Diffusion Stochastic Optimization for Min-Max Problems

• URL: http://arxiv.org/abs/2401.14585v1
• Date: Fri, 26 Jan 2024 01:16:59 GMT
• Title: Diffusion Stochastic Optimization for Min-Max Problems
• Authors: Haoyuan Cai, Sulaiman A. Alghunaim, Ali H. Sayed
• Abstract summary: The optimistic gradient method is useful in addressing minimax optimization problems. Motivated by the observation that the conventional version suffers from the need for a large batch size, we introduce and analyze a new formulation termed Samevareps-generativeOGOG.
• Score: 33.73046548872663
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The optimistic gradient method is useful in addressing minimax optimization problems. Motivated by the observation that the conventional stochastic version suffers from the need for a large batch size on the order of $\mathcal{O}(\varepsilon^{-2})$ to achieve an $\varepsilon$-stationary solution, we introduce and analyze a new formulation termed Diffusion Stochastic Same-Sample Optimistic Gradient (DSS-OG). We prove its convergence and resolve the large batch issue by establishing a tighter upper bound, under the more general setting of nonconvex Polyak-Lojasiewicz (PL) risk functions. We also extend the applicability of the proposed method to the distributed scenario, where agents communicate with their neighbors via a left-stochastic protocol. To implement DSS-OG, we can query the stochastic gradient oracles in parallel with some extra memory overhead, resulting in a complexity comparable to its conventional counterpart. To demonstrate the efficacy of the proposed algorithm, we conduct tests by training generative adversarial networks.

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