# Convergence analysis of the stochastic reflected forward-backward splitting algorithm

arXiv: https://arxiv.org/abs/2102.08906 · HTML: https://mlsanity.com/paper/2102.08906/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2021.

## Built on by (most cited first, 1 of 1)

- [Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers](https://mlsanity.com/paper/2106.13067/) (2021)

## Abstract (arXiv)

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased estimations of the Lipschitzian operator. We obtain the rate O(log(n)/n) in expectation for the strongly monotone case, as well as almost sure convergence for the general case. Furthermore, in the context of application to convex-concave saddle point problems, we derive the rate of the primal-dual gap. In particular, we also obtain O(1/n) rate convergence of the primal-dual gap in the deterministic setting.