Hedging Under Uncertainty: Regret Minimization Meets Exponentially Fast Convergence

This paper examines the problem of multi-agent learning in N -person non-cooperative games. For concreteness, we focus on the socalled “hedge” variant of the exponential weights (EW) algorithm, one of the most widely studied algorithmic schemes for regret minimization in online learning. In this multi-agent context, we show that a) dominated strategies become extinct (a.s.); and b) in generic games, pure Nash equilibria are attracting with high probability, even in the presence of uncertainty and noise of arbitrarily high variance. Moreover, if the algorithm’s step-size does not decay too fast, we show that these properties occur at a quasi-exponential rate – that is, much faster than the algorithm’s O(1/ √ T ) worst-case regret guarantee would suggest.