An Optimal Algorithm for Stochastic Three-Composite Optimization
Renbo Zhao, William B. Haskell, Vincent Y. F. Tan
Abstract
We develop an optimal primal-dual first-order algorithm for a class of stochastic three-composite convex minimization problems. The convergence rate of our method not only improves upon the existing methods, but also matches a lower bound derived for all first-order methods that solve this problem. We extend our proposed algorithm to solve a composite stochastic program with any finite number of nonsmooth functions. In addition, we generalize an optimal stochastic alternating direction method of multipliers (SADMM) algorithm proposed for the two-composite case to solve this problem, and establish its connection to our optimal primal-dual algorithm. We perform extensive numerical experiments on a variety of machine learning applications to demonstrate the superiority of our method via-a-vis the state-of-the-art.
BibTeX
@InProceedings{pmlr-v89-zhao19a,
title = {An Optimal Algorithm for Stochastic Three-Composite Optimization},
author = {Zhao, Renbo and Haskell, William B. and Tan, Vincent Y. F.},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
pages = {428--437},
year = {2019},
editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
volume = {89},
series = {Proceedings of Machine Learning Research},
month = {16--18 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v89/zhao19a/zhao19a.pdf},
url = {https://proceedings.mlr.press/v89/zhao19a.html},
abstract = {We develop an optimal primal-dual first-order algorithm for a class of stochastic three-composite convex minimization problems. The convergence rate of our method not only improves upon the existing methods, but also matches a lower bound derived for all first-order methods that solve this problem. We extend our proposed algorithm to solve a composite stochastic program with any finite number of nonsmooth functions. In addition, we generalize an optimal stochastic alternating direction method of multipliers (SADMM) algorithm proposed for the two-composite case to solve this problem, and establish its connection to our optimal primal-dual algorithm. We perform extensive numerical experiments on a variety of machine learning applications to demonstrate the superiority of our method via-a-vis the state-of-the-art.}
}