Multi-Environment POMDPs: Discrete Model Uncertainty Under Partial Observability

Eline M. Bovy, Caleb Probine, Marnix Suilen, ufuk topcu, Nils Jansen

Keywords: POMDPs, Robustness, Multi-environment

TL;DR: We characterize and provide algorithms for multi-environment POMDPs.

Abstract: Multi-environment POMDPs (ME-POMDPs) extend standard POMDPs with discrete model uncertainty. ME-POMDPs represent a finite set of POMDPs that share the same state, action, and observation spaces, but may arbitrarily vary in their transition, observation, and reward models. Such models arise, for instance, when multiple domain experts disagree on how to model a problem. The goal is to find a single policy that is robust against any choice of POMDP within the set, *i.e.*, a policy that maximizes the worst-case reward across all POMDPs. We generalize and expand on existing work in the following way. First, we show that ME-POMDPs can be generalized to POMDPs *with sets of initial beliefs*, which we call *adversarial-belief POMDPs* (AB-POMDPs). Second, we show that any arbitrary ME-POMDP can be reduced to a ME-POMDP that only varies in its transition and reward functions or only in its observation and reward functions, while preserving (optimal) policies. We then devise exact and approximate (point-based) algorithms to compute robust policies for AB-POMDPs, and thus ME-POMDPs. We demonstrate that we can compute policies for standard POMDP benchmarks extended to the multi-environment setting.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 23953