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 for solving structured nonconvex minimax optimization problems in the form of %24min_textbf{x} max_{textbf{y} in Y} f(textbf{x}%2C textbf{y})%24%2C where the objective function %24f(textbf{x}%2C textbf{y})%24 is nonconvex in %24textbf{x}%24 and concave in %24textbf{y}%24%2C and the constraint set %24Y subseteq mathbb{R}^n%24 is convex and bounded. In the convex-concave setting%2C the single-timescale gradient descent ascent (GDA) algorithm is widely used in applications and has been shown to have strong convergence guarantees. In more general settings%2C however%2C it can fail to converge. Our contribution is to design TTGDA algorithms that are effective beyond the convex-concave setting%2C efficiently finding a stationary point of the function %24Phi(cdot) :%3D max_{textbf{y} in Y} f(cdot%2C textbf{y})%24. We also establish theoretical bounds on the complexity of solving both smooth and nonsmooth nonconvex-concave minimax optimization problems. To the best of our knowledge%2C this is the first systematic analysis of TTGDA for nonconvex minimax optimization%2C shedding light on its superior performance in training generative adversarial networks (GANs) and in other real-world application problems.?quality=80&w=800)
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