Decentralized partially observable Markov decision process (DEC-POMDP) models sequential decision making problems by a team of agents. Since the planning of DEC-POMDP can be interpreted as the maximum likelihood estimation for the latent variable model, DEC-POMDP can be solved by the EM algorithm. However, in EM for DEC-POMDP, the forward--backward algorithm needs to be calculated up to the infinite horizon, which impairs the computational efficiency. In this paper, we propose the Bellman EM algorithm (BEM) and the modified Bellman EM algorithm (MBEM) by introducing the forward and backward Bellman equations into EM. BEM can be more efficient than EM because BEM calculates the forward and backward Bellman equations instead of the forward--backward algorithm up to the infinite horizon. However, BEM cannot always be more efficient than EM when the size of problems is large because BEM calculates an inverse matrix. We circumvent this shortcoming in MBEM by calculating the forward and backward Bellman equations without the inverse matrix. Our numerical experiments demonstrate that the convergence of MBEM is faster than that of EM.
Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space systems under partial observability. This places our work at the intersection of optimal filtering and optimal control. At the current state of research, a mathematical description for simultaneous decision making and filtering in continuous time with finite state and action spaces is still missing. In this paper, we give a mathematical description of a continuous…
Finding the minimal structural assumptions that empower sample-efficient learning is one of the most important research directions in Reinforcement Learning (RL). This paper advances our understanding of this fundamental question by introducing a new complexity measure -- Bellman Eluder (BE) dimension. We show that the family of RL problems of low BE dimension is remarkably rich, which subsumes a vast majority of existing tractable RL problems including but not limited to tabular MDPs, linear MDPs, reactive POMDPs, low Bellman rank problems as well as low Eluder dimension problems. This paper …
Solving Hierarchical Information-Sharing Dec-POMDPs: An Extensive-Form Game Approach
Université de Lyon（里昂大学）；INSA Lyon（里昂国立应用科学学院）；Inria（法国国家信息与自动化研究所）；Université de Lorraine（洛林大学）；CNRS（法国国家科学研究中心）；Bernoulli Institute（伯努利研究所）；University of Groningen（格罗宁根大学）
High entropy leads to symmetry-equivariant policies in Dec-POMDPs
FLAIR, Department of Engineering Science, University of Oxford（奥德赛实验室，工程科学系，牛津大学）；Collaborative Artificial Intelligence, University of Stuttgart（协同人工智能，斯图加特大学）
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 Pennsylvania State University（宾夕法尼亚州立大学）；ETH Zürich（苏黎世联邦理工学院）
Efficient integration of uncertain observations with decision-making optimization is key for prescribing informed intervention actions, able to preserve structural safety of deteriorating engineering systems. To this end, it is necessary that scheduling of inspection and monitoring strategies be objectively performed on the basis of their expected value-based gains that, among others, reflect quantitative metrics such as the Value of Information (VoI) and the Value of Structural Health Monitoring (VoSHM). In this work, we introduce and study the theoretical and computational foundations of the…
POMDPs are useful models for systems where the true underlying state is not known completely to an outside observer; the outside observer incompletely knows the true state of the system, and observes a noisy version of the true system state. When the number of system states is large in a POMDP that often necessitates the use of approximation methods to obtain near optimal solutions for control. This survey is centered around the origins, theory, and approximations of finite-state POMDPs. In order to understand POMDPs, it is required to have an understanding of finite-state Markov Decision Proc…
The partially observable Markov decision process (POMDP) framework is a common approach for decision making under uncertainty. Recently, multiple studies have shown that by integrating relevant domain knowledge into POMDP belief estimation, we can improve the learned policy's performance. In this study, we propose a novel method for integrating the domain knowledge into probabilistic belief update in POMDP framework using Jeffrey's rule and normalization. We show that the domain knowledge can be utilized to reduce the data requirement and improve performance for POMDP policy learning with RL.
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 …
Solving Truly Massive Budgeted Monotonic POMDPs with Oracle-Guided Meta-Reinforcement Learning
Department of Aerospace Engineering（航空航天工程系）；University of Illinois Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）；Department of Mathematics（数学系）；Engineer Research and Development Center（工程研究与发展中心）；U.S. Army Corps of Engineers（美国陆军工程兵团）
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…
Northeastern University（东北大学）；University of Liverpool（利物浦大学）
The POMDP is a powerful framework for reasoning under outcome and information uncertainty, but constructing an accurate POMDP model is difficult. Bayes-Adaptive Partially Observable Markov Decision Processes (BA-POMDPs) extend POMDPs to allow the model to be learned during execution. BA-POMDPs are a Bayesian RL approach that, in principle, allows for an optimal trade-off between exploitation and exploration. Unfortunately, BA-POMDPs are currently impractical to solve for any non-trivial domain. In this paper, we extend the Monte-Carlo Tree Search method POMCP to BA-POMDPs and show that the res…
FZI Research Center for Information Technology（FZI信息技术研究中心）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
Decision making under uncertainty can be framed as a partially observable Markov decision process (POMDP). Finding exact solutions of POMDPs is generally computationally intractable, but the solution can be approximated by sampling-based approaches. These sampling-based POMDP solvers rely on multi-armed bandit (MAB) heuristics, which assume the outcomes of different actions to be uncorrelated. In some applications, like motion planning in continuous spaces, similar actions yield similar outcomes. In this paper, we utilize variants of MAB heuristics that make Lipschitz continuity assumptions on…
The University of Texas at Austin（得克萨斯大学奥斯汀分校）；Radboud University（拉德堡德大学）；Albert-Ludwigs-Universität Freiburg（阿尔伯特-路德维希大学弗莱堡分校）；Concept Engineering GmbH（康赛普特工程有限公司）
We study strategy synthesis for partially observable Markov decision processes (POMDPs). The particular problem is to determine strategies that provably adhere to (probabilistic) temporal logic constraints. This problem is computationally intractable and theoretically hard. We propose a novel method that combines techniques from machine learning and formal verification. First, we train a recurrent neural network (RNN) to encode POMDP strategies. The RNN accounts for memory-based decisions without the need to expand the full belief space of a POMDP. Secondly, we restrict the RNN-based strategy …
State variables are easily the most subtle dimension of sequential decision problems. This is especially true in the context of active learning problems (bandit problems") where decisions affect what we observe and learn. We describe our canonical framework that models {\it any} sequential decision problem, and present our definition of state variables that allows us to claim: Any properly modeled sequential decision problem is Markovian. We then present a novel two-agent perspective of partially observable Markov decision problems (POMDPs) that allows us to then claim: Any model of a real dec…
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…
ETH Zürich（苏黎世联邦理工学院）；Swiss Federal Railways SBB（瑞士联邦铁路）；Technical University of Munich（慕尼黑工业大学）；Pennsylvania State Univ.（宾夕法尼亚州立大学）
Structural Health Monitoring (SHM) describes a process for inferring quantifiable metrics of structural condition, which can serve as input to support decisions on the operation and maintenance of infrastructure assets. Given the long lifespan of critical structures, this problem can be cast as a sequential decision making problem over prescribed horizons. Partially Observable Markov Decision Processes (POMDPs) offer a formal framework to solve the underlying optimal planning task. However, two issues can undermine the POMDP solutions. Firstly, the need for a model that can adequately describe…
POMDPs capture a broad class of decision making problems, but hardness results suggest that learning is intractable even in simple settings due to the inherent partial observability. However, in many realistic problems, more information is either revealed or can be computed during some point of the learning process. Motivated by diverse applications ranging from robotics to data center scheduling, we formulate a Hindsight Observable Markov Decision Process (HOMDP) as a POMDP where the latent states are revealed to the learner in hindsight and only during training. We introduce new algorithms f…
Princeton University（普林斯顿大学）；University of Washington（华盛顿大学）；Microsoft Research, NYC（微软研究院纽约分院）
Partial observability is a common challenge in many reinforcement learning applications, which requires an agent to maintain memory, infer latent states, and integrate this past information into exploration. This challenge leads to a number of computational and statistical hardness results for learning general Partially Observable Markov Decision Processes (POMDPs). This work shows that these hardness barriers do not preclude efficient reinforcement learning for rich and interesting subclasses of POMDPs. In particular, we present a sample-efficient algorithm, OOM-UCB, for episodic finite under…
We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any (PO)MDP can be transformed into an "equivalent" POMDP in which all state transitions (given the current state and action) are deterministic. This reduces the general problem of policy search to one in which we need only consider POMDPs with deterministic transitions. We give a natural way of estimating the value of all policies in these transformed POMDPs. P…
Much of reinforcement learning theory is built on top of oracles that are computationally hard to implement. Specifically for learning near-optimal policies in Partially Observable Markov Decision Processes (POMDPs), existing algorithms either need to make strong assumptions about the model dynamics (e.g. deterministic transitions) or assume access to an oracle for solving a hard optimistic planning or estimation problem as a subroutine. In this work we develop the first oracle-free learning algorithm for POMDPs under reasonable assumptions. Specifically, we give a quasipolynomial-time end-to-…
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…
Partially Observable Markov Decision Process (POMDP) is a framework applicable to many real world problems. In this work, we propose an approach to solve POMDPs with multimodal belief by relying on a policy that solves the fully observable version. By defininig a new, mixture value function based on the value function from the fully observable variant, we can use the corresponding greedy policy to solve the POMDP itself. We develop the mathematical framework necessary for discussion, and introduce a benchmark built on the task of Reconnaissance Blind TicTacToe. On this benchmark, we show that …
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…
We consider the estimation of the policy gradient in partially observable Markov decision processes (POMDP) with a special class of structured policies that are finite-state controllers. We show that the gradient estimation can be done in the Actor-Critic framework, by making the critic compute a "value" function that does not depend on the states of POMDP. This function is the conditional mean of the true value function that depends on the states. We show that the critic can be implemented using temporal difference (TD) methods with linear function approximations, and the analytical results o…
The partially observable Markov decision process (POMDP) is a principled general framework for robot decision making under uncertainty, but POMDP planning suffers from high computational complexity, when long-term planning is required. While temporally-extended macro-actions help to cut down the effective planning horizon and significantly improve computational efficiency, how do we acquire good macro-actions? This paper proposes Macro-Action Generator-Critic (MAGIC), which performs offline learning of macro-actions optimized for online POMDP planning. Specifically, MAGIC learns a macro-action…
Health-related data is noisy and stochastic in implying the true physiological states of patients, limiting information contained in single-moment observations for sequential clinical decision making. We model patient-clinician interactions as partially observable Markov decision processes (POMDPs) and optimize sequential treatment based on belief states inferred from history sequence. To facilitate inference, we build a variational generative model and boost state representation with a recurrent neural network (RNN), incorporating an auxiliary loss from sequence auto-encoding. Meanwhile, we o…
This work studies the problem of batch off-policy evaluation for Reinforcement Learning in partially observable environments. Off-policy evaluation under partial observability is inherently prone to bias, with risk of arbitrarily large errors. We define the problem of off-policy evaluation for Partially Observable Markov Decision Processes (POMDPs) and establish what we believe is the first off-policy evaluation result for POMDPs. In addition, we formulate a model in which observed and unobserved variables are decoupled into two dynamic processes, called a Decoupled POMDP. We show how off-poli…
Tsinghua University（清华大学）；The University of Hong Kong（香港大学）；Shanghai Qizhi Institute（上海期智研究院）
Partially Observable Markov Decision Process (POMDP) provides a principled and generic framework to model real world sequential decision making processes but yet remains unsolved, especially for high dimensional continuous space and unknown models. The main challenge lies in how to accurately obtain the belief state, which is the probability distribution over the unobservable environment states given historical information. Accurately calculating this belief state is a precondition for obtaining an optimal policy of POMDPs. Recent advances in deep learning techniques show great potential to le…
University of Waterloo（滑铁卢大学）；Monash University（莫纳什大学）
A promising characteristic of Deep Reinforcement Learning (DRL) is its capability to learn optimal policy in an end-to-end manner without relying on feature engineering. However, most approaches assume a fully observable state space, i.e. fully observable Markov Decision Processes (MDPs). In real-world robotics, this assumption is unpractical, because of issues such as sensor sensitivity limitations and sensor noise, and the lack of knowledge about whether the observation design is complete or not. These scenarios lead to Partially Observable MDPs (POMDPs). In this paper, we propose Long-Short…
University of California, Berkeley（加州大学伯克利分校）；University of Colorado Boulder（科罗拉多大学博尔德分校）
This paper introduces Voronoi Progressive Widening (VPW), a generalization of Voronoi optimistic optimization (VOO) and action progressive widening to partially observable Markov decision processes (POMDPs). Tree search algorithms can use VPW to effectively handle continuous or hybrid action spaces by efficiently balancing local and global action searching. This paper proposes two VPW-based algorithms and analyzes them from theoretical and simulation perspectives. Voronoi Optimistic Weighted Sparse Sampling (VOWSS) is a theoretical tool that justifies VPW-based online solvers, and it is the fi…
We present Mask Atari, a new benchmark to help solve partially observable Markov decision process (POMDP) problems with Deep Reinforcement Learning (DRL)-based approaches. To achieve a simulation environment for the POMDP problems, Mask Atari is constructed based on Atari 2600 games with controllable, moveable, and learnable masks as the observation area for the target agent, especially with the active information gathering (AIG) setting in POMDPs. Given that one does not yet exist, Mask Atari provides a challenging, efficient benchmark for evaluating the methods that focus on the above proble…
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）
