Tighter Lower Bounds for Shuffling SGD: Random Permutations and Beyond

arXiv2303.07160MaRDI QIDQ6429380

Author name not available (Why is that?)

Publication date: 13 March 2023

Abstract: We study convergence lower bounds of without-replacement stochastic gradient descent (SGD) for solving smooth (strongly-)convex finite-sum minimization problems. Unlike most existing results focusing on final iterate lower bounds in terms of the number of components $n$ and the number of epochs $K$, we seek bounds for arbitrary weighted average iterates that are tight in all factors including the condition number $kappa$. For SGD with Random Reshuffling, we present lower bounds that have tighter $kappa$ dependencies than existing bounds. Our results are the first to perfectly close the gap between lower and upper bounds for weighted average iterates in both strongly-convex and convex cases. We also prove weighted average iterate lower bounds for arbitrary permutation-based SGD, which apply to all variants that carefully choose the best permutation. Our bounds improve the existing bounds in factors of $n$ and $kappa$ and thereby match the upper bounds shown for a recently proposed algorithm called GraB.

Has companion code repository: https://github.com/garywei944/grab-sampler

This page was built for publication: Tighter Lower Bounds for Shuffling SGD: Random Permutations and Beyond

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6429380)