We consider the problem: is the optimal expected total reward to reach a goal state in a partially observable Markov decision process (POMDP) below a given threshold? We tackle this -- generally undecidable -- problem by computing under-approximations on these total expected rewards. This is done by abstracting finite unfoldings of the infinite belief MDP of the POMDP. The key issue is to find a suitable under-approximation of the value function. We provide two techniques: a simple (cut-off) technique that uses a good policy on the POMDP, and a more advanced technique (belief clipping) that uses minimal shifts of probabilities between beliefs. We use mixed-integer linear programming (MILP) to find such minimal probability shifts and experimentally show that our techniques scale quite well while providing tight lower bounds on the expected total reward.
University of Georgia（佐治亚大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Partially observable Markov decision processes (POMDPs) provide a principled framework for sequential planning in uncertain single agent settings. An extension of POMDPs to multiagent settings, called interactive POMDPs (I-POMDPs), replaces POMDP belief spaces with interactive hierarchical belief systems which represent an agent's belief about the physical world, about beliefs of other agents, and about their beliefs about others' beliefs. This modification makes the difficulties of obtaining solutions due to complexity of the belief and policy spaces even more acute. We describe a general met…
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…
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 Hamburg（汉堡大学）；TU Darmstadt（达姆施塔特工业大学）
Decentralized policies for information gathering are required when multiple autonomous agents are deployed to collect data about a phenomenon of interest without the ability to communicate. Decentralized partially observable Markov decision processes (Dec-POMDPs) are a general, principled model well-suited for such decentralized multiagent decision-making problems. In this paper, we investigate Dec-POMDPs for decentralized information gathering problems. An optimal solution of a Dec-POMDP maximizes the expected sum of rewards over time. To encourage information gathering, we set the reward as …
We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the p…
This paper studies the deception applied on agent in a partially observable Markov decision process. We introduce deceptive kernel function (the kernel) applied to agent's observations in a discrete POMDP. Based on value iteration, value function approximation and POMCP three characteristic algorithms used by agent, we analyze its belief being misled by falsified observations as the kernel's outputs and anticipate its probable threat on agent's reward and potentially other performance. We validate our expectation and explore more detrimental effects of the deception by experimenting on two POM…
Rather than augmenting rewards with penalties for undesired behavior, Constrained Partially Observable Markov Decision Processes (CPOMDPs) plan safely by imposing inviolable hard constraint value budgets. Previous work performing online planning for CPOMDPs has only been applied to discrete action and observation spaces. In this work, we propose algorithms for online CPOMDP planning for continuous state, action, and observation spaces by combining dual ascent with progressive widening. We empirically compare the effectiveness of our proposed algorithms on continuous CPOMDPs that model both toy…
Université de Lorraine（洛林大学）；INRIA（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；LORIA（洛林计算机科学与应用实验室）；École Normale Supérieure de Lyon（里昂高等师范学校）
In this article, we discuss how to solve information-gathering problems expressed as rho-POMDPs, an extension of Partially Observable Markov Decision Processes (POMDPs) whose reward rho depends on the belief state. Point-based approaches used for solving POMDPs have been extended to solving rho-POMDPs as belief MDPs when its reward rho is convex in B or when it is Lipschitz-continuous. In the present paper, we build on the POMCP algorithm to propose a Monte Carlo Tree Search for rho-POMDPs, aiming for an efficient on-line planner which can be used for any rho function. Adaptations are required…
We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated to every transition, and the payoff of an infinite path is the long-run average of the rewards. We consider two types of path constraints: (i) quantitative constraint defines the set of paths where the payoff is at least a given threshold λ in (0, 1]; and (ii) qualitative constraint which is a special case of quantitative constraint with λ = 1. We consider the computation of the almost-sure winning set, where the controller needs to ensure that…
We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated to every transition, and the payoff of an infinite path is the long-run average of the rewards. We consider two types of path constraints: (i) quantitative constraint defines the set of paths where the payoff is at least a given threshold lambda_1 in (0,1]; and (ii) qualitative constraint which is a special case of quantitative constraint with lambda_1=1. We consider the computation of the almost-sure winning set, where the controller needs to …
Centre for Artificial Intelligence Research（人工智能研究中心）；University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；CSIR Meraka（南非科学与工业研究理事会梅拉卡研究所）
This article presents an agent architecture for controlling an autonomous agent in stochastic environments. The architecture combines the partially observable Markov decision process (POMDP) model with the belief-desire-intention (BDI) framework. The Hybrid POMDP-BDI agent architecture takes the best features from the two approaches, that is, the online generation of reward-maximizing courses of action from POMDP theory, and sophisticated multiple goal management from BDI theory. We introduce the advances made since the introduction of the basic architecture, including (i) the ability to pursu…
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…
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…
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…
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…
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…
Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学研究所）；Faculty of Mathematics and Computer Science（数学与计算机科学学院）；Leipzig University（莱比锡大学）；Santa Fe Institute（圣塔菲研究所）
It is well known that for any finite state Markov decision process (MDP) there is a memoryless deterministic policy that maximizes the expected reward. For partially observable Markov decision processes (POMDPs), optimal memoryless policies are generally stochastic. We study the expected reward optimization problem over the set of memoryless stochastic policies. We formulate this as a constrained linear optimization problem and develop a corresponding geometric framework. We show that any POMDP has an optimal memoryless policy of limited stochasticity, which allows us to reduce the dimensional…
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…
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 …
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley（加利福尼亚大学伯克利分校电气工程与计算机科学系）；University of California, Berkeley（加利福尼亚大学伯克利分校）；Department of Electrical Engineering and Computer Sciences（电气工程与计算机科学系）；Electrical Engineering and Computer Sciences, University of California, Berkeley（加利福尼亚大学伯克利分校电气工程与计算机科学系）
Our goal is for AI systems to correctly identify and act according to their human user's objectives. Cooperative Inverse Reinforcement Learning (CIRL) formalizes this value alignment problem as a two-player game between a human and robot, in which only the human knows the parameters of the reward function: the robot needs to learn them as the interaction unfolds. Previous work showed that CIRL can be solved as a POMDP, but with an action space size exponential in the size of the reward parameter space. In this work, we exploit a specific property of CIRL---the human is a full information agent…
In this work, we provide theoretical guarantees for reward decomposition in deterministic MDPs. Reward decomposition is a special case of Hierarchical Reinforcement Learning, that allows one to learn many policies in parallel and combine them into a composite solution. Our approach builds on mapping this problem into a Reward Discounted Traveling Salesman Problem, and then deriving approximate solutions for it. In particular, we focus on approximate solutions that are local, i.e., solutions that only observe information about the current state. Local policies are easy to implement and do not r…
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…
Experimentally, it has been observed that humans and animals often make decisions that do not maximize their expected utility, but rather choose outcomes randomly, with probability proportional to expected utility. Probability matching, as this strategy is called, is equivalent to maximum entropy reinforcement learning (MaxEnt RL). However, MaxEnt RL does not optimize expected utility. In this paper, we formally show that MaxEnt RL does optimally solve certain classes of control problems with variability in the reward function. In particular, we show (1) that MaxEnt RL can be used to solve a c…
We investigate improving Monte Carlo Tree Search based solvers for Partially Observable Markov Decision Processes (POMDPs), when applied to adaptive sampling problems. We propose improvements in rollout allocation, the action exploration algorithm, and plan commitment. The first allocates a different number of rollouts depending on how many actions the agent has taken in an episode. We find that rollouts are more valuable after some initial information is gained about the environment. Thus, a linear increase in the number of rollouts, i.e. allocating a fixed number at each step, is not appropr…
We describe a probabilistic framework for synthesizing control policies for general multi-robot systems, given environment and sensor models and a cost function. Decentralized, partially observable Markov decision processes (Dec-POMDPs) are a general model of decision processes where a team of agents must cooperate to optimize some objective (specified by a shared reward or cost function) in the presence of uncertainty, but where communication limitations mean that the agents cannot share their state, so execution must proceed in a decentralized fashion. While Dec-POMDPs are typically intracta…
Multi-Environment POMDPs: Discrete Model Uncertainty Under Partial Observability
Radboud University（拉德堡德大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Antwerp（安特卫普大学）；Ruhr-University Bochum（波鸿鲁尔大学）；Radboud University Bochum（波鸿鲁尔大学）
UC Berkeley（加州大学伯克利分校）；Oregon State University（俄勒冈州立大学）
AI objectives are often hard to specify properly. Some approaches tackle this problem by regularizing the AI's side effects: Agents must weigh off "how much of a mess they make" with an imperfectly specified proxy objective. We propose a formal criterion for side effect regularization via the assistance game framework. In these games, the agent solves a partially observable Markov decision process (POMDP) representing its uncertainty about the objective function it should optimize. We consider the setting where the true objective is revealed to the agent at a later time step. We show that this…
Gradient-based approaches to direct policy search in reinforcement learning have received much recent attention as a means to solve problems of partial observability and to avoid some of the problems associated with policy degradation in value-function methods. In this paper we introduce GPOMDP, a simulation-based algorithm for generating a {\em biased} estimate of the gradient of the {\em average reward} in Partially Observable Markov Decision Processes (POMDPs) controlled by parameterized stochastic policies. A similar algorithm was proposed by Kimura, Yamamura, and Kobayashi (1995). The alg…
Autonomous agents are limited in their ability to observe the world state. Partially observable Markov decision processes (POMDPs) formally model the problem of planning under world state uncertainty, but POMDPs with continuous actions and nonlinear dynamics suitable for robotics applications are challenging to solve. In this paper, we present an efficient differential dynamic programming (DDP) algorithm for belief space planning in POMDPs with uncertainty over a discrete latent state, and continuous states, actions, observations, and nonlinear dynamics. This representation allows planning of …
Technion - Israel Institute of Technology（以色列理工学院）
Partially Observable Markov Decision Processes (POMDPs) are notoriously hard to solve. Most advanced state-of-the-art online solvers leverage ideas of Monte Carlo Tree Search (MCTS). These solvers rapidly converge to the most promising branches of the belief tree, avoiding the suboptimal sections. Most of these algorithms are designed to utilize straightforward access to the state reward and assume the belief-dependent reward is nothing but expectation over the state reward. Thus, they are inapplicable to a more general and essential setting of belief-dependent rewards. One example of such rew…
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…
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…
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）
Interactive partially observable Markov decision processes (I-POMDP) provide a formal framework for planning for a self-interested agent in multiagent settings. An agent operating in a multiagent environment must deliberate about the actions that other agents may take and the effect these actions have on the environment and the rewards it receives. Traditional I-POMDPs model this dependence on the actions of other agents using joint action and model spaces. Therefore, the solution complexity grows exponentially with the number of agents thereby complicating scalability. In this paper, we model…
WhizBang! Labs（惠兹邦实验室）；BIOwulf Technologies（比奥沃尔夫技术公司）；Australian National University（澳大利亚国立大学）
In this paper, we present algorithms that perform gradient ascent of the average reward in a partially observable Markov decision process (POMDP). These algorithms are based on GPOMDP, an algorithm introduced in a companion paper (Baxter and Bartlett, this volume), which computes biased estimates of the performance gradient in POMDPs. The algorithm's chief advantages are that it uses only one free parameter beta, which has a natural interpretation in terms of bias-variance trade-off, it requires no knowledge of the underlying state, and it can be applied to infinite state, control and observat…
