Convergence Analysis of Randomized SGDA under NC-PL Condition for Stochastic Minimax Optimization Problems

TL;DR

This paper presents a new convergence analysis for RSGDA in stochastic minimax problems under the NC-PL condition, introducing an acceleration strategy and validating its effectiveness empirically.

Contribution

It provides the first convergence analysis of RSGDA under the NC-PL condition and proposes an acceleration method to enhance its performance.

Findings

Improved convergence results under NC-PL condition

Effective acceleration strategy demonstrated empirically

Broadened applicability of RSGDA in stochastic minimax problems

Abstract

We introduce a new analytic framework to analyze the convergence of the Randomized Stochastic Gradient Descent Ascent (RSGDA) algorithm for stochastic minimax optimization problems. Under the so-called NC-PL condition on one of the variables, our analysis improves the state-of-the-art convergence results in the current literature and hence broadens the applicable range of the RSGDA. We also introduce a simple yet effective strategy to accelerate RSGDA , and empirically validate its efficiency on both synthetic data and real data.