arXiv subjects

Sabrina Bonandin

Publications and source records attributed to Sabrina Bonandin.

5 recordsLinked to original sources

arXiv2026

Exploiting Structure with Anisotropic Consensus-Based Optimization

Anisotropic consensus-based optimization (CBO), a multi-agent metaheuristic derivative-free optimization method, which reliably finds global minima of nonsmooth and nonconvex objective functions while being amenable to rigorous theoretical analysis, automatically detects and exploits additively separable structures of high-dimensional objective functions. This enables the algorithm to mitigate the curse of dimensionality where the objective function decomposes additively into lower-dimensional components. In this paper, we show this property proving that the computational complexity of anisotropic CBO depends exponentially only on the intrinsic dimension $\mathbf{d}$ of the objective function, rather than the ambient dimension $D\gg\mathbf{d}$. Additionally, we demonstrate that the computational complexity depends only on tractability conditions of the lower-dimensional components rather than on the full energy landscape, allowing for a more refined description of the objective function and algorithmic complexity, as the objective function landscape is captured directly at the level of the individual components. Our results highlight the effectiveness of anisotropic CBO for additively separable objective functions provided sufficient alignment between the structure of the anisotropic noise and the separability structure of the objective. This motivates the design of an enhanced algorithm that learns during optimization how to effectively explore the loss landscape by aligning the noise with the structure of the objective function, which we leave for future research. Numerical experiments validate our theoretical results, accentuating the influence of the intrinsic dimensionality $\mathbf{d}$, the level of separability, and the complexity and non-convexity of the objective within the separable components on performance and computational complexity of the anisotropic CBO algorithm.

math.OC↗

arXiv2025

Strong Global Convergence of the Consensus-Based Optimization Algorithm

Consensus-based optimization (CBO) is a multi-agent metaheuristic derivative-free optimization algorithm that has proven to be capable of globally minimizing nonconvex nonsmooth functions across a diverse range of applications while being amenable to theoretical analysis. The method leverages an interplay between exploration of the energy landscape of the objective function through a system of interacting particles subject to stochasticity and exploitation of the particles' positions through the computation of a global consensus about the location of the minimizer based on the Laplace principle. In this paper, we prove strong mean square convergence of the practical numerical time-discrete CBO algorithm to the global minimizer for a rich class of objective functions. For CBO with both isotropic and anisotropic diffusion, our convergence result features conditions on the choice of the hyperparameters as well as explicit rates of convergence in the time discretization step size $Δt$ and the number of particles $N$. By interpreting the time-discrete algorithm at the continuous-time level through a system of stochastic differential equations (SDEs), our proof strategy combines traditional finite-time convergence theory for numerical methods applied to SDEs with careful considerations due to the fact that the CBO coefficients do not satisfy a global Lipschitz condition. To accomodate the latter, we adopt a recently proposed generalization of Sznitman's classical argument, which allows to discard an event of small probability, controllable through fine moment estimates for the particle systems.

math.OC↗

arXiv2025

Consensus-based algorithms for stochastic optimization problems

We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on the search space are developed. The resulting methods are mathematically analyzed using a mean-field approximation and their connection is established. Several numerical experiments show the validity of the proposed algorithms and investigate their rates of convergence.

math.OC↗

arXiv2025

Kinetic variable-sample methods for stochastic optimization problems

We discuss kinetic-based particle optimization methods and variable-sample strategies for problems where the cost function represents the expected value of a random mapping. Kinetic-based optimization methods rely on a consensus mechanism targeting the global minimizer, and they exploit tools of kinetic theory to establish a rigorous framework for proving convergence to that minimizer. Variable-sample strategies replace the expected value by an approximation at each iteration of the optimization algorithm. We combine these approaches and introduce a novel algorithm based on instantaneous collisions governed by a linear Boltzmann-type equation. After proving the convergence of the resulting kinetic method under appropriate parameter constraints, we establish a connection to a recently introduced consensus-based method for solving the random problem in a suitable scaling. Finally, we showcase its enhanced computational efficiency compared to the aforementioned algorithm and validate the consistency of the proposed modeling approaches through several numerical experiments.

math.OC↗

arXiv2024

Effects of heterogeneous opinion interactions in many-agent systems for epidemic dynamics

In this work we define a kinetic model for understanding the impact of heterogeneous opinion formation dynamics on epidemics. The considered many-agent system is characterized by nonsymmetric interactions which define a coupled system of kinetic equations for the evolution of the opinion density in each compartment. In the quasi-invariant limit we may show positivity and uniqueness of the solution of the problem together with its convergence towards an equilibrium distribution exhibiting bimodal shape. The tendency of the system towards opinion clusters is further analyzed by means of numerical methods, which confirm the consistency of the kinetic model with its moment system whose evolution is approximated in several regimes of parameters.

physics.soc-ph↗