Efficient Learning in Polyhedral Games via Best Response Oracles

Published: 26 Oct 2023, Last Modified: 13 Dec 2023NeurIPS 2023 Workshop PosterEveryoneRevisionsBibTeX
Keywords: online learning, projection-free, frank-wolfe, polyhedral games, equilibrium computation
TL;DR: Projection-free algorithm learning algorithm that enjoys $O(\log T/T)$ convergence to Nash equilibria and linear-rate last-iterate convergence in polyhedral games.
Abstract: We study online learning and equilibrium computation in games with polyhedral decision sets with only first-order oracle and best-response oracle access. Our approach achieves constant regret in zero-sum games and $O(T^{1/4})$ in general-sum games while using only $O(\log t)$ best-response queries at a given iteration $t$. This convergence occurs at a linear rate, though with a condition-number dependence. Our algorithm also achieves best-iterate convergence at a rate of $O(1/\sqrt{T})$ without such a dependence. Our algorithm uses a linearly convergent variant of Frank-Wolfe (FW) whose linear convergence depends on a condition number of the polytope known as the facial distance. We show two broad new results, characterizing the facial distance when the polyhedral sets satisfy a certain structure.
Submission Number: 73