arXiv:2509.09238stat.MLcs.LG2025-09被引 1

用新方法优化随机函数,无需假设噪声分布。

Global Optimization of Stochastic Black-Box Functions with Arbitrary Noise Distributions using Wilson Score Kernel Density Estimation

  • 用威尔逊得分核密度估计构建通用置信区间。
  • 在[0,1]输出范围内,对任意噪声分布都有效。
  • 适合机器人、实验优化等需高效试错的场景。

机器人中的许多优化问题涉及耗时的黑箱函数,如复杂仿真或真实实验评估。这些函数常具有随机性,重复实验受不可测干扰影响。贝叶斯优化通过概率函数估计器提供置信度,以高效筛选搜索空间。其效果依赖于估计器的置信区间质量。现有方法需大量采样推断置信度,或依赖干扰建模。本文表明,威尔逊得分核密度估计器(WS-KDE)在输出范围为闭区间[0,1]的任意随机函数上,均能提供可靠置信界,且不依赖噪声分布假设。这一发现使WS-KDE可用于更广泛的代价函数稳定全局优化。其在模拟中验证,并应用于振动送料器自动陷阱设计问题。

原文摘要 · Abstract (English)

Many optimization problems in robotics involve the optimization of time-expensive black-box functions, such as those involving complex simulations or evaluation of real-world experiments. Furthermore, these functions are often stochastic as repeated experiments are subject to unmeasurable disturbances. Bayesian optimization can be used to optimize such methods in an efficient manner by deploying a probabilistic function estimator to estimate with a given confidence so that regions of the search space can be pruned away. Consequently, the success of the Bayesian optimization depends on the function estimator's ability to provide informative confidence bounds. Existing function estimators require many function evaluations to infer the underlying confidence or depend on modeling of the disturbances. In this paper, it is shown that the confidence bounds provided by the Wilson Score Kernel Density Estimator (WS-KDE) are applicable as excellent bounds to any stochastic function with an output confined to the closed interval [0;1] regardless of the distribution of the output. This finding opens up the use of WS-KDE for stable global optimization on a wider range of cost functions. The properties of WS-KDE in the context of Bayesian optimization are demonstrated in simulation and applied to the problem of automated trap design for vibrational part feeders.

贝叶斯优化随机优化置信区间机器人

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