# Stochastic ISTA/FISTA Adaptive Step Search Algorithms for Convex Composite Optimization

arXiv: https://arxiv.org/abs/2402.15646 · HTML: https://mlsanity.com/paper/2402.15646/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2024.

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

- [Stochastic Subspace Descent Accelerated via Bi-fidelity Line Search](https://mlsanity.com/paper/2505.00162/) (2025)
- [A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Lojasiewicz condition](https://mlsanity.com/paper/2608.05460/) (2026)

## Abstract (arXiv)

We develop and analyze stochastic variants of ISTA and a full backtracking FISTA algorithms [Beck and Teboulle, 2009, Scheinberg et al., 2014] for composite optimization without the assumption that stochastic gradient is an unbiased estimator. This work extends analysis of inexact fixed step ISTA/FISTA in [Schmidt et al., 2011] to the case of stochastic gradient estimates and adaptive step-size parameter chosen by backtracking. It also extends the framework for analyzing stochastic line-search method in [Cartis and Scheinberg, 2018] to the proximal gradient framework as well as to the accelerated first order methods.