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137
Perseus: Randomized pointbased value iteration for POMDPs
 Journal of Artificial Intelligence Research
, 2005
"... Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Pointbased approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agent’s belief space. We present a ra ..."
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Cited by 202 (16 self)
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Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Pointbased approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agent’s belief space. We present a randomized pointbased 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. Contrary to other pointbased methods, Perseus backs up only a (randomly selected) subset of points in the belief set, sufficient for improving the value of each belief point in the set. We show how the same idea can be extended to dealing with continuous action spaces. Experimental results show the potential of Perseus in large scale POMDP problems. 1.
SARSOP: Efficient PointBased POMDP Planning by Approximating Optimally Reachable Belief Spaces
"... Abstract — Motion planning in uncertain and dynamic environments is an essential capability for autonomous robots. Partially observable Markov decision processes (POMDPs) provide a principled mathematical framework for solving such problems, but they are often avoided in robotics due to high computa ..."
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Cited by 191 (16 self)
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Abstract — Motion planning in uncertain and dynamic environments is an essential capability for autonomous robots. Partially observable Markov decision processes (POMDPs) provide a principled mathematical framework for solving such problems, but they are often avoided in robotics due to high computational complexity. Our goal is to create practical POMDP algorithms and software for common robotic tasks. To this end, we have developed a new pointbased POMDP algorithm that exploits the notion of optimally reachable belief spaces to improve computational efficiency. In simulation, we successfully applied the algorithm to a set of common robotic tasks, including instances of coastal navigation, grasping, mobile robot exploration, and target tracking, all modeled as POMDPs with a large number of states. In most of the instances studied, our algorithm substantially outperformed one of the fastest existing pointbased algorithms. A software package implementing our algorithm is available for download at
Pointbased POMDP algorithms: Improved analysis and implementation
 in Proceedings of Uncertainty in Artificial Intelligence
"... Existing complexity bounds for pointbased POMDP value iteration algorithms focus either on the curse of dimensionality or the curse of history. We derive a new bound that relies on both and uses the concept of discounted reachability; our conclusions may help guide future algorithm design. We also ..."
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Cited by 154 (3 self)
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Existing complexity bounds for pointbased POMDP value iteration algorithms focus either on the curse of dimensionality or the curse of history. We derive a new bound that relies on both and uses the concept of discounted reachability; our conclusions may help guide future algorithm design. We also discuss recent improvements to our (pointbased) heuristic search value iteration algorithm. Our new implementation calculates tighter initial bounds, avoids solving linear programs, and makes more effective use of sparsity. Empirical results show speedups of more than two orders of magnitude. 1
MonteCarlo Planning in Large POMDPs
 In Advances in Neural Information Processing Systems 23
, 2010
"... This paper introduces a MonteCarlo algorithm for online planning in large POMDPs. The algorithm combines a MonteCarlo update of the agent’s belief state with a MonteCarlo tree search from the current belief state. The new algorithm, POMCP, has two important properties. First, MonteCarlo sampling ..."
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Cited by 111 (8 self)
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This paper introduces a MonteCarlo algorithm for online planning in large POMDPs. The algorithm combines a MonteCarlo update of the agent’s belief state with a MonteCarlo tree search from the current belief state. The new algorithm, POMCP, has two important properties. First, MonteCarlo sampling is used to break the curse of dimensionality both during belief state updates and during planning. Second, only a black box simulator of the POMDP is required, rather than explicit probability distributions. These properties enable POMCP to plan effectively in significantly larger POMDPs than has previously been possible. We demonstrate its effectiveness in three large POMDPs. We scale up a wellknown benchmark problem, rocksample, by several orders of magnitude. We also introduce two challenging new POMDPs: 10 × 10 battleship and partially observable PacMan, with approximately 10 18 and 10 56 states respectively. Our MonteCarlo planning algorithm achieved a high level of performance with no prior knowledge, and was also able to exploit simple domain knowledge to achieve better results with less search. POMCP is the first general purpose planner to achieve high performance in such large and unfactored POMDPs. 1
Online planning algorithms for POMDPs
 Journal of Artificial Intelligence Research
, 2008
"... Partially Observable Markov Decision Processes (POMDPs) provide a rich framework for sequential decisionmaking 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 ..."
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Cited by 109 (3 self)
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Partially Observable Markov Decision Processes (POMDPs) provide a rich framework for sequential decisionmaking 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 POMDP methods, analyze their properties and discuss their advantages and disadvantages; and to thoroughly evaluate these online approaches in different environments under various metrics (return, error bound reduction, lower bound improvement). Our experimental results indicate that stateoftheart online heuristic search methods can handle large POMDP domains efficiently. 1.
Anytime pointbased approximations for large pomdps
 Journal of Artificial Intelligence Research
, 2006
"... The Partially Observable Markov Decision Process has long been recognized as a rich framework for realworld planning and control problems, especially in robotics. However exact solutions in this framework are typically computationally intractable for all but the smallest problems. A wellknown tech ..."
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Cited by 102 (7 self)
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The Partially Observable Markov Decision Process has long been recognized as a rich framework for realworld planning and control problems, especially in robotics. However exact solutions in this framework are typically computationally intractable for all but the smallest problems. A wellknown 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 belief points which work well in practice. The point selection procedure is combined with pointbased value backups to form an effective anytime POMDP algorithm called PointBased Value Iteration (PBVI). The first aim of this paper is to introduce this algorithm and present a theoretical analysis justifying the choice of belief selection technique. The second aim of this paper is to provide a thorough empirical comparison between PBVI and other stateoftheart POMDP methods, in particular the Perseus algorithm, in an effort to highlight their similarities and differences. Evaluation is performed using both standard POMDP domains and realistic robotic tasks.
PointBased Value Iteration for Continuous POMDPs
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2006
"... We propose a novel approach to optimize Partially Observable Markov Decisions Processes (POMDPs) defined on continuous spaces. To date, most algorithms for modelbased POMDPs are restricted to discrete states, actions, and observations, but many realworld problems such as, for instance, robot na ..."
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Cited by 65 (4 self)
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We propose a novel approach to optimize Partially Observable Markov Decisions Processes (POMDPs) defined on continuous spaces. To date, most algorithms for modelbased POMDPs are restricted to discrete states, actions, and observations, but many realworld problems such as, for instance, robot navigation, are naturally defined on continuous spaces. In this work, we demonstrate that the value function for continuous POMDPs is convex in the beliefs over continuous state spaces, and piecewiselinear convex for the particular case of discrete observations and actions but still continuous states. We also demonstrate that continuous Bellman backups are contracting and isotonic ensuring the monotonic convergence of valueiteration algorithms. Relying on those properties, we extend the PERSEUS algorithm, originally developed for discrete POMDPs, to work in continuous state spaces by representing the observation, transition, and reward models using Gaussian mixtures, and the beliefs using Gaussian mixtures or particle sets. With these representations, the integrals that appear in the Bellman backup can be computed in closed form and, therefore, the algorithm is computationally feasible. Finally, we further extend PERSEUS to deal with continuous action and observation sets by designing effective sampling approaches.
Grasping POMDPs
 in Proc. IEEE Int. Conf. on Robotics and Automation (ICRA
, 2007
"... Abstract — We provide a method for planning under uncertainty for robotic manipulation by partitioning the configuration space into a set of regions that are closed under compliant motions. These regions can be treated as states in a partially observable Markov decision process (POMDP), which can be ..."
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Cited by 60 (3 self)
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Abstract — We provide a method for planning under uncertainty for robotic manipulation by partitioning the configuration space into a set of regions that are closed under compliant motions. These regions can be treated as states in a partially observable Markov decision process (POMDP), which can be solved to yield optimal control policies under uncertainty. We demonstrate the approach on simple grasping problems, showing that it can construct highly robust, efficiently executable solutions. I.
Planning under Uncertainty for Robotic Tasks with Mixed Observability
"... Partially observable Markov decision processes (POMDPs) provide a principled, general framework for robot motion planning in uncertain and dynamic environments. They have been applied to various robotic tasks. However, solving POMDPs exactly is computationally intractable. A major challenge is to sc ..."
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Cited by 45 (4 self)
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Partially observable Markov decision processes (POMDPs) provide a principled, general framework for robot motion planning in uncertain and dynamic environments. They have been applied to various robotic tasks. However, solving POMDPs exactly is computationally intractable. A major challenge is to scale up POMDP algorithms for complex robotic tasks. Robotic systems often have mixed observability: even when a robot’s state is not fully observable, some components of the state may still be so. We use a factored model to represent separately the fully and partially observable components of a robot’s state and derive a compact lowerdimensional representation of its belief space. This factored representation can be combined with any pointbased algorithm to compute approximate POMDP solutions. Experimental results show that on standard test problems, our approach improves the performance of a leading pointbased POMDP algorithm by many times. 1
Motion Planning under Uncertainty for Robotic Tasks with Long Time Horizons
"... Abstract Partially observable Markov decision processes (POMDPs) are a principled mathematical framework for planning under uncertainty, a crucial capability for reliable operation of autonomous robots. By using probabilistic sampling, pointbased POMDP solvers have drastically improved the speed of ..."
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Cited by 39 (2 self)
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Abstract Partially observable Markov decision processes (POMDPs) are a principled mathematical framework for planning under uncertainty, a crucial capability for reliable operation of autonomous robots. By using probabilistic sampling, pointbased POMDP solvers have drastically improved the speed of POMDP planning, enabling POMDPs to handle moderately complex robotic tasks. However, robot motion planning tasks with long time horizons remain a severe obstacle for even the fastest pointbased POMDP solvers today. This paper proposes Milestone Guided Sampling (MiGS), a new pointbased POMDP solver, which exploits state space information to reduce the effective planning horizon. MiGS samples a set of points, called milestones, from a robot’s state space, uses them to construct a compact, sampled representation of the state space, and then uses this representation of the state space to guide sampling in the belief space. This strategy reduces the effective planning horizon, while still capturing the essential features of the belief space with a small number of sampled points. Preliminary results are very promising. We tested MiGS in simulation on several difficult POMDPs modeling distinct robotic tasks with long time horizons; they are impossible with the fastest pointbased POMDP solvers today. MiGS solved them in a few minutes. 1