Convergence of projected stochastic approximation algorithm
Optimization and Control
2025-01-15 v1
Abstract
We study the Robbins-Monro stochastic approximation algorithm with projections on a hyperrectangle and prove its convergence. This work fills a gap in the convergence proof of the classic book by Kushner and Yin. Using the ODE method, we show that the algorithm converges to stationary points of a related projected ODE. Our results provide a better theoretical foundation for stochastic optimization techniques, including stochastic gradient descent and its proximal version. These results extend the algorithm's applicability and relax some assumptions of previous research.
Cite
@article{arxiv.2501.08256,
title = {Convergence of projected stochastic approximation algorithm},
author = {Michał Borowski and Błażej Miasojedow},
journal= {arXiv preprint arXiv:2501.08256},
year = {2025}
}