Related papers: Consensus based optimization via jump-diffusion st…
We investigate the implementation of a new stochastic Kuramoto-Vicsek-type model for global optimization of nonconvex functions on the sphere. This model belongs to the class of Consensus-Based Optimization. In fact, particles move on the…
In this work we introduce a new class of gradient-free global optimization methods based on a binary interaction dynamics governed by a Boltzmann type equation. In each interaction the particles act taking into account both the best…
In this paper, we develop a novel dynamic distributed optimal safe consensus protocol to simultaneously achieve safety requirements and output optimal consensus. Specifically, we construct a distributed projection optimization algorithm…
We consider a class of optimization problems on the space of probability measures motivated by the mean-field approach to studying neural networks. Such problems can be solved by constructing continuous-time gradient flows that converge to…
Despite the growing interest in designing truly interactive hyperparameter optimization (HPO) methods, to date, only a few allow to include human feedback. Existing interactive Bayesian optimization (BO) methods incorporate human beliefs by…
We study two interacting particle systems, both modeled as a system of $N$ stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate…
The random batch method provides an efficient algorithm for computing statistical properties of a canonical ensemble of interacting particles. In this work, we study the error estimates of the fully discrete random batch method, especially…
In this paper we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the…
In Causal Bayesian Optimization (CBO), an agent intervenes on an unknown structural causal model to maximize a downstream reward variable. In this paper, we consider the generalization where other agents or external events also intervene on…
In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogonal (DyBO) method was developed to explore low-dimensional…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
This paper considers an $n$-particle jump-diffusion system with mean filed interaction, where the coefficients are locally Lipschitz continuous. We address the convergence as $n\to\infty$ of the empirical measure of the jump-diffusions to…
We propose a multi-swarm approach to approximate the Pareto front of general multi-objective optimization problems that is based on the Consensus-based Optimization method (CBO). The algorithm is motivated step by step beginning with a…
We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction and diffusion functions from the path of one single particle in the system. Our estimator is obtained by…
We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183--204, 2017], which is a gradient-free optimization method for general…
In this paper we are concerned with the global minimization of a possibly non-smooth and non-convex objective function constrained on the unit hypersphere by means of a multi-agent derivative-free method. The proposed algorithm falls into…
Bayesian optimization is a powerful optimization tool for problems where native first-order derivatives are unavailable. Recently, constrained Bayesian optimization (CBO) has been applied to many engineering applications where constraints…
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…
We consider the stochastic system of interacting neurons introduced in De Masi et al. (2015) and in Fournier and L\"ocherbach (2016) and then further studied in Erny, L\"ocherbach and Loukianova (2021) in a diffusive scaling. The system…
The recent work arXiv:2407.17373 proposes a derivative-free consensus-based particle method that computes global solutions to nonconvex-nonconcave min-max problems and establishes global exponential convergence in the sense of the…