# Convergence of projected stochastic approximation algorithm

arXiv: https://arxiv.org/abs/2501.08256 · HTML: https://mlsanity.com/paper/2501.08256/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2025.

## Built on by (most cited first, 2 of 2)

- [Quantitative Convergence Analysis of Projected Stochastic Gradient Descent for Non-Convex Losses via the Goldstein Subdifferential](https://mlsanity.com/paper/2510.02735/) (2025)
- [Finite-Time Concentration and Convergence Rates for Projected Two-Time-Scale Stochastic Approximation with Markov Noise](https://mlsanity.com/paper/2609.34791/) (2026)

## Abstract (arXiv)

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.