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Stochastic nonconvex-concave min-max saddle point problems appear in manymachine learning and control problems including distributionally robustoptimization, generative adversarial networks, and adversarial learning. Inthis paper, we consider a class of nonconvex saddle point problems where theobjective function satisfies the Polyak-{\L}ojasiewicz condition with respectto the minimization variable and it is concave with respect to the maximizationvariable. The existing methods for solving nonconvex-concave saddle pointproblems often suffer from slow convergence and/or contain multiple loops. Ourmain contribution lies in proposing a novel single-loop accelerated primal-dualalgorithm with new convergence rate results appearing for the first time in theliterature, to the best of our knowledge. In particular, in the stochasticregime, we demonstrate a convergence rate of $\mathcal O(\epsilon^{-4})$ tofind an $\epsilon$-gap solution which can be improved to $\mathcalO(\epsilon^{-2})$ in deterministic setting.

Accelerated Primal-dual Scheme for a Class of Stochastic Nonconvex-concave Saddle Point Problems