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Adaptive gradient methods have shown their ability to adjust the stepsizes onthe fly in a parameter-agnostic manner, and empirically achieve fasterconvergence for solving minimization problems. When it comes to nonconvexminimax optimization, however, current convergence analyses of gradient descentascent (GDA) combined with adaptive stepsizes require careful tuning ofhyper-parameters and the knowledge of problem-dependent parameters. Such adiscrepancy arises from the primal-dual nature of minimax problems and thenecessity of delicate time-scale separation between the primal and dual updatesin attaining convergence. In this work, we propose a single-loop adaptive GDAalgorithm called TiAda for nonconvex minimax optimization that automaticallyadapts to the time-scale separation. Our algorithm is fully parameter-agnosticand can achieve near-optimal complexities simultaneously in deterministic andstochastic settings of nonconvex-strongly-concave minimax problems. Theeffectiveness of the proposed method is further justified numerically for anumber of machine learning applications.

TiAda: A Time-scale Adaptive Algorithm for Nonconvex Minimax Optimization