Related papers: Self-interacting CBO: Existence, uniqueness, and l…
In this paper, we focus on finding the global minimizer of a general unconstrained nonsmooth nonconvex optimization problem. Taking advantage of the smoothing method and the consensus-based optimization (CBO) method, we propose a novel…
Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of…
Recently a continuous description of the particle swarm optimization (PSO) based on a system of stochastic differential equations was proposed by Grassi and Pareschi in arXiv:2012.05613 where the authors formally showed the link between PSO…
Bayesian optimization is a class of data efficient model based algorithms typically focused on global optimization. We consider the more general case where a user is faced with multiple problems that each need to be optimized conditional on…
A model for continuous-opinion dynamics is proposed and studied by taking advantage of its similarities with a mono-dimensional granular gas. Agents interact as in the Deffuant model, with a parameter $\alpha$ controlling the persuasibility…
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…
We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation, and their optimization behavior under a single set of…
We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We also introduce an interacting particle system in order to…
We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…
Consensus based optimization (CBO) employs a swarm of particles evolving as a system of stochastic differential equations (SDEs). Recently, it has been adapted to yield a derivative free sampling method referred to as consensus based…
The theory of ultracold, dilute Bose gases is the subject of intensive studies, driven by new experimental applications, which also motivate the study of Bose-Einstein condensation (BEC) in low dimensions. From the theoretical point of view…
Causal Bayesian Optimization (CBO) is a methodology designed to optimize an outcome variable by leveraging known causal relationships through targeted interventions. Traditional CBO methods require a fully and accurately specified causal…
Comparison-Based Optimization (CBO) is an optimization paradigm that assumes only very limited access to the objective function f(x). Despite the growing relevance of CBO to real-world applications, this field has received little attention…
We propose a gradient-free deep reinforcement learning algorithm to solve high-dimensional, finite-horizon stochastic control problems. Although the recently developed deep reinforcement learning framework has achieved great success in…
This paper studies a recently proposed continuous-time distributed self-appraisal model with time-varying interactions among a network of $n$ individuals which are characterized by a sequence of time-varying relative interaction matrices.…
We study Consensus-Based Optimization (CBO) for two-layer neural network training. We compare the performance of CBO against Adam on two test cases and demonstrate how a hybrid approach, combining CBO with Adam, provides faster convergence…
We have proposed a simple one-dimensional model of internal particle dynamics. The model is based on the assumption that self-interaction can be represented by a nonlinear feedback and described by a quadratic recurrent map. Charge plays…
Due to their remarkable properties, systems that exhibit self-organization of their components resulting from intrinsic microscopic activity have been extensively studied in the last two decades. In a generic class of active matter, the…
Polymeric nano- and micro-scale particles have critical roles in tackling critical healthcare and energy challenges with their miniature characteristics. However, tailoring their synthesis process to meet specific design targets has…
We introduce multi-population opinion dynamics models linked to the bounded confidence model, aiming to explore how interactions between individuals contribute to the emergence of consensus, polarization, or fragmentation. Existing models…