Efficient Kernelized Learning in Polyhedral Games beyond Full Information: From Colonel Blotto to Congestion Games

We examine the problem of efficiently learning coarse correlated equilibria (CCE) in polyhedral games, that is, normal-form games with an exponentially large number of actions per player and an underlying combinatorial structure--such as the classic Colonel Blotto game or congestion games. Achieving computational efficiency in this setting requires learning algorithms whose regret and per-iteration complexity scale at most polylogarithmically with the size of the players' action sets. This challenge has recently been addressed in the full-information setting, primarily through the use of kernelization; however, in the more realistic partial information setting, the situation is much more challenging, and existing approaches result in suboptimal and impractical runtime complexity to learn CCE. We address this gap via a novel kernelization-based framework for payoff-based learning in polyhedral games, which we then apply to certain key classes of polyhedral games--namely Colonel Blotto, graphic matroid and network congestion games. In so doing, we obtain a range of computationally efficient payoff-based learning algorithms which significantly improve upon prior work in terms of the runtime for learning CCE.