New insight into hybrid stochastic gradient descent: Beyond with-replacement sampling and convexity

• Main Authors: ZHOU, Pan, YUAN, Xiao-Tong, FENG, Jiashi
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: OS and Networks
• Online Access: https://ink.library.smu.edu.sg/sis_research/9007; https://ink.library.smu.edu.sg/context/sis_research/article/10010/viewcontent/NeurIPS_2018_new_insight_into_hybrid_stochastic_gradient_descent_beyond_with_replacement_sampling_and_convexity_Paper.pdf
• Institution: Singapore Management University

As an incremental-gradient algorithm, the hybrid stochastic gradient descent (HSGD) enjoys merits of both stochastic and full gradient methods for finite-sum problem optimization. However, the existing rate-of-convergence analysis for HSGD is made under with-replacement sampling (WRS) and is restricted to convex problems. It is not clear whether HSGD still carries these advantages under the common practice of without-replacement sampling (WoRS) for non-convex problems. In this paper, we affirmatively answer this open question by showing that under WoRS and for both convex and non-convex problems, it is still possible for HSGD (with constant step-size) to match full gradient descent in rate of convergence, while maintaining comparable sample-size-independent incremental first-order oracle complexity to stochastic gradient descent. For a special class of finite-sum problems with linear prediction models, our convergence results can be further improved in some cases. Extensive numerical results confirm our theoretical affirmation and demonstrate the favorable efficiency of WoRS-based HSGD.