Point-Based Value Iteration for Continuous POMDPs

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Point-Based Value Iteration for Continuous POMDPs (2006)

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by Josep M. Porta , Nikos Vlassis , Matthijs T. J. Spaan , Pascal Poupart

Venue:	JOURNAL OF MACHINE LEARNING RESEARCH
Citations:	74 - 4 self

BibTeX

@ARTICLE{Porta06point-basedvalue,
    author = {Josep M. Porta and Nikos Vlassis and Matthijs T. J. Spaan and Pascal Poupart},
    title = {Point-Based Value Iteration for Continuous POMDPs},
    journal = {JOURNAL OF MACHINE LEARNING RESEARCH},
    year = {2006},
    volume = {7},
    pages = {2329--2367}
}

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Abstract

We propose a novel approach to optimize Partially Observable Markov Decisions Processes (POMDPs) defined on continuous spaces. To date, most algorithms for model-based POMDPs are restricted to discrete states, actions, and observations, but many real-world 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 piecewise-linear 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 value-iteration 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.

Keyphrases

continuous pomdps point-based value iteration gaussian mixture continuous state space continuous space continuous bellman backup partially observable markov decision process novel approach effective sampling approach closed form value function monotonic convergence discrete observation reward model observation set model-based pomdps value-iteration algorithm robot navigation perseus algorithm piecewise-linear convex bellman backup continuous action discrete pomdps many real-world problem particle set particular case continuous state

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