论文标题
Nesterov符合乐观：最佳的可分离最小值优化
Nesterov Meets Optimism: Rate-Optimal Separable Minimax Optimization
论文作者
论文摘要
我们提出了一种新的一阶优化算法 - 可分离的凸孔conconconconconconconconconconconconconconconconconconconconconconconconconimax优化。我们算法的主要思想是仔细利用最小值问题的结构，对单个组件进行Nesterov加速，并在耦合组件上进行乐观梯度。配备了适当的重新启动，我们表明AG-OG达到了各种设置的最佳收敛速率（达到一个恒定），包括双线性耦合强烈凸出的凹入凹入的最小值优化（BI-SC-SC），双线性双线性的convex-sttrongly convex-stronglongy凹入minimax优化（Bi-c-c-c-SC）和BILIN（BILIN）和BILIN和BILIN和BILIN和BILIN和BILIN和BILIN和BILIN。我们还将算法扩展到随机设置，并在BI-SC-SC和BI-C-SC设置中达到最佳收敛速率。 AG-OG是第一个单单算法，在确定性和随机设置中，双线耦合的最小值优化问题都具有最佳的收敛速率。
We propose a new first-order optimization algorithm -- AcceleratedGradient-OptimisticGradient (AG-OG) Descent Ascent -- for separable convex-concave minimax optimization. The main idea of our algorithm is to carefully leverage the structure of the minimax problem, performing Nesterov acceleration on the individual component and optimistic gradient on the coupling component. Equipped with proper restarting, we show that AG-OG achieves the optimal convergence rate (up to a constant) for a variety of settings, including bilinearly coupled strongly convex-strongly concave minimax optimization (bi-SC-SC), bilinearly coupled convex-strongly concave minimax optimization (bi-C-SC), and bilinear games. We also extend our algorithm to the stochastic setting and achieve the optimal convergence rate in both bi-SC-SC and bi-C-SC settings. AG-OG is the first single-call algorithm with optimal convergence rates in both deterministic and stochastic settings for bilinearly coupled minimax optimization problems.
