A Local Convergence Theory for the Stochastic Gradient Descent Method in Non-Convex Optimization with NonIsolated Local Minima

IF 4.3 3区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Journal of Machine Learning Research Pub Date : 2023-06-01 DOI:10.4208/jml.230106

Taehee Ko and Xiantao Li

引用次数: 0

Abstract

Non-convex loss functions arise frequently in modern machine learning, and for the theoretical analysis of stochastic optimization methods, the presence of non-isolated minima presents a unique challenge that has remained under-explored. In this paper, we study the local convergence of the stochastic gradient descent method to non-isolated global minima. Under mild assumptions, we estimate the probability for the iterations to stay near the minima by adopting the notion of stochastic stability. After establishing such stability, we present the lower bound complexity in terms of various error criteria for a given error tolerance ǫ and a failure probability γ .

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具有非孤立局部极小值的非凸优化随机梯度下降法的局部收敛理论

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Machine Learning Research 工程技术-计算机：人工智能

CiteScore

18.80

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.