# Well-posedness and mean-field limit estimate of a consensus-based algorithm for min-max problems

arXiv: https://arxiv.org/abs/2602.12886 · HTML: https://mlsanity.com/paper/2602.12886/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2026.

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

- [Convergence of Consensus-Based Particle Methods for Nonconvex Bi-Level Optimization](https://mlsanity.com/paper/2605.19667/) (2026)

## Abstract (arXiv)

The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the mean-field law. This paper aims to address the theoretical gaps in arXiv:2407.17373, specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics.