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

2024-12-31

AI Summary

To address the divergence and slow convergence of the stochastic extra-gradient (SEG) method in unconstrained finite-sum and minimax optimization, this paper proposes SEG-FFA, which integrates a flip-flop (FF) shuffling scheme with an anchoring (A) mechanism. We establish, for the first time, global convergence of SEG-FFA under convex–concave settings; under strongly convex–strongly concave assumptions, we derive its optimal convergence rate of $O(1/T^2)$, substantially outperforming standard SEG and existing shuffling-based variants. Theoretical analysis reveals that the FF–A mechanism effectively curbs variance accumulation and enhances algorithmic stability, thereby overcoming fundamental convergence bottlenecks inherent in conventional shuffling approaches. Extensive experiments on benchmark minimax problems demonstrate SEG-FFA’s robustness and consistent acceleration over state-of-the-art methods.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Stochastic Excess Gradient Algorithm
• Unconstrained Minimax Optimization
• Performance Improvement

Innovation

• SEG-FFA
• Unconstrained Minimax Optimization
• Faster Convergence