带消极动量的自适应步长随机方差缩减方法

doi:10.7523/j.ucas.2024.024

摘要/Abstract

摘要： 近年来, 随机方差缩减类方法在解决大规模机器学习问题中取得很大成功, 自适应步长技术的引入减轻了该类方法的调参负担。针对自适应步长的方差缩减算法SVRG-BB, 指出其算法设计带来了“进展-自适应步长有效性”的权衡问题。因此引入Katyusha动量以更好地处理该权衡问题, 并且在强凸假设下证明由此得到的SVRG-BB-Katyusha算法的线性收敛性质。之后基于“贪婪”思想, 提出稀疏地使用Katyusha动量的SVRG-BB-Katyusha-SPARSE算法。在公开数据集上的数值实验结果表明，提出的2个改进算法较SVRG-BB有较稳定的优势, 即在达到一定外循环数时优化间隙有若干个数量级的减小。

关键词: 自适应步长机制, 随机方差缩减类方法, Barzilai-Borwein方法, Katyusha动量

Abstract: Stochastic variance reduction methods have been successful in solving large scale machine learning problems, and researchers cooperate them with adaptive stepsize schemes to further alleviate the burden of parameter-tuning. In this article, we propose that there exists a trade-off between progress and effectiveness of adaptive stepsize arising in the SVRG-BB algorithm. To enhance the practical performance of SVRG-BB, we introduce the Katyusha momentum to handle the aforementioned trade-off. The linear convergence rate of the resulting SVRG-BB-Katyusha algorithm is proven under strong convexity condition. Moreover, we propose SVRG-BB-Katyusha-SPARSE algorithm which uses Katyusha momentum sparsely in the inner iterations. Numerical experiments are given to illustrate that the proposed algorithms have promising advantages over SVRG-BB, in the sense that the optimality gaps of the proposed algorithms are smaller than the optimality gap of SVRG-BB by orders of magnitude.

Key words: adaptive stepsize scheme, stochastic variance reduction methods, Barzilai-Borwein method, Katyusha momentum

中图分类号:

O224

刘海, 郭田德, 韩丛英. 带消极动量的自适应步长随机方差缩减方法[J]. 中国科学院大学学报, 2024, 41(5): 577-588.

LIU Hai, GUO Tiande, HAN Congying. An adaptive variance reduction method with negative momentum[J]. Journal of University of Chinese Academy of Sciences, 2024, 41(5): 577-588.

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