Planning in POMDPs Using Multiplicity Automata

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 automata with no increase in the representation size. Furthermore, we show that the size of the multiplicity automaton is equal to the rank of the predictive state representation. Therefore, we relate both the predictive state representation and POMDPs to the well-founded multiplicity automata literature. Based on the multiplicity automata representation, we provide a planning algorithm which is exponential only in the multiplicity automata rank rather than the number of states of the POMDP. As a result, whenever the predictive state representation is logarithmic in the standard POMDP representation, our planning algorithm is efficient.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005

Perseus: Randomized Point-based Value Iteration for POMDPs

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. Contrary to other point-based 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

A Model Approximation Scheme for Planning in Partially Observable Stochastic Domains

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 original POMDP. We propose to solve the transformed POMDP and use its optimal policy to construct an approximate policy for the original POMDP. By controlling the amount of additional information that the oracle provides, it is possible to find a proper tradeoff between computational time and approximation quality. In terms of algorithmic contributions, we study in details how to exploit region observability in solving the transformed POMDP. To facilitate the study, we also propose a new exact algorithm for general POMDPs. The algorithm is conceptually simple and yet is significantly more efficient than all previous exact algorithms.Comment: See http://www.jair.org/ for any accompanying file

Les POMDP: une solution pour modéliser des problèmes de gestion adaptative en biologie de la conservation

National audienceEn biologie de la conservation, la gestion adaptative est un processus itératif d'amélioration de la gestion par la réduction de l'incertitude à travers une surveillance. La gestion adaptative est l'outil principal pour la conservation d'espèces menacées par les changements planétaires, toutefois les problèmes de gestion adaptative souffrent d'un ensemble pauvre de méthodes de résolution. L'approche courante employée pour résoudre un problème de gestion adaptative est de faire l'hypothèse que l'état du système est connu et que sa dynamique est dans un ensemble de modèles pré-définis. La méthode de résolution utilisée n'est pas satisfaisante parce qu'elle emploie l'algorithme d'itération sur la valeur sur un belief MDP discrétisé qui restreint l'étude à de très petits problèmes. Nous montrons comment dépasser cette limitation en modélisant un problème de gestion adaptative par un type particulier de processus de décision markovien partiellement observable (POMDP) appelé MDP à observabilité mixte (MOMDP). Nous montrons comment simplifier la fonction de valeur, l'opérateur de mise à jour de la fonction de valeur et le calcul de mise à jour de l'état de croyance. Ceci ouvre la voie à des améliorations des algorithmes de résolution des POMDP. Nous illustrons l'utilisation de notre MOMDP "adaptatif" à la gestion d'une population de pinsons diamants de Gould, une espèce d'oiseaux endémique de l'Australie du nord. Notre approche de modélisation simple est une grande avancée pour la résolution de problèmes de gestion adaptative pour la conservation en utilisant des méthodes efficaces pour les POMDP