Learning from time-dependent streaming data with online stochastic algorithms

TL;DR

This paper provides a comprehensive analysis of online stochastic optimization methods for streaming data with time-dependent biases, introducing novel heuristics and demonstrating their effectiveness through theoretical insights and experiments.

Contribution

It introduces new heuristics linking dependence, bias, and convexity, showing how time-varying mini-batch SGD can break dependence and how Polyak-Ruppert averaging accelerates convergence.

Findings

Time-varying mini-batch SGD breaks dependence structures.

Biased SGD can perform comparably to unbiased methods.

Polyak-Ruppert averaging accelerates convergence.

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.