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Reward Objectives for Robust (PO)MDPs: A Law-Preserving Equivalence with (Partially Observable) Games

Durgam Latha, Dion Reji, Dorde Zikelic, Shankara Narayanan Krishna · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26568 · cited by 0 works (OpenAlex) · open-access PDF

Korean

POSward는 부분적으로 관찰할 수 있는 Markov 의사 결정 프로세스 모델 에이전트를 보여줍니다. POSward는 부분적으로 관찰할 수 있는 프레임에서 작용하는 상대적 환경이 전환 확률에서 불확실성을 해결하는 반면 POSward는 부분적으로 관찰할 수 있는 모델 에이전트를 보여줍니다. POSward는 discounted-sum, long-run average and cumulative reward under finite and infinite horizons와 같은 보상 목표를 보여줍니다. 우리는 RPOMDP를 모든 네 개의 보상 목표 아래에서 해결하는 문제를 고려합니다. 목표는 보상 목표와 관련된 위험 측정의 가치가 주어진 한계를 초과하는지 결정하는 것입니다. 우리는 (1)~예상치 않은 가치, (2)~평균 변수 (MV), (3)~조건적 인 가치

Machine translation (Meta M2M100); the English original follows.

Abstract

Robust partially observable Markov decision processes model agents that act under partial observability while adversarial environment resolves uncertainty in the transition probabilities. Reward objectives such as discounted-sum, long-run average and cumulative reward under finite and infinite horizons allow quantifying the utility of an agent. We consider the problem of solving RPOMDPs under all four reward objectives, where the goal is to decide whether the value of a risk measure with respect to a reward objective exceeds a given threshold. We consider different risk measures, such as (1)~expected value, (2)~mean-variance (MV), (3)~conditional value-at-risk (CVaR), and (4)~entropic risk (ERisk). Our results can be summarized as follows. First, we formalize the class of law-invariant risk measures, that subsume all four risk measures above. Second, we propose a unified framework for solving RPOMDPs with discounted-sum, long-run average and cumulative reward objectives under any law-invariant risk measure, by reducing the problem to solving partially observable stochastic games (POSGs). Our unified framework applies to (s,a)-rectangular RPOMDPs with polytopic uncertainty sets, which we show to be {\em equivalent} to POSGs, for each of the four reward objectives and any law-invariant risk measure. We prove equivalence by designing logspace reductions between the RPOMDP and POSG models, that map strategies to strategies and preserve the distribution of the reward objective, up to a constant rescaling factor. Third, as a corollary, we derive new computational complexity results for R(PO)MDPs and POSGs. In particular, we show that solving (s,a)-rectangular RMDPs is as hard as solving simple stochastic games.

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Topics: Equivalence (formal languages), Observability, Markov decision process, Mathematics, Markov process, Mathematical optimization

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