中等种群规模已可证明对噪声具有强鲁棒性
Already Moderate Population Sizes Provably Yield Strong Robustness to Noise
AI总结：
本文通过新颖的有偏均匀交叉证明思路，首次证明中等对数规模种群即可使$(1+λ)$和$(1,λ)$进化算法在恒定噪声下保持OneMax基准的渐近最优运行时间，显著强于此前需超线性种群的结果。
摘要：
经验表明，典型的进化算法能够很好地应对随机扰动，例如带噪声的函数评估。本文首次对存在先验逐位噪声的$(1+λ)$和$(1,λ)$进化算法进行数学运行时间分析，证明这两种算法都能容忍恒定噪声概率，且不会增加在OneMax基准上的渐近运行时间。为此，种群规模$λ$只需至少与问题规模$n$的对数同阶即可。此前该方向的唯一结果针对的是不太现实的单比特噪声模型，要求种群规模为问题规模的超线性函数，并证明了在OneMax基准上运行时间约为无噪声运行时间的三次方的保证。我们显著更强的结果基于一个新的证明思路：无噪声后代可视为父代与带噪声后代之间的有偏均匀交叉。我们乐观地认为，由这一洞见得到的技术引理也将在未来进化算法的数学运行时间分析中找到应用。
英文摘要：
Experience shows that typical evolutionary algorithms can cope well with stochastic disturbances such as noisy function evaluations. In this first mathematical runtime analysis of the $(1+λ)$ and $(1,λ)$ evolutionary algorithms in the presence of prior bit-wise noise, we show that both algorithms can tolerate constant noise probabilities without increasing the asymptotic runtime on the OneMax benchmark. For this, a population size $λ$ suffices that is at least logarithmic in the problem size $n$. The only previous result in this direction regarded the less realistic one-bit noise model, required a population size super-linear in the problem size, and proved a runtime guarantee roughly cubic in the noiseless runtime for the OneMax benchmark. Our significantly stronger results are based on the novel proof argument that the noiseless offspring can be seen as a biased uniform crossover between the parent and the noisy offspring. We are optimistic that the technical lemmas resulting from this insight will find applications also in future mathematical runtime analyses of evolutionary algorithms.
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。
