标题： 重新审视收敛性：超越利普希茨光滑性的洗牌复杂性 显示英文标题

标题： Revisiting Convergence: Shuffling Complexity Beyond Lipschitz Smoothness

摘要： 洗牌类型梯度方法因其简单性和快速的经验性能而在实践中受到青睐。 尽管近年来在各种假设下对收敛性保证进行了广泛的发展，但大多数方法都需要Lipschitz光滑性条件，而这一条件在常见的机器学习模型中往往不成立。 我们通过具体的反例突出了这一问题。 为了解决这一差距，我们重新审视了不假设Lipschitz光滑性的洗牌类型梯度方法的收敛速率。 使用我们的步长策略，洗牌类型梯度算法不仅在较弱的假设下收敛，而且达到了当前已知的最佳收敛速率，从而扩大了其适用性。 我们在一般的有界方差条件下，证明了非凸、强凸和非强凸情况下的收敛速率，每种情况都分别在随机重排和任意洗牌方案下进行证明。 数值实验进一步验证了我们的洗牌类型梯度算法的性能，强调了其实际有效性。 显示英文摘要

摘要： Shuffling-type gradient methods are favored in practice for their simplicity and rapid empirical performance. Despite extensive development of convergence guarantees under various assumptions in recent years, most require the Lipschitz smoothness condition, which is often not met in common machine learning models. We highlight this issue with specific counterexamples. To address this gap, we revisit the convergence rates of shuffling-type gradient methods without assuming Lipschitz smoothness. Using our stepsize strategy, the shuffling-type gradient algorithm not only converges under weaker assumptions but also match the current best-known convergence rates, thereby broadening its applicability. We prove the convergence rates for nonconvex, strongly convex, and non-strongly convex cases, each under both random reshuffling and arbitrary shuffling schemes, under a general bounded variance condition. Numerical experiments further validate the performance of our shuffling-type gradient algorithm, underscoring its practical efficacy.