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arXiv · 1805.06792

Faster Rates for Convex-Concave Games

Jacob Abernethy·Kevin A. Lai·Kfir Y. Levy·Jun-Kun Wang
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Abstract

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.

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Jacob Abernethy, Kevin A. Lai, Kfir Y. Levy, Jun-Kun Wang. 2018-05-17. Faster Rates for Convex-Concave Games. https://arxiv.org/abs/1805.06792

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