Regret Minimization with Adaptive Opponents in Repeated Games

2026-06-06 · Source: cs.AI updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning · Depth: Expert, medium

Summary

A new research paper introduces Repeated Policy Regret (RP-Regret), a game-theoretic metric designed for repeated games with adaptive opponents. Developed by researchers from MIT, OpenAI, and the University of Maryland, and accepted for COLT 2026, RP-Regret addresses the limitations of standard external regret, which fails to account for opponents' responsiveness to play history. This new metric measures the difference between realized and best-in-hindsight accumulated utility, allowing dynamic comparator strategies and enabling the discovery of more cooperative, higher-utility equilibria, such as in Stag-Hunt. Despite the non-convexity of RP-Regret minimization, the authors propose three algorithms: one using an optimization oracle, another minimizing a convex linearized surrogate called Local Repeated Policy Regret (LRP-Regret), and a third for scenarios where opponents change strategies slowly. The work also establishes conditions for sublinear RP-Regret and its relationship to learning subgame perfect equilibria.

Key takeaway

For AI Scientists and Research Scientists developing multi-agent learning systems, relying solely on external regret in repeated games can lead to suboptimal outcomes. You should consider adopting Repeated Policy Regret (RP-Regret) or its linearized variant, LRP-Regret, to account for adaptive opponents. Implementing these new regret notions can enable your agents to learn more cooperative strategies and converge to higher-utility subgame perfect equilibria, as demonstrated in games like Stag-Hunt. This approach offers a robust method for achieving superior collective performance in dynamic, interactive environments.

Key insights

Repeated Policy Regret (RP-Regret) enables finding higher-utility equilibria in repeated games by modeling adaptive opponents and dynamic strategies.

Principles

• External regret fails with adaptive opponents.
• Adaptive opponent models can achieve better game equilibria.
• Non-convex regret minimization can be tackled via linearization.

Method

Minimize the non-convex RP-Regret using an optimization oracle, a convex linearized surrogate (LRP-Regret), or direct minimization for slowly changing opponents, leveraging Markov game reformulations.

In practice

• Achieve more cooperative solutions in games like Stag-Hunt.
• Learn subgame perfect equilibria in repeated games.

Topics

• Repeated Games
• Regret Minimization
• Adaptive Opponents
• Non-convex Optimization
• Multi-Agent Learning
• Game Theory Equilibria

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.