POMDPs under Probabilistic Semantics

Krishnendu Chatterjee; Martin Chmelík

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arXiv · 1308.4846

POMDPs under Probabilistic Semantics

Krishnendu Chatterjee·Martin Chmelík

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Abstract

We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated to every transition, and the payoff of an infinite path is the long-run average of the rewards. We consider two types of path constraints: (i) quantitative constraint defines the set of paths where the payoff is at least a given threshold λ in (0, 1]; and (ii) qualitative constraint which is a special case of quantitative constraint with λ = 1. We consider the computation of the almost-sure winning set, where the controller needs to ensure that the path constraint is satisfied with probability 1. Our main results for qualitative path constraint are as follows: (i) the problem of deciding the existence of a finite-memory controller is EXPTIME-complete; and (ii) the problem of deciding the existence of an infinite-memory controller is undecidable. For quantitative path constraint we show that the problem of deciding the existence of a finite-memory controller is undecidable.

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Krishnendu Chatterjee, Martin Chmelík. 2013-08-22. POMDPs under Probabilistic Semantics. https://arxiv.org/abs/1308.4846

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