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.

Robust partially observable Markov decision processes (RPOMDPs) model sequential decision-making problems under partial observability, where an agent must be robust against a range of dynamics. RPOMDPs can be viewed as a two-player game between an agent, who selects actions, and nature, who adversarially selects the dynamics. Evaluating an agent policy requires finding an adversarial nature policy, which is computationally challenging. In this paper, we advance the evaluation of agent policies for RPOMDPs in three ways. First, we discuss suitable benchmarks. We observe that for some RPOMDPs, an optimal agent policy can be found by considering only subsets of nature policies, making them easier to solve. We formalize this concept of solvability and construct three benchmarks that are only solvable for expressive sets of nature policies. Second, we describe a new method to evaluate agent policies for RPOMDPs by solving an equivalent MDP. Third, we lift two well-known upper bounds from POMDPs to RPOMDPs, which can be used to efficiently approximate the optimality gap of a policy and serve as baselines. Our experimental evaluation shows that (1) our proposed benchmarks cannot be solved by assuming naive nature policies, (2) our method of evaluating policies is accurate, and (3) the upper bounds provide solid baselines for evaluation.