首次为变分不等式中的随机洗牌方法提供理论收敛保障
Shuffling Heuristic in Variational Inequalities: Establishing New Convergence Guarantees
- 通过数据洗牌替代独立采样，提升算法稳定性
- 证明洗牌方法收敛速度优于传统独立采样
- 适用于需要高效求解的机器学习优化场景
变分不等式在机器学习与优化研究中受到广泛关注。尽管现有随机方法通常假设数据独立采样，本文探讨了一种替代策略——洗牌启发法：在顺序处理前对数据集进行随机重排，确保所有数据点获得同等关注。尽管该方法在实践中广受青睐，其在变分不等式框架下的理论性质仍缺乏研究。本文首次为该类方法建立了理论收敛估计，提供了严格的收敛界与速率分析，拓展了此类重要算法的理论基础。通过在多种基准变分不等式问题上的大量实验验证，结果表明洗牌方法相比独立采样具有更快的收敛速度。
原文摘要 · Abstract (English)
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.
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