Convergence of adaptive algorithms for weakly convex constrained optimization
Machine Learning
2020-06-12 v1 Machine Learning
Optimization and Control
Abstract
We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the rate of convergence for the norm of the gradient of Moreau envelope, which is the standard stationarity measure for this class of problems. It matches the known rates that adaptive algorithms enjoy for the specific case of unconstrained smooth stochastic optimization. Our analysis works with mini-batch size of , constant first and second order moment parameters, and possibly unbounded optimization domains. Finally, we illustrate the applications and extensions of our results to specific problems and algorithms.
Keywords
Cite
@article{arxiv.2006.06650,
title = {Convergence of adaptive algorithms for weakly convex constrained optimization},
author = {Ahmet Alacaoglu and Yura Malitsky and Volkan Cevher},
journal= {arXiv preprint arXiv:2006.06650},
year = {2020}
}