Regret Minimization with Adaptive Opponents in Repeated Games

This research explores regret minimization within the context of repeated games, specifically addressing scenarios where opponents exhibit adaptive behaviors based on historical play. Traditional external regret metrics in online learning are often insufficient to capture such dynamic adaptivity. To overcome this limitation, the concept of Repeated Policy Regret (RP-Regret) is introduced as a novel game-theoretic metric. RP-Regret quantifies the disparity between the accumulated utility realized during play and the optimal utility achievable in hindsight, assuming all players can dynamically adjust their strategies in response to the evolving game history. This metric offers advantages over existing regret notions by being inherently suited for repeated game dynamics, enabling more robust comparators and

accommodating less constrained opponent strategies, potentially leading to the discovery of superior equilibria when universally minimized. The study identifies critical conditions necessary for achieving sublinear RP-Regret over time, focusing on the variability of comparator strategies and the memory capacities of both comparator and opponent strategies. Furthermore, the project investigates algorithmic approaches to minimize RP-Regret, acknowledging its inherent non-convexity within the strategy space, and proposes specific algorithms to address this challenge.

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