Probabilistic Guarantees of Stochastic Recursive Gradient in Non-Convex Finite Sum Problems
Abstract
This paper develops a new dimension-free Azuma-Hoeffding type bound on summation norm of a martingale difference sequence with random individual bounds. With this novel result, we provide high-probability bounds for the gradient norm estimator in the proposed algorithm Prob-SARAH, which is a modified version of the StochAstic Recursive grAdient algoritHm (SARAH), a state-of-art variance reduced algorithm that achieves optimal computational complexity in expectation for the finite sum problem. The in-probability complexity by Prob-SARAH matches the best in-expectation result up to logarithmic factors. Empirical experiments demonstrate the superior probabilistic performance of Prob-SARAH on real datasets compared to other popular algorithms.
Keywords
Cite
@article{arxiv.2401.15890,
title = {Probabilistic Guarantees of Stochastic Recursive Gradient in Non-Convex Finite Sum Problems},
author = {Yanjie Zhong and Jiaqi Li and Soumendra Lahiri},
journal= {arXiv preprint arXiv:2401.15890},
year = {2024}
}
Comments
41 pages, 3 figures, accepted to PAKDD 2024