High Probability Convergence for Accelerated Stochastic Mirror Descent
Optimization and Control
2022-10-04 v1 Data Structures and Algorithms
Machine Learning
Abstract
In this work, we describe a generic approach to show convergence with high probability for stochastic convex optimization. In previous works, either the convergence is only in expectation or the bound depends on the diameter of the domain. Instead, we show high probability convergence with bounds depending on the initial distance to the optimal solution as opposed to the domain diameter. The algorithms use step sizes analogous to the standard settings and are universal to Lipschitz functions, smooth functions, and their linear combinations.
Cite
@article{arxiv.2210.00679,
title = {High Probability Convergence for Accelerated Stochastic Mirror Descent},
author = {Alina Ene and Huy L. Nguyen},
journal= {arXiv preprint arXiv:2210.00679},
year = {2022}
}