An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problems
This work addresses optimization challenges in machine learning and signal processing, but it is incremental as it improves upon existing single-loop algorithms for a specific problem class.
The paper tackles stochastic nonconvex-concave minimax problems by proposing an accelerated first-order regularized momentum descent ascent algorithm (FORMDA), achieving an iteration complexity of $ ilde{\mathcal{O}}(\varepsilon^{-6.5})$ to obtain an $\varepsilon$-stationary point, which matches the best-known bound for single-loop algorithms in this setting.
Stochastic nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose an accelerated first-order regularized momentum descent ascent algorithm (FORMDA) for solving stochastic nonconvex-concave minimax problems. The iteration complexity of the algorithm is proved to be $\tilde{\mathcal{O}}(\varepsilon ^{-6.5})$ to obtain an $\varepsilon$-stationary point, which achieves the best-known complexity bound for single-loop algorithms to solve the stochastic nonconvex-concave minimax problems under the stationarity of the objective function.