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

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.

Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG)

arXiv:2609.16751 [cs.GT]

(or arXiv:2609.16751v1 [cs.GT] for this version)

https://doi.org/10.48550/arXiv.2609.16751 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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