Learning from time-dependent streaming data with online stochastic algorithms
Abstract
This paper addresses stochastic optimization in a streaming setting with time-dependent and biased gradient estimates. We analyze several first-order methods, including Stochastic Gradient Descent (SGD), mini-batch SGD, and time-varying mini-batch SGD, along with their Polyak-Ruppert averages. Our non-asymptotic analysis establishes novel heuristics that link dependence, biases, and convexity levels, enabling accelerated convergence. Specifically, our findings demonstrate that (i) time-varying mini-batch SGD methods have the capability to break long- and short-range dependence structures, (ii) biased SGD methods can achieve comparable performance to their unbiased counterparts, and (iii) incorporating Polyak-Ruppert averaging can accelerate the convergence of the stochastic optimization algorithms. To validate our theoretical findings, we conduct a series of experiments using both simulated and real-life time-dependent data.
Cite
@article{arxiv.2205.12549,
title = {Learning from time-dependent streaming data with online stochastic algorithms},
author = {Antoine Godichon-Baggioni and Nicklas Werge and Olivier Wintenberger},
journal= {arXiv preprint arXiv:2205.12549},
year = {2023}
}