Convergence of projected stochastic approximation algorithm

Michał Borowski; Błażej Miasojedow

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arXiv · 2501.08256

Convergence of projected stochastic approximation algorithm

Michał Borowski·Błażej Miasojedow

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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.

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Michał Borowski, Błażej Miasojedow. 2025-01-14. Convergence of projected stochastic approximation algorithm. https://arxiv.org/abs/2501.08256

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