Fast convergence of learning in games (invited talk)

A plethora of recent work has analyzed properties of outcomes in games when each player employs a no-regret learning algorithm. Many algorithms achieve regret against the best fixed action in hindisght that decays at a rate of O(1/'T), when the game is played for T iterations. The latter rate is optimal in adversarial settings. However, in a game a player's opponents are minimizing their own regret, rather than maximizing the player's regret. (Daskalakis et al. 2014) and (Rakhlin and Sridharan 2013) showed that in two player zero-sum games O(1/T) rates are achievable. In (Syrgkanis et al. 2015), we show that O(1/T3/4) rates are achievable in general multi-player games and also analyze convergence of the dynamics to approximately optimal social welfare, where we show a convergence rate of O(1/T). The latter result was subsequently generalized to a broader class of learning algorithms by (Foster et al. 2016). This is based on joint work with Alekh Agarwal, Haipeng Luo and Robert E. Schapire.