Faster Rates for Convex-Concave Games
This work provides incremental improvements in optimization algorithms for game theory, benefiting researchers in machine learning and optimization.
The paper tackles the problem of computing equilibria in convex-concave games using no-regret algorithms, achieving faster convergence rates of O(1/T^2) and linear O(exp(-T)) under specific conditions, with concrete bounds like O(1/T^2) and O(exp(-T)).
We consider the use of no-regret algorithms to compute equilibria for particular classes of convex-concave games. While standard regret bounds would lead to convergence rates on the order of $O(T^{-1/2})$, recent work \citep{RS13,SALS15} has established $O(1/T)$ rates by taking advantage of a particular class of optimistic prediction algorithms. In this work we go further, showing that for a particular class of games one achieves a $O(1/T^2)$ rate, and we show how this applies to the Frank-Wolfe method and recovers a similar bound \citep{D15}. We also show that such no-regret techniques can even achieve a linear rate, $O(\exp(-T))$, for equilibrium computation under additional curvature assumptions.