Unpredictable Planning Under Partial Observability

• Main Authors: Hibbard, Michael, Savas, Yagiz, Wu, Bo, Tanaka, Takashi, Topcu, Ufuk
• Format: Journal Article
• Language: English
• Published: 18.03.2019
• Subjects: Mathematics - Optimization and Control
• DOI: 10.48550/arxiv.1903.07665

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.