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We examine the problem of regret minimization when the learner is involved ina continuous game with other optimizing agents: in this case, if all playersfollow a no-regret algorithm, it is possible to achieve significantly lowerregret relative to fully adversarial environments. We study this problem in thecontext of variationally stable games (a class of continuous games whichincludes all convex-concave and monotone games), and when the players only haveaccess to noisy estimates of their individual payoff gradients. If the noise isadditive, the game-theoretic and purely adversarial settings enjoy similarregret guarantees; however, if the noise is multiplicative, we show that thelearners can, in fact, achieve constant regret. We achieve this faster rate viaan optimistic gradient scheme with learning rate separation -- that is, themethod's extrapolation and update steps are tuned to different schedules,depending on the noise profile. Subsequently, to eliminate the need fordelicate hyperparameter tuning, we propose a fully adaptive method that attainsnearly the same guarantees as its non-adapted counterpart, while operatingwithout knowledge of either the game or of the noise profile.

No-Regret Learning in Games with Noisy Feedback: Faster Rates and Adaptivity via Learning Rate Separation