Newest papers

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

French

POSward est l'objectif résolument observable des modèles de processus de décision de Markov qui agissent sous l'observabilité partielle tandis que l'environnement adversaire résout l'incertitude dans les probabilités de transition. Objectifs de récompense tels que la somme réduite, la moyenne à long terme et la récompense cumulative sous les horizons fini et infini permettent de quantifier l'utilité d'un agent. Nous considérons le problème de résoudre les RPOMDPs sous les quatre objectifs de récompense, où l'objectif est de décider si la valeur d'une mesure de risque par rapport à un objectif de récompense dépasse un seuil donné. Nous considérons différentes mesures de risque, telles que (1)~la valeur attendue et les horizons inf

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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