发表机构
LTCI, Télécom Paris, Institut Polytechnique de Paris（巴黎理工学院电信学院通信与电子学实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出无动量粒子群优化的连续时间极限模型，保留不连续的个人与全局最优选择，证明弱极限满足随机微分包含，并在正则条件下恢复原始选择器及唯一性。
AI 中文摘要
粒子群优化（PSO）是一类流行的无梯度全局优化方法。我们研究了一个具有个人最优记忆和全局最优交互的无动量粒子群优化的连续时间模型。与依赖平滑逼近的先前模型不同，我们保留了原始不连续的个人最优和全局最优过程。我们研究了小步长极限，并证明弱极限点满足随机微分包含：个人最优变量服从松弛的记录条件，而全局最优选择器的快速切换导致凸化的交互。随后，我们给出了恢复真实原始选择器的条件。在适当的正则性和非退化假设下，布朗噪声使我们能够将个人最优过程与极限轨迹的最新记录位置等同起来，并证明在几乎每个时刻达到全局最优的粒子是唯一的。由此产生的连续时间动力学在不平滑的情况下保留了两种选择规则。
英文摘要
Particle swarm optimization (PSO) is a popular class of gradient-free methods for global optimization. We study a continuous-time model for momentum-free PSO with personal-best memory and global-best interaction. Unlike previous models which rely on smooth approximations, we keep the original discontinuous personal- and global-best processes. We study the small-step limit and show that weak limit points satisfy a stochastic differential inclusion: personal-best variables obey a relaxed record condition, while fast switching of the global-best selector leads to a convexified interaction. We then give conditions under which the true original selectors are recovered. Under suitable regularity and nondegeneracy assumptions, Brownian noise allows us to identify the personal-best processes with the latest record positions of the limiting trajectories and to prove that the particle attaining the global best is unique at almost every time. The resulting continuous-time dynamics retain both selection rules without smoothing them.
Comments25 pages, 1 figure
