The partially observable Markov decision process (POMDP) provides a principled general model for planning under uncertainty. However, solving a general POMDP is computationally intractable in the worst case. This paper introduces POMDP-lite, a subclass of POMDPs in which the hidden state variables are constant or only change deterministically. We show that a POMDP-lite is equivalent to a set of fully observable Markov decision processes indexed by a hidden parameter and is useful for modeling a variety of interesting robotic tasks. We develop a simple model-based Bayesian reinforcement learning algorithm to solve POMDP-lite models. The algorithm performs well on large-scale POMDP-lite models with up to $10^{20}$ states and outperforms the state-of-the-art general-purpose POMDP algorithms. We further show that the algorithm is near-Bayesian-optimal under suitable conditions.
POMDPPlanners: Open-Source Package for POMDP Planning
Faculty of Mathematics Technion - Israel Institute of Technology（数学系技术学院 - 以色列理工学院）；Stephen B. Klein Faculty of Aerospace Engineering Faculty of Data and Decision Sciences Technion - Israel Institute of Technology（Stephen B. Klein航空航天工程系数据与决策科学系技术学院 - 以色列理工学院）
Planning in partially observable Markov decision processes (POMDPs) remains a challenging topic in the artificial intelligence community, in spite of recent impressive progress in approximation techniques. Previous research has indicated that online planning approaches are promising in handling large-scale POMDP domains efficiently as they make decisions "on demand" instead of proactively for the entire state space. We present a Factored Hybrid Heuristic Online Planning (FHHOP) algorithm for large POMDPs. FHHOP gets its power by combining a novel hybrid heuristic search strategy with a recentl…
Hong Kong University of Science and Technology（香港科技大学）
This paper is concerned with planning in stochastic domains by means of partially observable Markov decision processes (POMDPs). POMDPs are difficult to solve. This paper identifies a subclass of POMDPs called region observable POMDPs, which are easier to solve and can be used to approximate general POMDPs to arbitrary accuracy.
Partially Observable Markov Decision Processes (POMDP) is a widely used model to represent the interaction of an environment and an agent, under state uncertainty. Since the agent does not observe the environment state, its uncertainty is typically represented through a probabilistic belief. While the set of possible beliefs is infinite, making exact planning intractable, the belief space's complexity (and hence planning complexity) is characterized by its covering number. Many POMDP solvers uniformly discretize the belief space and give the planning error in terms of the (typically unknown) c…
Partially observable Markov decision processes (POMDPs) are a natural model for planning problems where effects of actions are nondeterministic and the state of the world is not completely observable. It is difficult to solve POMDPs exactly. This paper proposes a new approximation scheme. The basic idea is to transform a POMDP into another one where additional information is provided by an oracle. The oracle informs the planning agent that the current state of the world is in a certain region. The transformed POMDP is consequently said to be region observable. It is easier to solve than the or…
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…
Partially Observable Markov Decision Processes (POMDPs) provide a rich framework for sequential decision-making under uncertainty in stochastic domains. However, solving a POMDP is often intractable except for small problems due to their complexity. Here, we focus on online approaches that alleviate the computational complexity by computing good local policies at each decision step during the execution. Online algorithms generally consist of a lookahead search to find the best action to execute at each time step in an environment. Our objectives here are to survey the various existing online P…
ACEMS & Queensland University of Technology（ACEMS 与昆士兰科技大学）；National University of Singapore（新加坡国立大学）
The partially observable Markov decision process (POMDP) provides a principled general framework for planning under uncertainty, but solving POMDPs optimally is computationally intractable, due to the "curse of dimensionality" and the "curse of history". To overcome these challenges, we introduce the Determinized Sparse Partially Observable Tree (DESPOT), a sparse approximation of the standard belief tree, for online planning under uncertainty. A DESPOT focuses online planning on a set of randomly sampled scenarios and compactly captures the "execution" of all policies under these scenarios. W…
Hong Kong University of Science & Technology（香港科技大学）
There is much interest in using partially observable Markov decision processes (POMDPs) as a formal model for planning in stochastic domains. This paper is concerned with finding optimal policies for POMDPs. We propose several improvements to incremental pruning, presently the most efficient exact algorithm for solving POMDPs.
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…
University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
Decentralized POMDPs provide an expressive framework for multi-agent sequential decision making. While fnite-horizon DECPOMDPs have enjoyed signifcant success, progress remains slow for the infnite-horizon case mainly due to the inherent complexity of optimizing stochastic controllers representing agent policies. We present a promising new class of algorithms for the infnite-horizon case, which recasts the optimization problem as inference in a mixture of DBNs. An attractive feature of this approach is the straightforward adoption of existing inference techniques in DBNs for solving DEC-POMDPs…
Maastricht University（马斯特里赫特大学）；Delft University of Technology（代尔夫特理工大学）；Massachusetts Institute of Technology（麻省理工学院）；University of Amsterdam（阿姆斯特丹大学）
This article presents the state-of-the-art in optimal solution methods for decentralized partially observable Markov decision processes (Dec-POMDPs), which are general models for collaborative multiagent planning under uncertainty. Building off the generalized multiagent A* (GMAA*) algorithm, which reduces the problem to a tree of one-shot collaborative Bayesian games (CBGs), we describe several advances that greatly expand the range of Dec-POMDPs that can be solved optimally. First, we introduce lossless incremental clustering of the CBGs solved by GMAA*, which achieves exponential speedups w…
Tel-Aviv University（特拉维夫大学）；University of Pennsylvania（宾夕法尼亚大学）
Planning and learning in Partially Observable MDPs (POMDPs) are among the most challenging tasks in both the AI and Operation Research communities. Although solutions to these problems are intractable in general, there might be special cases, such as structured POMDPs, which can be solved efficiently. A natural and possibly efficient way to represent a POMDP is through the predictive state representation (PSR) - a representation which recently has been receiving increasing attention. In this work, we relate POMDPs to multiplicity automata- showing that POMDPs can be represented by multiplicity…
This work examines the hypothesis that partially observable Markov decision process (POMDP) planning with human driver internal states can significantly improve both safety and efficiency in autonomous freeway driving. We evaluate this hypothesis in a simulated scenario where an autonomous car must safely perform three lane changes in rapid succession. Approximate POMDP solutions are obtained through the partially observable Monte Carlo planning with observation widening (POMCPOW) algorithm. This approach outperforms over-confident and conservative MDP baselines and matches or outperforms QMDP…
University of California, Irvine（加州大学尔湾分校）；French Institute for Research in Computer Science and Automation (Inria)（法国国家信息与自动化研究所）
Planning plays an important role in the broad class of decision theory. Planning has drawn much attention in recent work in the robotics and sequential decision making areas. Recently, Reinforcement Learning (RL), as an agent-environment interaction problem, has brought further attention to planning methods. Generally in RL, one can assume a generative model, e.g. graphical models, for the environment, and then the task for the RL agent is to learn the model parameters and find the optimal strategy based on these learnt parameters. Based on environment behavior, the agent can assume various ty…
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…
Arizona State University（亚利桑那州立大学）；SUNY Binghamton（纽约州立大学宾汉姆顿分校）
To be responsive to dynamically changing real-world environments, an intelligent agent needs to perform complex sequential decision-making tasks that are often guided by commonsense knowledge. The previous work on this line of research led to the framework called "interleaved commonsense reasoning and probabilistic planning" (icorpp), which used P-log for representing commmonsense knowledge and Markov Decision Processes (MDPs) or Partially Observable MDPs (POMDPs) for planning under uncertainty. A main limitation of icorpp is that its implementation requires non-trivial engineering efforts to …
Adaptive mine planning under geological uncertainty: A POMDP framework for sequential decision-making
Geology & Sustainable Mining Institute (GSMI), University Mohammed VI Polytechnic (UM6P)（地质与可持续采矿研究所（GSMI），穆罕默德六世理工学院（UM6P））；Department of Earth and Planetary Sciences, Stanford University（地球与行星科学系，斯坦福大学）
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…
This paper presents a hybrid online Partially Observable Markov Decision Process (POMDP) planning system that addresses the problem of autonomous navigation in the presence of multi-modal uncertainty introduced by other agents in the environment. As a particular example, we consider the problem of autonomous navigation in dense crowds of pedestrians and among obstacles. Popular approaches to this problem first generate a path using a complete planner (e.g., Hybrid A*) with ad-hoc assumptions about uncertainty, then use online tree-based POMDP solvers to reason about uncertainty with control ov…
College of Engineering & Computer Science, The Australian National University（澳大利亚国立大学工程与计算机科学学院）
Planning under partial obervability is essential for autonomous robots. A principled way to address such planning problems is the Partially Observable Markov Decision Process (POMDP). Although solving POMDPs is computationally intractable, substantial advancements have been achieved in developing approximate POMDP solvers in the past two decades. However, computing robust solutions for problems with continuous observation spaces remains challenging. Most on-line solvers rely on discretising the observation space or artificially limiting the number of observations that are considered during pla…
Instituto Nacional de Astrofísica, Óptica y Electrónica（国家天体物理、光学与电子学研究所）；Instituto Nacional de Enfermedades Respiratorias（国家呼吸系统疾病研究所）；University of Bristol（布里斯托大学）；Centro de Investigaciones en Matemáticas（数学研究中心）
The main goal in task planning is to build a sequence of actions that takes an agent from an initial state to a goal state. In robotics, this is particularly difficult because actions usually have several possible results, and sensors are prone to produce measurements with error. Partially observable Markov decision processes (POMDPs) are commonly employed, thanks to their capacity to model the uncertainty of actions that modify and monitor the state of a system. However, since solving a POMDP is computationally expensive, their usage becomes prohibitive for most robotic applications. In this …
Simplifying Complex Observation Models in Continuous POMDP Planning with Probabilistic Guarantees and Practice
Technion Autonomous Systems Program (TASP), Technion - Israel Institute of Technology（以色列理工学院自主系统项目（TASP），以色列理工学院）；Department of Aerospace Engineering, Technion - Israel Institute of Technology（以色列理工学院航空航天工程系）
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…
Robots operating in households must find objects on shelves, under tables, and in cupboards. In such environments, it is crucial to search efficiently at 3D scale while coping with limited field of view and the complexity of searching for multiple objects. Principled approaches to object search frequently use Partially Observable Markov Decision Process (POMDP) as the underlying framework for computing search strategies, but constrain the search space in 2D. In this paper, we present a POMDP formulation for multi-object search in a 3D region with a frustum-shaped field-of-view. To efficiently …
University of Amsterdam（阿姆斯特丹大学）；Instituto Superior Técnico（里斯本高等理工学院）；Technical University of Crete（克里特理工大学）
Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define…
Partially-Observable Markov Decision Processes (POMDPs) are typically solved by finding an approximate global solution to a corresponding belief-MDP. In this paper, we offer a new planning algorithm for POMDPs with continuous state, action and observation spaces. Since such domains have an inherent notion of locality, we can find an approximate solution using local optimization methods. We parameterize the belief distribution as a Gaussian mixture, and use the Extended Kalman Filter (EKF) to approximate the belief update. Since the EKF is a first-order filter, we can marginalize over the obser…
We develop a qualitative theory of Markov Decision Processes (MDPs) and Partially Observable MDPs that can be used to model sequential decision making tasks when only qualitative information is available. Our approach is based upon an order-of-magnitude approximation of both probabilities and utilities, similar to epsilon-semantics. The result is a qualitative theory that has close ties with the standard maximum-expected-utility theory and is amenable to general planning techniques.
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…
REBA: A Revealed Belief Automaton Framework for Online Planning in Continuous POMDPs
School of Computer Science and Technology, Dalian University of Technology（大连理工大学计算机科学与技术学院）；School of Computer Science and Artificial Intelligence, Liaoning Normal University（辽宁师范大学计算机科学与人工智能学院）；Human-Centered AI Lab, Department of Ecosystem Management, Climate and Biodiversity, BOKU University（BOKU大学生态系统管理与气候生物多样性系人本人工智能实验室）；Institute of Human-Centered Computing, Graz University of Technology（格拉茨技术大学人本计算研究所）
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…
Finite-Time Analysis of MCTS in Continuous POMDP Planning
Technion Autonomous Systems Program (TASP)（技术离子自主系统计划（TASP））；Technion – Israel Institute of Technology（技术离子–以色列理工学院）；Stephen B. Klein Faculty of Aerospace Engineering（史蒂文·B·克莱因航空航天工程学院）；Faculty of Data and Decision Sciences（数据与决策科学学院）
Penetration Testing is a methodology for assessing network security, by generating and executing possible attacks. Doing so automatically allows for regular and systematic testing without a prohibitive amount of human labor. A key question then is how to generate the attacks. This is naturally formulated as a planning problem. Previous work (Lucangeli et al. 2010) used classical planning and hence ignores all the incomplete knowledge that characterizes hacking. More recent work (Sarraute et al. 2011) makes strong independence assumptions for the sake of scaling, and lacks a clear formal concep…
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…
Online POMDP Planning with Anytime Deterministic Optimality Guarantees
Technion Autonomous Systems Program (TASP)（技术学院自主系统计划）；Stephen B. Klein Faculty of Aerospace Engineering（斯蒂芬·B·克莱因航空航天工程学院）；Faculty of Data and Decision Sciences（数据与决策科学学院）
Decentralized planning in uncertain environments is a complex task generally dealt with by using a decision-theoretic approach, mainly through the framework of Decentralized Partially Observable Markov Decision Processes (DEC-POMDPs). Although DEC-POMDPS are a general and powerful modeling tool, solving them is a task with an overwhelming complexity that can be doubly exponential. In this paper, we study an alternate formulation of DEC-POMDPs relying on a sequence-form representation of policies. From this formulation, we show how to derive Mixed Integer Linear Programming (MILP) problems that…
IST Austria（奥地利科学技术研究所）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Partially observable Markov decision processes (POMDPs) are widely used in probabilistic planning problems in which an agent interacts with an environment using noisy and imprecise sensors. We study a setting in which the sensors are only partially defined and the goal is to synthesize "weakest" additional sensors, such that in the resulting POMDP, there is a small-memory policy for the agent that almost-surely (with probability~1) satisfies a reachability objective. We show that the problem is NP-complete, and present a symbolic algorithm by encoding the problem into SAT instances. We illustr…
Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Point-based approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agents belief space. We present a randomized point-based value iteration algorithm called Perseus. The algorithm performs approximate value backup stages, ensuring that in each backup stage the value of each point in the belief set is improved; the key observation is that a single backup may improve the value of many belief points. Con…
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…
Faculty of Informatics, Masaryk University（马萨里克大学信息学院）
We consider partially observable Markov decision processes (POMDPs) modeling an agent that needs a supply of a certain resource (e.g., electricity stored in batteries) to operate correctly. The resource is consumed by agent's actions and can be replenished only in certain states. The agent aims to minimize the expected cost of reaching some goal while preventing resource exhaustion, a problem we call \emph{resource-constrained goal optimization} (RSGO). We take a two-step approach to the RSGO problem. First, using formal methods techniques, we design an algorithm computing a \emph{shield} for …
Geological carbon capture and sequestration (CCS), where CO$_2$ is stored in subsurface formations, is a promising and scalable approach for reducing global emissions. However, if done incorrectly, it may lead to earthquakes and leakage of CO$_2$ back to the surface, harming both humans and the environment. These risks are exacerbated by the large amount of uncertainty in the structure of the storage formation. For these reasons, we propose that CCS operations be modeled as a partially observable Markov decision process (POMDP) and decisions be informed using automated planning algorithms. To …
