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New Insight into Hybrid Stochastic Gradient Descent: Beyond With-Replacement Sampling and Convexity
Pan Zhou · Xiaotong Yuan · Jiashi Feng

Thu Dec 06 02:00 PM -- 04:00 PM (PST) @ Room 210 #46

As an incremental-gradient algorithm, the hybrid stochastic gradient descent (HSGD) enjoys merits of both stochastic and full gradient methods for finite-sum minimization problem. 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.

Author Information

Pan Zhou (National University of Singapore)
Xiaotong Yuan (Nanjing University of Information Science and Technology)
Jiashi Feng (National University of Singapore)

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