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Previous studies on stochastic primal-dual algorithms for solving min-maxproblems with faster convergence heavily rely on the bilinear structure of theproblem, which restricts their applicability to a narrowed range of problems.The main contribution of this paper is the design and analysis of newstochastic primal-dual algorithms that use a mixture of stochastic gradientupdates and a logarithmic number of deterministic dual updates for solving afamily of convex-concave problems with no bilinear structure assumed. Fasterconvergence rates than $O(1/\sqrt{T})$ with $T$ being the number of stochasticgradient updates are established under some mild conditions of involvedfunctions on the primal and the dual variable. For example, for a family ofproblems that enjoy a weak strong convexity in terms of the primal variable andhas a strongly concave function of the dual variable, the convergence rate ofthe proposed algorithm is $O(1/T)$. We also investigate the effectiveness ofthe proposed algorithms for learning robust models and empirical AUCmaximization.

Stochastic Primal-Dual Algorithms with Faster Convergence than $O(1/\sqrt{T})$ for Problems without Bilinear Structure