# Consensus-Based Optimization for Saddle Point Problems

arXiv: https://arxiv.org/abs/2212.12334 · HTML: https://mlsanity.com/paper/2212.12334/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2022.

## Built on by (most cited first, 3 of 3)

- [FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization](https://mlsanity.com/paper/2305.02894/) (2023)
- [Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies](https://mlsanity.com/paper/2506.24048/) (2025)
- [Multi-level Optimal Control with Neural Surrogate Models](https://mlsanity.com/paper/2402.07763/) (2024)

## Abstract (arXiv)

In this paper, we propose consensus-based optimization for saddle point problems (CBO-SP), a novel multi-particle metaheuristic derivative-free optimization method capable of provably finding global Nash equilibria. Following the idea of swarm intelligence, the method employs a group of interacting particles, which perform a minimization over one variable and a maximization over the other. This paradigm permits a passage to the mean-field limit, which makes the method amenable to theoretical analysis and allows to obtain rigorous convergence guarantees under reasonable assumptions about the initialization and the objective function, which most notably include nonconvex-nonconcave objectives.