Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are continuous or hybrid, which is often the case for physical systems. While recent online sampling-based POMDP algorithms that plan with observation likelihood weighting have shown practical effectiveness, a general theory characterizing the approximation error of the particle filtering techniques that these algorithms use has not previously been proposed. Our main contribution is bounding the error between any POMDP and its corresponding finite sample particle belief MDP (PB-MDP) approximation. This fundamental bridge between PB-MDPs and POMDPs allows us to adapt any sampling-based MDP algorithm to a POMDP by solving the corresponding particle belief MDP, thereby extending the convergence guarantees of the MDP algorithm to the POMDP. Practically, this is implemented by using the particle filter belief transition model as the generative model for the MDP solver. While this requires access to the observation density model from the POMDP, it only increases the transition sampling complexity of the MDP solver by a factor of $\mathcal{O}(C)$, where $C$ is the number of particles. Thus, when combined with sparse sampling MDP algorithms, this approach can yield algorithms for POMDPs that have no direct theoretical dependence on the size of the state and observation spaces. In addition to our theoretical contribution, we perform five numerical experiments on benchmark POMDPs to demonstrate that a simple MDP algorithm adapted using PB-MDP approximation, Sparse-PFT, achieves performance competitive with other leading continuous observation POMDP solvers.
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.
Belief compression improves the tractability of large-scale partially observable Markov decision processes (POMDPs) by finding projections from high-dimensional belief space onto low-dimensional approximations, where solving to obtain action selection policies requires fewer computations. This paper develops a unified theoretical framework to analyse three existing linear belief compression approaches, including value-directed compression and two non-negative matrix factorisation (NMF) based algorithms. The results indicate that all the three known belief compression methods have their own cri…
University of British Columbia（不列颠哥伦比亚大学）；University of Toronto（多伦多大学）
We consider the problem belief-state monitoring for the purposes of implementing a policy for a partially-observable Markov decision process (POMDP), specifically how one might approximate the belief state. Other schemes for belief-state approximation (e.g., based on minimixing a measures such as KL-diveregence between the true and estimated state) are not necessarily appropriate for POMDPs. Instead we propose a framework for analyzing value-directed approximation schemes, where approximation quality is determined by the expected error in utility rather than by the error in the belief state it…
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…
Planning robust executions under uncertainty is a fundamental challenge for building autonomous robots. Partially Observable Markov Decision Processes (POMDPs) provide a standard framework for modeling uncertainty in many applications. In this work, we study POMDPs with safe-reachability objectives, which require that with a probability above some threshold, a goal state is eventually reached while keeping the probability of visiting unsafe states below some threshold. This POMDP formulation is different from the traditional POMDP models with optimality objectives and we show that in some case…
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…
Massachusetts Institute of Technology（麻省理工学院）；Carnegie Mellon University（卡内基梅隆大学）；Stanford University（斯坦福大学）
Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a consequence of computing an exact, optimal policy over the entire belief space. However, in real-world POMDP problems, computing the optimal policy for the full belief space is often unnecessary for good control even for problems with complicated policy classes. The beliefs experienced by the controller often lie near a structured, low-dimensional subspace emb…
Tru-POMDP: Task Planning Under Uncertainty via Tree of Hypotheses and Open-Ended POMDPs
Shanghai Jiao Tong University（上海交通大学）；Shanghai Innovation Institute（上海创新研究院）；East China Normal University（华东师范大学）；Beijing University of Posts and Telecommunications（北京邮电大学）
Partially Observable Markov Decision Processes (POMDPs) offer a promising world representation for autonomous agents, as they can model both transitional and perceptual uncertainties. Calculating the optimal solution to POMDP problems can be computationally expensive as they require reasoning over the (possibly infinite) space of beliefs. Several approaches have been proposed to overcome this difficulty, such as discretizing the belief space, point-based belief sampling, and Monte Carlo tree search. The Real-Time Dynamic Programming approach of the RTDP-Bel algorithm approximates the value fun…
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…
Technion - Israel Institute of Technology（以色列理工学院）
Although risk awareness is fundamental to an online operating agent, it has received less attention in the challenging continuous domain and under partial observability. This paper presents a novel formulation and solution for risk-averse belief-dependent probabilistically constrained continuous POMDP. We tackle a demanding setting of belief-dependent reward and constraint operators. The probabilistic confidence parameter makes our formulation genuinely risk-averse and much more flexible than the state-of-the-art chance constraint. Our rigorous analysis shows that in the stiffest probabilistic…
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…
Department of Computer Science（计算机科学系）；Department of Aerospace EngineeringTechnion - Israel Institute of Technology（以色列理工学院航空航天工程系）；Technion - Israel Institute of Technology（以色列理工学院）；Technion - Israel Institute of Technology, Haifa 32000, Israel（以色列理工学院（海法））
In this paper, we consider online planning in partially observable domains. Solving the corresponding POMDP problem is a very challenging task, particularly in an online setting. Our key contribution is a novel algorithmic approach, Simplified Information Theoretic Belief Space Planning (SITH-BSP), which aims to speed-up POMDP planning considering belief-dependent rewards, without compromising on the solution's accuracy. We do so by mathematically relating the simplified elements of the problem to the corresponding counterparts of the original problem. Specifically, we focus on belief simplifi…
The Partially Observable Markov Decision Process has long been recognized as a rich framework for real-world planning and control problems, especially in robotics. However exact solutions in this framework are typically computationally intractable for all but the smallest problems. A well-known technique for speeding up POMDP solving involves performing value backups at specific belief points, rather than over the entire belief simplex. The efficiency of this approach, however, depends greatly on the selection of points. This paper presents a set of novel techniques for selecting informative b…
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 us…
Rutgers University（罗格斯大学）；Electronics and Telecommunications Research Institute（电子与电信研究所）；Rutgers Center for Cognitive Science（罗格斯认知科学中心）
Object-centric world models provide structured representation of the scene and can be an important backbone in reinforcement learning and planning. However, existing approaches suffer in partially-observable environments due to the lack of belief states. In this paper, we propose Structured World Belief, a model for learning and inference of object-centric belief states. Inferred by Sequential Monte Carlo (SMC), our belief states provide multiple object-centric scene hypotheses. To synergize the benefits of SMC particles with object representations, we also propose a new object-centric dynamic…
University of Alberta（阿尔伯塔大学）；Charles University（查理大学）；EquiLibre Technologies, Inc.（EquiLibre科技公司）；Alberta Machine Intelligence Institute (Amii)（阿尔伯塔机器智能研究所）
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）
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）
We present a major improvement to the incremental pruning algorithm for solving partially observable Markov decision processes. Our technique targets the cross-sum step of the dynamic programming (DP) update, a key source of complexity in POMDP algorithms. Instead of reasoning about the whole belief space when pruning the cross-sums, our algorithm divides the belief space into smaller regions and performs independent pruning in each region. We evaluate the benefits of the new technique both analytically and experimentally, and show that it produces very significant performance gains. The resul…
In this study I proposed a filtering beliefs method for improving performance of Partially Observable Markov Decision Processes(POMDPs), which is a method wildly used in autonomous robot and many other domains concerning control policy. My method search and compare every similar belief pair. Because a similar belief have insignificant influence on control policy, the belief is filtered out for reducing training time. The empirical results show that the proposed method outperforms the point-based approximate POMDPs in terms of the quality of training results as well as the efficiency of the met…
Online Hybrid-Belief POMDP with Coupled Semantic-Geometric Models
Department of Aerospace Engineering, Technion - Israel Institute of Technology（航空航天工程系，技术离子理工学院）；Department of Aerospace Engineering and with the Department of Data and Decision Science（航空航天工程系和数据与决策科学系）；Technion - Israel Institute of Technology（技术离子理工学院）
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…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
In real-world scenarios, the observation data for reinforcement learning with continuous control is commonly noisy and part of it may be dynamically missing over time, which violates the assumption of many current methods developed for this. We addressed the issue within the framework of partially observable Markov Decision Process (POMDP) using a model-based method, in which the transition model is estimated from the incomplete and noisy observations using a newly proposed surrogate loss function with local approximation, while the policy and value function is learned with the help of belief …
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…
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…
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 …
The focus of this paper is on solving multi-robot planning problems in continuous spaces with partial observability. Decentralized partially observable Markov decision processes (Dec-POMDPs) are general models for multi-robot coordination problems, but representing and solving Dec-POMDPs is often intractable for large problems. To allow for a high-level representation that is natural for multi-robot problems and scalable to large discrete and continuous problems, this paper extends the Dec-POMDP model to the decentralized partially observable semi-Markov decision process (Dec-POSMDP). The Dec-…
This paper proposes a reinforcement learning method for controller synthesis of autonomous systems in unknown and partially-observable environments with subjective time-dependent safety constraints. Mathematically, we model the system dynamics by a partially-observable Markov decision process (POMDP) with unknown transition/observation probabilities. The time-dependent safety constraint is captured by iLTL, a variation of linear temporal logic for state distributions. Our Reinforcement learning method first constructs the belief MDP of the POMDP, capturing the time evolution of estimated state…
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）
IRIT – Paul Sabatier University（IRIT - 图卢兹第三大学（保罗·萨巴蒂埃大学））；Onera – The French Aerospace Lab（法国国家航空航天研究中心）
Possibilistic and qualitative POMDPs (pi-POMDPs) are counterparts of POMDPs used to model situations where the agent's initial belief or observation probabilities are imprecise due to lack of past experiences or insufficient data collection. However, like probabilistic POMDPs, optimally solving pi-POMDPs is intractable: the finite belief state space exponentially grows with the number of system's states. In this paper, a possibilistic version of Mixed-Observable MDPs is presented to get around this issue: the complexity of solving pi-POMDPs, some state variables of which are fully observable, …
Interleaved POMDP Planning for Multi-Object Search in Unknown Multi-Room Household Environments
Georgia Institute of Technology（佐治亚理工学院）；The Hong Kong University of Science and Technology（香港科技大学）；Ising AI（伊辛人工智能公司）；MIT（麻省理工学院）；Notre Dame University（圣母大学）
In this article we propose a qualitative (ordinal) counterpart for the Partially Observable Markov Decision Processes model (POMDP) in which the uncertainty, as well as the preferences of the agent, are modeled by possibility distributions. This qualitative counterpart of the POMDP model relies on a possibilistic theory of decision under uncertainty, recently developed. One advantage of such a qualitative framework is its ability to escape from the classical obstacle of stochastic POMDPs, in which even with a finite state space, the obtained belief state space of the POMDP is infinite. Instead…
