# A consensus-based algorithm for multi-objective optimization and its mean-field description

arXiv: https://arxiv.org/abs/2203.16384 · HTML: https://mlsanity.com/paper/2203.16384/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2022.

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

- [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)

## Abstract (arXiv)

We present a multi-agent algorithm for multi-objective optimization problems, which extends the class of consensus-based optimization methods and relies on a scalarization strategy. The optimization is achieved by a set of interacting agents exploring the search space and attempting to solve all scalar sub-problems simultaneously. We show that those dynamics are described by a mean-field model, which is suitable for a theoretical analysis of the algorithm convergence. Numerical results show the validity of the proposed method.