A unified variance-reduced accelerated gradient method for convex optimization

Guanghui Lan; Zhize Li; Yi Zhou

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arXiv · 1905.12412

A unified variance-reduced accelerated gradient method for convex optimization

Guanghui Lan·Zhize Li·Yi Zhou

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Abstract

We propose a novel randomized incremental gradient algorithm, namely, VAriance-Reduced Accelerated Gradient (Varag), for finite-sum optimization. Equipped with a unified step-size policy that adjusts itself to the value of the condition number, Varag exhibits the unified optimal rates of convergence for solving smooth convex finite-sum problems directly regardless of their strong convexity. Moreover, Varag is the first accelerated randomized incremental gradient method that benefits from the strong convexity of the data-fidelity term to achieve the optimal linear convergence. It also establishes an optimal linear rate of convergence for solving a wide class of problems only satisfying a certain error bound condition rather than strong convexity. Varag can also be extended to solve stochastic finite-sum problems.

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BibTeX RIS

Guanghui Lan, Zhize Li, Yi Zhou. 2019-05-29. A unified variance-reduced accelerated gradient method for convex optimization. https://arxiv.org/abs/1905.12412

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