标题： 变分不等式中的洗牌启发式：建立新的收敛保证 显示英文标题

标题： Shuffling Heuristic in Variational Inequalities: Establishing New Convergence Guarantees

摘要： 变分不等式在机器学习和优化研究中引起了广泛关注。 虽然求解这些问题的随机方法通常假设独立数据采样，我们研究了一种替代方法——洗牌启发式方法。 该策略涉及在顺序处理之前对数据集进行排列，确保所有数据点得到同等考虑。 尽管其具有实际效用，但关于变分不等式中洗牌的理论保证仍未被探索。 我们通过提供此背景下洗牌方法的第一个理论收敛估计来填补这一空白。 我们的分析建立了严格的界限和收敛速率，扩展了这一重要算法类别的理论框架。 我们通过在各种基准变分不等式问题上进行大量实验来验证我们的发现，证明了洗牌方法相比独立采样方法具有更快的收敛性。 显示英文摘要

摘要： 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.