Strategizing against No-regret Learners

Understand

How should a player who repeatedly plays a game against a no-regret learner strategize to maximize his utility? We study this question and show that under some mild assumptions, the player can always guarantee himself a utility of at least what he would get in a Stackelberg equilibrium of the game.

• When the no-regret learner has only two actions, we show that the player cannot get any higher utility than the Stackelberg equilibrium utility.
• But when the no-regret learner has more than two actions and plays a mean-based no-regret strategy, we show that the player can get strictly higher than the Stackelberg equilibrium utility.
• We provide a characterization of the optimal game-play for the player against a mean-based no-regret learner as a solution to a control problem.