随机洗牌算法在凸优化中彻底击败随机梯度下降，理论误区终被破解

Mathematics > Optimization and Control

arXiv:2606.32005v1 (math) [Submitted on 30 Jun 2026]

Title:Random Reshuffling Dominates Stochastic Gradient Descent

Authors:Zijian Liu View a PDF of the paper titled Random Reshuffling Dominates Stochastic Gradient Descent, by Zijian Liu View PDF HTML (experimental)

Abstract:Stochastic Gradient Descent ($\textsf{SGD}$) is one of the most classical optimization algorithms with favorable theoretical guarantees, yet the practical implementation of $\textsf{SGD}$ differs subtly from its well-known form and is often referred to as Shuffling Stochastic Gradient Descent ($\textsf{Shuffling SGD}$). A particularly popular strategy in $\textsf{Shuffling SGD}$ is Random Reshuffling ($\textsf{RR}$), which has achieved great empirical success across numerous experiments. Despite its strong performance, $\textsf{RR}$ has long been considered a heuristic due to a lack of theoretical support. Over the last decade, people have finally established provable convergence rates for $\textsf{RR}$, thus justifying its observed superiority. However, for smooth convex optimization, two clouds over the convergence theory of $\textsf{RR}$ remain to this day. More precisely, according to the current theory, $\textsf{Shuffling SGD}$ under $\textsf{RR}$ converges only when the stepsize is smaller than a threshold proportional to $1/n$, where $n$ is the number of summands in the objective (or the number of data points). Consequently, the optimally tuned theoretical rate of $\textsf{Shuffling SGD}$ under $\textsf{RR}$ is strictly worse than that of $\textsf{SGD}$ when the number of epochs is smaller than another threshold proportional to $n$. These two restrictions heavily limit the applicability of existing theories and leave a critical mismatch with practice. In this work, for the first time, we prove that $\textsf{RR}$ dominates $\textsf{SGD}$ in smooth convex optimization under any reasonable stepsize after any finite number of epochs, thereby addressing a longstanding open question.

Comments:	COLT 2026
Subjects:	Optimization and Control (math.OC); Machine Learning (cs.LG); Machine Learning (stat.ML)
Cite as:	arXiv:2606.32005 [math.OC]
	(or arXiv:2606.32005v1 [math.OC] for this version)
	https://doi.org/10.48550/arXiv.2606.32005 Focus to learn more arXiv-issued DOI via DataCite

Submission history

From: Zijian Liu [view email]
[v1] Tue, 30 Jun 2026 17:38:22 UTC (37 KB)
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