论文标题
基于时间滴定共识的优化算法的收敛性和错误估计值
Convergence and error estimates for time-discrete consensus-based optimization algorithms
论文作者
论文摘要
我们介绍了[Arxiv：1909.09249]中提出的基于时间 - 分散共识的优化（CBO）算法的收敛性和误差估计。在作者最近的工作[ARXIV：1910.08239]中，对[ARXIV：1909.09249]中提出的一阶共识优化算法进行严格的误差分析，而未通过平均场限制求解到动力学方程。然而，相应的时间滴定算法的误差分析不是主要是由于缺乏ITô随机演算的离散类似物而进行的。在本文中，我们为基于一般时间差异共识的优化算法提供了简单而基本的收敛性和错误分析，其中包括[ARXIV：1909.09249]中的三种离散算法。我们的分析提供了三种算法的数值稳定性和收敛条件，以及对全局最小值的错误估计。
We present convergence and error estimates of the time-discrete consensus-based optimization(CBO) algorithms proposed in [arXiv:1909.09249] for general nonconvex functions. In authors' recent work [arxiv: 1910.08239], rigorous error analysis of the first-order consensus-based optimization algorithm proposed in [arXiv:1909.09249] was studied at the particle level without resorting to the kinetic equation via a mean-field limit. However, the error analysis for the corresponding time-discrete algorithm was not done mainly due to lack of discrete analogue of Itô's stochastic calculus. In this paper, we provide a simple and elementary convergence and error analysis for a general time-discrete consensus-based optimization algorithm, which includes the three discrete algorithms in [arXiv:1909.09249]. Our analysis provides numerical stability and convergence conditions for the three algorithms, as well as error estimates to the global minimum.
