Probabilistic Guarantees of Stochastic Recursive Gradient in Non-Convex Finite Sum Problems

• URL: http://arxiv.org/abs/2401.15890v1
• Date: Mon, 29 Jan 2024 05:05:03 GMT
• Title: Probabilistic Guarantees of Stochastic Recursive Gradient in Non-Convex Finite Sum Problems
• Authors: Yanjie Zhong, Jiaqi Li, Soumendra Lahiri
• Abstract summary: This paper develops a new dimension-free Azuma-Hoeffding type bound on norm of a martingale difference sequence with random individual bounds. We provide high-probability bounds for the gradient norm estimator in the proposed algorithm Prob-SARAH.
• Score: 1.5586874069708228
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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