A unified variance-reduced accelerated gradient method for convex optimization
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.
Cite
@article{arxiv.1905.12412,
title = {A unified variance-reduced accelerated gradient method for convex optimization},
author = {Guanghui Lan and Zhize Li and Yi Zhou},
journal= {arXiv preprint arXiv:1905.12412},
year = {2019}
}
Comments
33rd Conference on Neural Information Processing Systems (NeurIPS 2019)