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Verified regret matching and finite-time equilibrium computation

Arthur Freitas Ramos

Palomar Registrypalomar/PALOMAR-2026-09-08-000002Sep 8, 2026cs.GTscore 0

For finite nonempty action sets and unit-interval full-information payoffs, regret matching and regret matching+ have cumulative external regret at most the square root of the product of the number of actions and the horizon, against every fixed pure or mixed comparator. In finite two-player zero-sum matrix games, simultaneous self-play gives an explicit finite-time approximate Nash guarantee for uniformly averaged strategies. A finite-vector implementation is proved to reproduce the abstract averages. Square-root-free accuracy budgets and finite rational payoff inequalities certify…

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