发表机构
California Institute of Technology; Brown University（加州理工学院; 布朗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分析粒子群优化（PSO）参数耦合对基于共识优化（CBO）收敛保证的影响，通过显式构造证明存在非空参数集使保证成立，但范围缩小，故CBO保证不能直接扩展至经典PSO，并用数值模拟验证。
AI 中文摘要
粒子群优化（PSO）是一种广泛使用的算法，出现在许多最先进的优化工具包中。然而，严格的性能保证仍然缺乏。标准的PSO动力学不允许自然的平均场描述，而这将为理论分析提供途径。通过修改PSO公式，可以恢复带有记忆的基于共识优化（CBO）算法，该算法允许平均场极限并促进严格的收敛性分析。这些理论保证在很大程度上依赖于这样一个事实：对于CBO，漂移和噪声强度可以独立选择，而对于PSO，它们是耦合的。我们分析了PSO参数耦合如何影响现有的CBO及其带记忆效应的变体的收敛保证。我们通过显式构造表明，这种耦合仍然为非空的参数集留下了空间，使得这些收敛保证成立。然而，在用于恢复PSO的极限中，可允许的参数范围会缩小。因此，从CBO得到的收敛保证不能直接扩展到经典的PSO模型。我们提供了数值模拟，以说明理论分析中展示的参数权衡。
英文摘要
Particle swarm optimization (PSO) is a widely used algorithm featured in many state-of-the-art optimization tool-kits. However, rigorous performance guarantees are still lacking. The standard PSO dynamics do not admit a natural mean-field description, which would provide an avenue for theoretical analysis. By modifying the PSO formulation, one can recover the consensus-based optimization (CBO) algorithm with memory, which admits a mean-field limit and facilitates rigorous convergence analysis. These theoretical guarantees rely heavily on the fact that for CBO, the drift and noise strengths can be chosen independently, whereas they are coupled for PSO. We analyze how the PSO parameter coupling affects existing convergence guarantees for CBO and its variant with memory effect. We show, by an explicit construction, that the coupling still leaves a non-empty set of admissible parameters for these convergence guarantees to hold. However, the admissible parameter ranges shrink in the limits used to recover PSO. The resulting convergence guarantees from CBO therefore do not directly extend to the classical PSO model. We provide numerical simulations illustrating the parameter tradeoffs shown in the theoretical analysis.
Comments27 pages, 1 figure, submitted to DynaFront2026: Dynamics at the Frontiers of Optimization, Sampling, and Games (NeurIPS 2026 Workshop)
