Robust partially observable Markov decision processes (robust POMDPs) extend classical POMDPs to handle additional uncertainty on the transition and observation probabilities via so-called uncertainty sets. Policies for robust POMDPs must not only be memory-based to account for partial observability but also robust against model uncertainty to account for the worst-case instances from the uncertainty sets. We propose the pessimistic iterative planning (PIP) framework, which finds robust memory-based policies for robust POMDPs. PIP alternates between two main steps: (1) selecting an adversarial (non-robust) POMDP via worst-case probability instances from the uncertainty sets; and (2) computing a finite-state controller (FSC) for this adversarial POMDP. We evaluate the performance of this FSC on the original robust POMDP and use this evaluation in step (1) to select the next adversarial POMDP. Within PIP, we propose the rFSCNet algorithm. In each iteration, rFSCNet finds an FSC through a recurrent neural network trained using supervision policies optimized for the adversarial POMDP. The empirical evaluation in four benchmark environments showcases improved robustness against a baseline method in an ablation study and competitive performance compared to a state-of-the-art robust POMDP solver.

Partially observable Markov decision processes (POMDPs) rely on the key assumption that probability distributions are precisely known. Robust POMDPs (RPOMDPs) alleviate this concern by defining imprecise probabilities, referred to as uncertainty sets. While robust MDPs have been studied extensively, work on RPOMDPs is limited and primarily focuses on algorithmic solution methods. We expand the theoretical understanding of RPOMDPs by showing that 1) different assumptions on the uncertainty sets affect optimal policies and values; 2) RPOMDPs have a partially observable stochastic game (POSG) semantic; and 3) the same RPOMDP with different assumptions leads to semantically different POSGs and, thus, different policies and values. These novel semantics for RPOMDPS give access to results for the widely studied POSG model; concretely, we show the existence of a Nash equilibrium. Finally, we classify the existing RPOMDP literature using our semantics, clarifying under which uncertainty assumptions these existing works operate.

Partial observability and uncertainty are common problems in sequential decision-making that particularly impede the use of formal models such as Markov decision processes (MDPs). However, in practice, agents may be able to employ costly sensors to measure their environment and resolve partial observability by gathering information. Moreover, imprecise transition functions can capture model uncertainty. We combine these concepts and extend MDPs to robust active-measuring MDPs (RAM-MDPs). We present an active-measure heuristic to solve RAM-MDPs efficiently and show that model uncertainty can, counterintuitively, let agents take fewer measurements. We propose a method to counteract this behavior while only incurring a bounded additional cost. We empirically compare our methods to several baselines and show their superior scalability and performance.