Stochastic Extragradient with Flip-Flop Shuffling & Anchoring: Provable Improvements

TL;DR

This paper introduces a novel stochastic extragradient method with flip-flop shuffling and anchoring, providing provable convergence and faster rates for minimax optimization in convex-concave problems.

Contribution

It proposes SEG-FFA, a new shuffling-based stochastic extragradient method with anchoring, ensuring convergence in unconstrained convex-concave minimax problems, which was previously challenging.

Findings

SEG-FFA converges in convex-concave problems.

SEG-FFA has faster convergence rates than existing shuffling methods.

Anchoring is key to ensuring convergence in stochastic extragradient methods.

Abstract

In minimax optimization, the extragradient (EG) method has been extensively studied because it outperforms the gradient descent-ascent method in convex-concave (C-C) problems. Yet, stochastic EG (SEG) has seen limited success in C-C problems, especially for unconstrained cases. Motivated by the recent progress of shuffling-based stochastic methods, we investigate the convergence of shuffling-based SEG in unconstrained finite-sum minimax problems, in search of convergent shuffling-based SEG. Our analysis reveals that both random reshuffling and the recently proposed flip-flop shuffling alone can suffer divergence in C-C problems. However, with an additional simple trick called anchoring, we develop the SEG with flip-flop anchoring (SEG-FFA) method which successfully converges in C-C problems. We also show upper and lower bounds in the strongly-convex-strongly-concave setting, demonstrating that SEG-FFA has a provably faster convergence rate compared to other shuffling-based methods.