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arXiv 2402.16237cs.LGcs.AI
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连续搜索空间中具有理论保证的主动水平集估计

Active Level Set Estimation for Continuous Search Space with Theoretical Guarantee

Applied Artificial Intelligence Institute (A2I2)(应用人工智能研究所)

Giang Ngo, Dang Nguyen, Dat Phan-Trong, Sunil Gupta

AI总结:

本文针对连续搜索空间中的黑盒函数水平集估计问题,提出一种无需离散化、基于置信度采集函数的新算法,并给出理论收敛保证,在多个数据集上优于现有方法。

摘要:

在许多实际应用中常见的一个问题是水平集估计,其目标是确定函数域中函数高于或低于给定阈值的区域。当函数是黑盒且评估代价高昂时,需要在最少的函数评估次数内找到水平集。现有方法通常假设离散搜索空间,使用有限的数据点集合进行函数评估和水平集估计。当应用于连续搜索空间时,这些方法往往需要先对空间进行离散化,这会导致结果较差,同时需要较高的计算时间。虽然一些方法适用于连续设置,但它们仍然缺乏适当的理论收敛保证。为了解决这个问题,我们提出了一种新算法,该算法不需要任何离散化,可以直接在连续搜索空间中工作。我们的方法通过构造一个采集函数来建议评估点,该采集函数被定义为函数高于或低于给定阈值的置信度度量。我们提供了该算法收敛到精确解的理论分析。在多个合成数据集和真实世界数据集上,我们的算法成功地优于最先进的方法。

英文摘要:

A common problem encountered in many real-world applications is level set estimation where the goal is to determine the region in the function domain where the function is above or below a given threshold. When the function is black-box and expensive to evaluate, the level sets need to be found in a minimum set of function evaluations. Existing methods often assume a discrete search space with a finite set of data points for function evaluations and estimating the level sets. When applied to a continuous search space, these methods often need to first discretize the space which leads to poor results while needing high computational time. While some methods cater for the continuous setting, they still lack a proper guarantee for theoretical convergence. To address this problem, we propose a novel algorithm that does not need any discretization and can directly work in continuous search spaces. Our method suggests points by constructing an acquisition function that is defined as a measure of confidence of the function being higher or lower than the given threshold. A theoretical analysis for the convergence of the algorithm to an accurate solution is provided. On multiple synthetic and real-world datasets, our algorithm successfully outperforms state-of-the-art methods.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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