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arXiv · 1903.07665

Unpredictable Planning Under Partial Observability

Michael Hibbard·Yagiz Savas·Bo Wu·Takashi Tanaka·Ufuk Topcu
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Abstract

We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of a decision-maker's trajectories while guaranteeing the completion of a task expressed by a reward function. First, we prove that a decision-maker with perfect observations can randomize its paths at least as well as a decision-maker with partial observations. Then, focusing on finite-state controllers, we recast the entropy maximization problem as a so-called parameter synthesis problem for a parametric Markov chain (pMC). We show that the maximum entropy of a POMDP is lower bounded by the maximum entropy of this pMC. Finally, we present an algorithm, based on a nonlinear optimization problem, to synthesize an FSC that locally maximizes the entropy of a POMDP over FSCs with the same number of memory states. In numerical examples, we demonstrate the proposed algorithm on motion planning scenarios.

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Michael Hibbard, Yagiz Savas, Bo Wu, Takashi Tanaka, Ufuk Topcu. 2019-03-18. Unpredictable Planning Under Partial Observability. https://arxiv.org/abs/1903.07665

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