No-Regret Learning in General Games

Abstract

This thesis investigates the regret performance of no-regret learning algorithms in the competitive, though not fully-adversarial, environment of games. We establish exponential improvements on previously best-known external and internal regret bounds for these settings.

We show that Optimistic Hedge – a common variant of multiplicative-weights-updates with recency bias – attains poly(log T) regret in multi-player general-sum games. In particular, when every player of the game uses Optimistic Hedge to iteratively update her strategy in response to the history of play so far, then after T rounds of interaction, each player experiences total regret that is poly(log T). Our bound improves, exponentially, the O(T¹ᐟ²) regret attainable by standard no-regret learners in games, the O(T¹ᐟ⁴) regret attainable by no-regret learners with recency bias [Syr+15], and the O(T¹ᐟ⁶) bound that was recently shown for Optimistic Hedge in the special case of two-player games [CP20]. A corollary of our bound is that Optimistic Hedge converges to coarse correlated equilibrium in general games at a rate of [formula].

We then extend this result from external regret to internal and swap regret, thereby establishing uncoupled learning dynamics that converge to an approximate correlated equilibrium at the rate of [formula]. This substantially improves over the prior best rate of convergence for correlated equilibria of O(T⁻³ᐟ⁴) due to Chen and Peng (NeurIPS ‘20), and it is optimal up to polylogarithmic factors in T.

The results presented here originate from my works [DFG21] and [Ana+22].