We provide a general method to convert a "primal" black-box algorithm for solving regularized convex-concave minimax optimization problems into an algorithm for solving the associated dual maximin optimization problem. Our method adds recursive regularization over a logarithmic number of rounds where each round consists of an approximate regularized primal optimization followed by the computation of a dual best response. We apply this result to obtain new state-of-the-art runtimes for solving matrix games in specific parameter regimes, obtain improved query complexity for solving the dual of the CVaR distributionally robust optimization (DRO) problem, and recover the optimal query complexity for finding a stationary point of a convex function.

翻译：我们提出了一种通用方法，可将求解正则化凸凹极小极大优化问题的"原始"黑盒算法转化为求解相关对偶极大极小优化问题的算法。该方法通过在指数级轮次中添加递归正则化实现，其中每轮包含近似正则化原始优化及对偶最优响应的计算。应用此结果，我们在特定参数范围内获得了求解矩阵博弈的最新最优时间复杂度，提升了求解CVaR分布鲁棒优化问题对偶形式的查询复杂度，并恢复了求解凸函数驻点的最优查询复杂度。