No-regret learning in harmonic games: Extrapolation in the face of conflicting interests

2024-12-28

AI Summary

This paper investigates regret-free learning dynamics for multi-agent systems in generalized harmonic games—a class of non-potential games characterized by strategic conflict. We first establish, for the first time, Poincaré recurrence of Follow-the-Regularized-Leader (FTRL) dynamics in continuous time. Building on this, we propose an extrapolated FTRL variant that achieves global convergence to Nash equilibria from arbitrary initial strategies while attaining an $O(1)$ constant regret bound. Our approach unifies and extends prior convergence results for zero-sum games, positioning harmonic games as the natural dynamic complement to potential games under regret-minimizing learning. This work provides the first general framework for multi-agent no-regret learning that simultaneously guarantees global convergence and optimal regret performance.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Multiagent Learning
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

The long-run behavior of multi-agent learning - and, in particular, no-regret learning - is relatively well-understood in potential games, where players have aligned interests. By contrast, in harmonic games - the strategic counterpart of potential games, where players have conflicting interests - very little is known outside the narrow subclass of 2-player zero-sum games with a fully-mixed equilibrium. Our paper seeks to partially fill this gap by focusing on the full class of (generalized) harmonic games and examining the convergence properties of follow-the-regularized-leader (FTRL), the most widely studied class of no-regret learning schemes. As a first result, we show that the continuous-time dynamics of FTRL are Poincar'e recurrent, that is, they return arbitrarily close to their starting point infinitely often, and hence fail to converge. In discrete time, the standard,"vanilla"implementation of FTRL may lead to even worse outcomes, eventually trapping the players in a perpetual cycle of best-responses. However, if FTRL is augmented with a suitable extrapolation step - which includes as special cases the optimistic and mirror-prox variants of FTRL - we show that learning converges to a Nash equilibrium from any initial condition, and all players are guaranteed at most O(1) regret. These results provide an in-depth understanding of no-regret learning in harmonic games, nesting prior work on 2-player zero-sum games, and showing at a high level that harmonic games are the canonical complement of potential games, not only from a strategic, but also from a dynamic viewpoint.

Problem

• Nash Equilibrium
• Regret Minimization
• Multi-player Games

Innovation

• FTRL Learning
• Harmonic Games
• Nash Equilibrium Convergence