# On the mean-field limit for the consensus-based optimization

arXiv: https://arxiv.org/abs/2105.12919 · HTML: https://mlsanity.com/paper/2105.12919/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2021.

## Built on by (most cited first, 5 of 5)

- [FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization](https://mlsanity.com/paper/2305.02894/) (2023)
- [Mean-Field Model for Two-Layer Neural Networks Trained with Consensus-Based Optimization](https://mlsanity.com/paper/2511.21466/) (2025)
- [MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data](https://mlsanity.com/paper/2604.00333/) (2026)
- [Ensemble-based gradient inference for particle methods in optimization and sampling](https://mlsanity.com/paper/2209.15420/) (2022)
- [Consensus Based Stochastic Control](https://mlsanity.com/paper/2501.17801/) (2025)

## Abstract (arXiv)

This paper is concerned with the large particle limit for the consensus-based optimization (CBO), which was postulated in the pioneering works [6,28]. In order to solve this open problem, we adapt a compactness argument by first proving the tightness of the empirical measures μNN≥ 2 associated to the particle system and then verifying that the limit measure μ is the unique weak solution to the mean-field CBO equation. Such results are extended to the model of particle swarm optimization (PSO).