Constant Swap Regret in General-Sum Games via Optimistic Transition Matrices

2026-09-15

AI Summary

本文提出了在全信息反馈下有限多人常和博弈中实现恒定个体交换遗憾的学习动态方法，通过预测偏差收益并更新转移矩阵来达成。

Abstract

We give deterministic and uncoupled learning dynamics for finite multiplayer general-sum games under full-information feedback that achieve constant individual swap regret, independent of the horizon $T$. With $n$ players and at most $m$ actions each, the individual swap regret of every player is $O(\sqrt{n} m \log m \log^{5/2}(nm))$ at every finite horizon. Each player predicts the deviation gains, then uses these predictions to update a row-stochastic transition matrix, and plays its stationary distribution. The proof combines a potential argument exploiting stationarity with a two-scale higher-order prediction analysis, using rooted-tree representations to handle the nonlinear dependence of deviation gains on the stationary distributions. An adversarially robust variant, obtained through a generic common-prefix switching wrapper, preserves the self-play bound up to a universal constant and guarantees individual swap regret at most $7\sqrt{m T \log m}$ in the adversarial setting.

Problem

• swap regret
• general-sum games
• learning dynamics

Innovation

• constant individual swap regret
• optimistic transition matrices
• full-information feedback
• rooted-tree representations