Centered Permutation Prefixes for SGD with Random Reshuffling: Sharp Rates, H\"older Geometry, and Composite Proximal Extensions
The last-epoch rate is proved, matching the known quadratic lower bound in its $(n,K)$-dependence, and it is shown that the $\beta_\star^2/K^2$ splitting term is unavoidable and obtain a matching lower bound up to logarithms in the stated constant-stepsize regime.