Accelerated variance-reduced methods for saddle-point problems

We consider composite minimax optimization problems where the goal is to find a saddle-point of large sum non-bilinear objective functions augmented by simple regularizers for primal and dual variables. For such problems, under average-smoothness assumption, we propose accelerated stochastic variance-reduced algorithms with optimal up logarithmic factors complexity bounds. In particular, strongly-convex-strongly-concave, convex-strongly-concave, convex-concave objectives. To best our knowledge, these are first nearly-optimal this setting. • First bounds empirical problems.