A Stochastic Composite Gradient Method with Incremental Variance Reduction
Abstract
We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic composite gradient method that employs an incremental variance-reduced estimator for both the inner vector mapping and its Jacobian. We show that this method achieves the same orders of complexity as the best known first-order methods for minimizing expected-value and finite-sum nonconvex functions, despite the additional outer composition which renders the composite gradient estimator biased. This finding enables a much broader range of applications in machine learning to benefit from the low complexity of incremental variance-reduction methods.
Cite
@article{arxiv.1906.10186,
title = {A Stochastic Composite Gradient Method with Incremental Variance Reduction},
author = {Junyu Zhang and Lin Xiao},
journal= {arXiv preprint arXiv:1906.10186},
year = {2019}
}