Centered Permutation Prefixes for SGD with Random Reshuffling: Sharp Rates, H\"older Geometry, and Composite Proximal Extensions

On September 7, 2026, arXiv cs.LG published the research paper “Centered Permutation Prefixes for SGD with Random Reshuffling: Sharp Rates, H”lder Geometry, and Composite Proximal Extensions”. This study explores the impact of introducing centered permutation prefixes on the stochastic gradient descent (SGD) algorithm in the context of random reshuffling. The paper analyzes the performance of this method under different geometric structures, particularly for Hölder continuous function classes, and derives precise theoretical bounds on convergence rates. Additionally, the study expands the application scenarios of composite proximal extensions, providing a new theoretical framework and algorithmic approach for handling non-smooth optimization problems.