@article{Cheng2022, 
author = {Yiyuan Cheng and Yongquan Zhang and Xingxing Zha and Dongyin Wang},
title = {On stochastic accelerated gradient with non-strongly convexity},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {1445-1459},
keywords = {least-square regression, logistic regression, accelerated stochastic approximation, convergence rate},
url = {https://www.sciopen.com/article/10.3934/math.2022085},
doi = {10.3934/math.2022085},
abstract = {In this paper, we consider stochastic approximation algorithms for least-square and logistic regression with no strong-convexity assumption on the convex loss functions. We develop two algorithms with varied step-size motivated by the accelerated gradient algorithm which is initiated for convex stochastic programming. We analyse the developed algorithms that achieve a rate of    O  (  1      /        n          2        ) where    n is the number of samples, which is tighter than the best convergence rate    O  (  1      /    n  ) achieved so far on non-strongly-convex stochastic approximation with constant-step-size, for classic supervised learning problems. Our analysis is based on a non-asymptotic analysis of the empirical risk (in expectation) with less assumptions that existing analysis results. It does not require the finite-dimensionality assumption and the Lipschitz condition. We carry out controlled experiments on synthetic and some standard machine learning data sets. Empirical results justify our theoretical analysis and show a faster convergence rate than existing other methods.}
}