Faster Rates for Convex-Concave Games

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 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 . We also show that such no-regret techniques can even achieve a linear rate, O(exp(-T)), for equilibrium computation under additional curvature assumptions.