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arXiv 2409.00306cs.NE
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进化算法在忽略噪声时对噪声的鲁棒性显著更强

Evolutionary Algorithms Are Significantly More Robust to Noise When They Ignore It

Denis Antipov, Benjamin Doerr

AI总结:

本文首次对无重新评估的进化算法进行噪声环境下的数学运行时间分析,证明 $(1+1)$ 进化算法可在常数噪声率下优化 LeadingOnes,表明重新评估并非必要且可能有害。

摘要:

随机搜索启发式(RSHs)已知对噪声具有一定的鲁棒性。旨在严格量化 RSHs 在噪声目标函数访问下鲁棒程度的数学分析通常假设每个解在与其他解比较时都会被重新评估。这种做法旨在防止单次噪声评估产生持久的负面影响,但计算代价高昂,并且要求用户预见到噪声的存在(因为在无噪声环境中,人们永远不会重新评估解)。在本工作中,我们首次对一种在不进行重新评估的情况下求解单目标噪声问题的进化算法进行了数学运行时间分析。我们证明,不进行重新评估的 $(1+1)$ 进化算法可以在高达常数噪声率的情况下优化经典的 LeadingOnes 基准问题,这与进行重新评估的版本形成鲜明对比,后者仅能容忍噪声率为 $O(n^{-2} \log n)$ 的噪声。这一结果表明,重新评估远不如之前所认为的那样必要,而且实际上可能非常有害。我们数学证明中的洞见表明,类似的结果对于其他经典基准问题也是合理的。

英文摘要:

Randomized search heuristics (RSHs) are known to have a certain robustness to noise. Mathematical analyses trying to quantify rigorously how robust RSHs are to a noisy access to the objective function typically assume that each solution is re-evaluated whenever it is compared to others. This aims at preventing that a single noisy evaluation has a lasting negative effect, but is computationally expensive and requires the user to foresee that noise is present (as in a noise-free setting, one would never re-evaluate solutions). In this work, we conduct the first mathematical runtime analysis of an evolutionary algorithm solving a single-objective noisy problem without re-evaluations. We prove that the $(1+1)$ evolutionary algorithm without re-evaluations can optimize the classic LeadingOnes benchmark with up to constant noise rates, in sharp contrast to the version with re-evaluations, where only noise with rates $O(n^{-2} \log n)$ can be tolerated. This result suggests that re-evaluations are much less needed than what was previously thought, and that they actually can be highly detrimental. The insights from our mathematical proofs indicate that this similar results are plausible for other classic benchmarks.

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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