# Universal bounds for fixed point iterations via optimal transport metrics

arXiv: https://arxiv.org/abs/2108.00300 · HTML: https://mlsanity.com/paper/2108.00300/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2021.

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

- [Stochastic Halpern iteration in normed spaces and applications to reinforcement learning](https://mlsanity.com/paper/2403.12338/) (2024)
- [Faster Fixed-Point Methods for Multichain MDPs](https://mlsanity.com/paper/2506.20910/) (2025)

## Abstract (arXiv)

We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for general Krasnosel'skii-Mann fixed point iterations for non-expansive maps. We also describe some of their very special properties, including their monotonicity and the so-called "convex quadrangle inequality" that yields a greedy algorithm to compute them efficiently.