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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

Chinese

POSward 顯示可觀察部分對象的 Markov 決策過程模型代理,在部分可觀察的框架下運作,而對抗環境解決了過渡概率的不確定性。 報酬目標,如折扣總和長期平均值,以及在有限和無限地平線下累積的報酬,允許量化代理的效用性。 我們考慮在所有四個報酬目標下解決 RPOMDP 的問題,其中目標是決定任何風險措施的價值是否超過一定的值。 我們考慮到不同的風險措施,如 (1)~預期值, (2)~平均差異(MV), (3)~有條件的法則價值 - 風險 (VaPO),和 (4)～分解風險(ERisk)。 我們的結果可以以以下簡單的形式分解。 我們

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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