# Trends in Consensus-based optimization

arXiv: https://arxiv.org/abs/2104.01383 · HTML: https://mlsanity.com/paper/2104.01383/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2021.

## Built on by (most cited first, 8 of 8)

- [Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups](https://mlsanity.com/paper/2410.02698/) (2024)
- [Stochastic Zeroth order Descent with Structured Directions](https://mlsanity.com/paper/2206.05124/) (2022)
- [FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization](https://mlsanity.com/paper/2305.02894/) (2023)
- [Adaptive State-Dependent Diffusion for Derivative-Free Optimization](https://mlsanity.com/paper/2302.04370/) (2023)
- [An Algebraically Converging Stochastic Gradient Descent Algorithm for Global Optimization](https://mlsanity.com/paper/2204.05923/) (2022)
- [Multi-level Optimal Control with Neural Surrogate Models](https://mlsanity.com/paper/2402.07763/) (2024)
- [Ensemble-based gradient inference for particle methods in optimization and sampling](https://mlsanity.com/paper/2209.15420/) (2022)
- [Non-intrusive surrogate modelling using sparse random features with applications in crashworthiness analysis](https://mlsanity.com/paper/2212.14507/) (2022)

## Abstract (arXiv)

In this chapter we give an overview of the consensus-based global optimization algorithm and its recent variants. We recall the formulation and analytical results of the original model, then we discuss variants using component-wise independent or common noise. In combination with mini-batch approaches those variants were tailored for machine learning applications. Moreover, it turns out that the analytical estimates are dimension independent, which is useful for high-dimensional problems. We discuss the relationship of consensus-based optimization with particle swarm optimization, a method widely used in the engineering community. Then we survey a variant of consensus-based optimization that is proposed for global optimization problems constrained to hyper-surfaces. We conclude the chapter with remarks on applications, preprints and open problems.