Robust Finite-State Controllers for Uncertain POMDPs

Uncertain partially observable Markov decision processes (uPOMDPs) allow the probabilistic transition and observation functions of standard POMDPs to belong a so-called uncertainty set. Such uncertainty, referred as epistemic captures uncountable sets probability distributions caused by, for instance, lack data available. We develop an algorithm compute finite-memory policies uPOMDPs that robustly satisfy specifications against any admissible distribution. In general, computing such is theoretically practically intractable. provide efficient solution this problem in four steps. (1) state underlying nonconvex optimization with infinitely many constraints. (2) A dedicated dualization scheme yields dual still but has finitely (3) linearize (4) solve resulting finite linear program obtain locally optimal solutions original problem. The formulation exponentially smaller than those from existing methods. demonstrate applicability our using large instances aircraft collision-avoidance scenario novel spacecraft motion planning case study.