symbolic (here, Reward Machine) vocabulary -- commonly known as the labelling function -- is uncertain from the perspective of the agent. We formulate the problem of policy learning in Reward Machines with noisy symbolic…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Army Research Laboratory（陆军研究实验室）
We study the problem of inverse reinforcement learning (IRL), where the learning agent recovers a reward function using expert demonstrations. Most of the existing IRL techniques make the often unrealistic assumption that the agent has access to full information about the environment. We remove this assumption by developing an algorithm for IRL in partially observable Markov decision processes (POMDPs). The algorithm addresses several limitations of existing techniques that do not take the information asymmetry between the expert and the learner into account. First, it adopts causal entropy as…
A novel LEarning-based Spectrum Sensing and Access (LESSA) framework is proposed, wherein a cognitive radio (CR) learns a time-frequency correlation model underlying spectrum occupancy of licensed users (LUs) in a radio ecosystem; concurrently, it devises an approximately optimal spectrum sensing and access policy under sensing constraints. A Baum-Welch algorithm is proposed to learn a parametric Markov transition model of LU spectrum occupancy based on noisy spectrum measurements. Spectrum sensing and access are cast as a Partially-Observable Markov Decision Process, approximately optimized v…
Model-free reinforcement learning is known to be memory and computation efficient and more amendable to large scale problems. In this paper, two model-free algorithms are introduced for learning infinite-horizon average-reward Markov Decision Processes (MDPs). The first algorithm reduces the problem to the discounted-reward version and achieves $\mathcal{O}(T^{2/3})$ regret after $T$ steps, under the minimal assumption of weakly communicating MDPs. To our knowledge, this is the first model-free algorithm for general MDPs in this setting. The second algorithm makes use of recent advances in ada…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Sony AI（索尼人工智能研究院）
Agents that operate in an unknown environment are bound to make mistakes while learning, including, at least occasionally, some that lead to catastrophic consequences. When humans make catastrophic mistakes, they are expected to learn never to repeat them, such as a toddler who touches a hot stove and immediately learns never to do so again. In this work we consider a novel class of POMDPs, called POMDP with Catastrophic Actions (POMDP-CA) in which pairs of states and actions are labeled as catastrophic. Agents that act in a POMDP-CA do not have a priori knowledge about which (state, action) p…
We show two average-reward off-policy control algorithms, Differential Q-learning (Wan, Naik, & Sutton 2021a) and RVI Q-learning (Abounadi Bertsekas & Borkar 2001), converge in weakly communicating MDPs. Weakly communicating MDPs are the most general MDPs that can be solved by a learning algorithm with a single stream of experience. The original convergence proofs of the two algorithms require that the solution set of the average-reward optimality equation only has one degree of freedom, which is not necessarily true for weakly communicating MDPs. To the best of our knowledge, our results are …
Reward Machines for Deep RL in Noisy and Uncertain Environments
University of Toronto（多伦多大学）；Vector Institute（矢量研究所）；Cornell University（康奈尔大学）；Pontificia Universidad Católica de Chile（智利天主教大学）；Centro Nacional de Inteligencia Artificial（国家人工智能中心）；Schwartz Reisman Institute for Technology and Society（施瓦茨·赖斯曼技术与社会研究所）
Consider an agent interacting with an environment in cycles. In every interaction cycle the agent is rewarded for its performance. We compare the average reward U from cycle 1 to m (average value) with the future discounted reward V from cycle k to infinity (discounted value). We consider essentially arbitrary (non-geometric) discount sequences and arbitrary reward sequences (non-MDP environments). We show that asymptotically U for m->infinity and V for k->infinity are equal, provided both limits exist. Further, if the effective horizon grows linearly with k or faster, then existence of the li…
