Practical Schemes for Finding Near-Stationary Points of Convex Finite-Sums

• URL: http://arxiv.org/abs/2105.12062v1
• Date: Tue, 25 May 2021 16:46:35 GMT
• Title: Practical Schemes for Finding Near-Stationary Points of Convex Finite-Sums
• Authors: Kaiwen Zhou, Lai Tian, Anthony Man-Cho So, James Cheng
• Abstract summary: We conduct a systematic study of the algorithmic techniques in finding near-stationary points of convex finite-sums. Our main contributions are several algorithmic discoveries. We put an emphasis on the simplicity and practicality of the new schemes, which could facilitate future developments.
• Score: 45.91933657088324
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The problem of finding near-stationary points in convex optimization has not been adequately studied yet, unlike other optimality measures such as minimizing function value. Even in the deterministic case, the optimal method (OGM-G, due to Kim and Fessler (2021)) has just been discovered recently. In this work, we conduct a systematic study of the algorithmic techniques in finding near-stationary points of convex finite-sums. Our main contributions are several algorithmic discoveries: (1) we discover a memory-saving variant of OGM-G based on the performance estimation problem approach (Drori and Teboulle, 2014); (2) we design a new accelerated SVRG variant that can simultaneously achieve fast rates for both minimizing gradient norm and function value; (3) we propose an adaptively regularized accelerated SVRG variant, which does not require the knowledge of some unknown initial constants and achieves near-optimal complexities. We put an emphasis on the simplicity and practicality of the new schemes, which could facilitate future developments.

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