Policy Regret Minimization in Partially Observable Markov Games

ICLR 2026 Conference Withdrawn SubmissionLan Sang, Thanh Nguyen-Tang
Partially Observable Markov GamesPolicy RegretWeakly-RevealingObservable Operator Model
Abstract:

We study policy regret minimization in partially observable Markov games (POMGs) between a learner and a strategic adaptive opponent who adapts to the learner's past strategies. We develop a model-based optimistic framework that operates on the learner-observable process using \emph{joint} MLE confidence set and introduce an Observable Operator Model-based causal decomposition that disentangles the coupling between the world and the adversary model. Under multi-step weakly revealing observations and a bounded-memory, stationary and posterior-Lipschitz opponent, we prove an O(T)\mathcal{O}(\sqrt{T}) policy regret bound. This work advances regret analysis from Markov games to POMGs and provides the first policy regret guarantee under imperfect information against an adaptive opponent.

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Overview

Overall Novelty Assessment

The paper contributes a model-based optimistic framework for policy regret minimization in partially observable Markov games against adaptive opponents, achieving the first O(√T) policy regret bound under imperfect information. It resides in the 'Policy Regret Minimization Against Adaptive Opponents' leaf, which contains only two papers total. This represents a sparse research direction within the broader taxonomy of nine papers across four main branches, suggesting the work addresses a relatively underexplored intersection of partial observability, strategic adaptation, and regret guarantees.

The taxonomy reveals neighboring work in counterfactual regret minimization, policy gradient methods, and value function approaches, but these branches tackle different aspects of the problem. Counterfactual regret methods focus on regret matching without the model-based optimism framework presented here. Policy gradient and actor-critic branches emphasize gradient-based optimization rather than regret-theoretic guarantees. The formal models branch establishes foundational frameworks but does not provide algorithmic regret bounds. The paper's position bridges theoretical regret analysis with partial observability in competitive settings, a boundary less populated than adjacent areas.

Among twenty candidates examined, the joint MLE confidence set contribution shows one refutable candidate from ten examined, indicating some prior work on confidence-based exploration in related settings. The Observable Operator Model decomposition was not tested against candidates, leaving its novelty less characterized by this search. The policy regret guarantee contribution examined ten candidates with none refuting it, suggesting this specific combination—POMGs, adaptive opponents, imperfect information—has limited direct precedent within the search scope. The analysis reflects top-K semantic matches and citation expansion, not exhaustive coverage.

Given the limited search scope of twenty candidates and the sparse taxonomy leaf, the work appears to occupy a relatively novel position at the intersection of partial observability and adaptive regret minimization. The analysis does not capture the full landscape of related work in broader game theory or reinforcement learning communities, so conclusions remain provisional pending deeper literature review.

Taxonomy

Core-task Taxonomy Papers
9
3
Claimed Contributions
20
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: policy regret minimization in partially observable Markov games. The field structure reflects a blend of algorithmic innovation and theoretical rigor. The taxonomy organizes work into four main branches: Regret Minimization Algorithms and Theory, which develops guarantees and convergence properties for learning in competitive settings; Policy Gradient and Actor-Critic Methods, which leverage gradient-based optimization to handle high-dimensional or continuous action spaces; Value Function and Dynamic Programming Approaches, which build on classical planning techniques adapted to partial observability and multi-agent interaction; and Formal Models and Theoretical Foundations, which establish the mathematical underpinnings of equilibrium concepts and information structures. Representative works such as HSVI Zero-Sum[1] illustrate value-based planning under partial observability, while Actor-Critic POMDP[4] and Deep Decentralized Combat[7] demonstrate gradient-based methods in complex domains. Sampling Nash Equilibria[6] and Provable Extensive-Form Learning[9] contribute equilibrium computation and convergence analysis, and Rethinking POMDP Models[8] and History Process[5] refine the formal modeling of belief and history. A particularly active line of work focuses on regret bounds and sample efficiency when facing adaptive opponents, where the challenge is to learn policies that minimize regret even as adversaries adjust their strategies. Policy Regret POMG[0] sits squarely in this branch, emphasizing policy regret guarantees against adaptive opponents in partially observable settings. It shares thematic ground with Sample-Efficient POMG[3], which also targets sample complexity in multi-agent partial observability, and with Regret Deep RL[2], which explores regret-based objectives in deep reinforcement learning. The main trade-offs revolve around computational tractability versus theoretical guarantees: gradient methods scale well but often lack tight regret bounds, while value-based and equilibrium-focused approaches offer stronger theory at the cost of higher computational overhead. Open questions include tightening regret bounds under weaker assumptions and bridging the gap between provable algorithms and practical deep learning techniques.

Claimed Contributions

Model-based optimistic framework with joint MLE confidence set

The authors propose a unified algorithmic framework (MOMLE) that maintains a single joint confidence set over both world and adversary model parameters, rather than separate confidence sets. This design addresses the fundamental identifiability challenge in POMGs where the learner's observations entangle environment dynamics and opponent strategies.

10 retrieved papers
Can Refute
Observable Operator Model-based causal decomposition

The authors develop a novel causal factorization showing that each per-step operator decomposes as a composition of a world channel operator (depending only on environment parameters) and an adversary channel operator (depending only on adversary and learner policy). This decomposition enables separate analysis of world and adversary model learning despite their coupled dynamics.

0 retrieved papers
First policy regret guarantee for POMGs under adaptive opponents

The authors prove an O(√T) policy regret bound for multi-step weakly revealing POMGs with bounded-memory, stationary, and posterior-Lipschitz adaptive opponents. This represents the first sublinear policy regret result for partially observable settings, extending prior work that was limited to fully observable Markov games.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Model-based optimistic framework with joint MLE confidence set

The authors propose a unified algorithmic framework (MOMLE) that maintains a single joint confidence set over both world and adversary model parameters, rather than separate confidence sets. This design addresses the fundamental identifiability challenge in POMGs where the learner's observations entangle environment dynamics and opponent strategies.

Contribution

Observable Operator Model-based causal decomposition

The authors develop a novel causal factorization showing that each per-step operator decomposes as a composition of a world channel operator (depending only on environment parameters) and an adversary channel operator (depending only on adversary and learner policy). This decomposition enables separate analysis of world and adversary model learning despite their coupled dynamics.

Contribution

First policy regret guarantee for POMGs under adaptive opponents

The authors prove an O(√T) policy regret bound for multi-step weakly revealing POMGs with bounded-memory, stationary, and posterior-Lipschitz adaptive opponents. This represents the first sublinear policy regret result for partially observable settings, extending prior work that was limited to fully observable Markov games.

Policy Regret Minimization in Partially Observable Markov Games | Novelty Validation