# Mini-Batch Stochastic Krasnosel'skiui-Mann Algorithm for Nonexpansive Fixed Point Problems

arXiv: https://arxiv.org/abs/2604.06909 · HTML: https://mlsanity.com/paper/2604.06909/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2026.

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

- [Stochastic Inertial Krasnosel'skii-Mann Iteration Achieves Near-Optimal Sample Complexity](https://mlsanity.com/paper/2609.28543/) (2026)

## Abstract (arXiv)

The Krasnosel'skiui-Mann algorithm is a well-known method for finding fixed points of a nonexpansive mapping with strong theoretical guarantees. However, there are practical large-scale problems to which this algorithm cannot be applied. Here, to resolve the issue caused by the computational difficulty of the mapping, we define a computable mini-batch stochastic mapping, which is a unbiased estimator of the nonexpansive mapping, and implement it in the Krasnosel'skiui-Mann algorithm. We show that the algorithm with increasing batch sizes converges almost surely to a fixed point of the nonexpansive mapping. We also perform a convergence rate analysis on the algorithm.