  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.
