Shuffling Heuristic in Variational Inequalities: Establishing New Convergence Guarantees

2025-09-04

AI Summary

Variational inequality (VI) problems commonly rely on stochastic methods assuming independent and identically distributed (i.i.d.) sampling, whereas practical implementations frequently adopt shuffling heuristics—randomly permuting data once and traversing it sequentially—despite the absence of rigorous theoretical foundations. Method: We propose a novel analytical framework tailored to non-i.i.d., sequential sampling, enabling the first rigorous convergence analysis of shuffling for VI problems. Contribution/Results: Our analysis establishes explicit iteration complexity upper bounds and proves that shuffling achieves convergence rates comparable to—or even better than—the optimal stochastic methods under both strongly monotone and monotone settings. The theoretical guarantees are validated across diverse benchmark VI problems, including saddle-point optimization and equilibrium computation. Empirical results demonstrate that shuffling significantly accelerates convergence over standard stochastic gradient methods, offering both computational efficiency and practical applicability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: The sharing economy
• Security and Privacy: Large-scale security measurements

Abstract

Variational inequalities have gained significant attention in machine learning and optimization research. While stochastic methods for solving these problems typically assume independent data sampling, we investigate an alternative approach -- the shuffling heuristic. This strategy involves permuting the dataset before sequential processing, ensuring equal consideration of all data points. Despite its practical utility, theoretical guarantees for shuffling in variational inequalities remain unexplored. We address this gap by providing the first theoretical convergence estimates for shuffling methods in this context. Our analysis establishes rigorous bounds and convergence rates, extending the theoretical framework for this important class of algorithms. We validate our findings through extensive experiments on diverse benchmark variational inequality problems, demonstrating faster convergence of shuffling methods compared to independent sampling approaches.

Problem

• Analyzing convergence guarantees for shuffling heuristic
• Extending theoretical framework for variational inequalities
• Comparing shuffling methods against independent sampling approaches

Innovation

• Shuffling heuristic by permuting dataset sequentially
• Establishing first theoretical convergence guarantees rigorously
• Validating faster convergence than independent sampling methods