论文标题
通过跳跃扩散随机微分方程基于共识的优化
Consensus based optimization via jump-diffusion stochastic differential equations
论文作者
论文摘要
我们引入了一种新的基于共识的优化方法（CBO）方法，其中相互作用的粒子系统由跳跃随机微分方程驱动。我们研究粒子系统及其平均场极限的适合性。本文的主要贡献是相互作用的粒子系统趋向于平均场限制和离散粒子系统收敛的证据，并在均方根意义上向连续时间动力学收敛。我们还证明，对于大量的目标函数，平均场跳水扩散SDE与全球最小化器的融合。我们证明了在基准目标函数上的数值模拟中，提出的CBO方法比早期CBO方法的性能提高了。
We introduce a new consensus based optimization (CBO) method where interacting particle system is driven by jump-diffusion stochastic differential equations. We study well-posedness of the particle system as well as of its mean-field limit. The major contributions of this paper are proofs of convergence of the interacting particle system towards the mean-field limit and convergence of a discretized particle system towards the continuous-time dynamics in the mean-square sense. We also prove convergence of the mean-field jump-diffusion SDEs towards global minimizer for a large class of objective functions. We demonstrate improved performance of the proposed CBO method over earlier CBO methods in numerical simulations on benchmark objective functions.
