mlsanityData to 7 Oct 2026

A consensus-based model for global optimization and its mean-field limit

arXiv 1604.05648 ↗First posted 19 Apr 2016math.PR math.OCcited by 21

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Abstract (arXiv)

We introduce a novel first-order stochastic swarm intelligence (SI) model in the spirit of consensus formation models, namely a consensus-based optimization (CBO) algorithm, which may be used for the global optimization of a function in multiple dimensions. The CBO algorithm allows for passage to the mean-field limit, which results in a nonstandard, nonlocal, degenerate parabolic partial differential equation (PDE). Exploiting tools from PDE analysis we provide convergence results that help to understand the asymptotic behavior of the SI model. We further present numerical investigations underlining the feasibility of our approach.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Apr 2016.

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Citing papers per year: 2022: 2; 2023: 5; 2024: 2; 2025: 5; 2026: 7.

21 papers.

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  1. 2023A mathematical perspective on Transformerscited by 160
  2. 2022Birth-death dynamics for sampling: Global convergence, approximations and their asymptoticscited by 30
  3. 2023Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimationcited by 17
  4. 2025Neural ODE Transformers: Analyzing Internal Dynamics and Adaptive Fine-tuningcited by 12
  5. 2023FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimizationcited by 7
  6. 2024Kinetic Interacting Particle Langevin Monte Carlocited by 7
  7. 2026Quantifying Concentration Phenomena of Mean-Field Transformers in the Low-Temperature Regimecited by 4
  8. 2023Reproducing kernel Hilbert spaces in the mean field limitcited by 3
  9. 2023Gradient is All You Need? How Consensus-Based Optimization can be Interpreted as a Stochastic Relaxation of Gradient Descentcited by 3
  10. 2025Adaptive Heavy-Tailed Stochastic Gradient Descentcited by 2
  11. 2024Defending Against Diverse Attacks in Federated Learning Through Consensus-Based Bi-Level Optimizationcited by 1
  12. 2025Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategiescited by 1
9 more
  1. 2025Global Optimization via Softmin Energy Minimizationcited by 1
  2. 2026Stochastic Control Methods for Optimizationcited by 1
  3. 2026To discretize continually: Mean shift interacting particle systems for Bayesian inferencecited by 1
  4. 2022Ensemble-based gradient inference for particle methods in optimization and samplingcited by 0
  5. 2025Mean-Field Model for Two-Layer Neural Networks Trained with Consensus-Based Optimizationcited by 0
  6. 2026A Generative Sampler for distributions with possible discrete parameter based on Reversibilitycited by 0
  7. 2026From Mean-Field Limits to Semiclassical Concentration: Global Convergence of the Canonical Evolutionary Strategycited by 0
  8. 2026Operator Calculus for Population-Based Optimization: Modular Convergence and Finite-Population Guaranteescited by 0
  9. 2026Bridging Spherical Black-Box Optimizerscited by 0