Evolutionary computation-based neural architecture search (ENAS) is a popular technique for automating architecture design of deep neural networks. Despite its groundbreaking applications, there is no theoretical study for ENAS. The expected hitting time (EHT) is one of the most important theoretical issues, since it implies the average computational time complexity. This paper proposes a general method by integrating theory and experiment for estimating the EHT of ENAS algorithms, which includes common configuration, search space partition, transition probability estimation, population distribution fitting, and hitting time analysis. By exploiting the proposed method, we consider the ($\lambda$+$\lambda$)-ENAS algorithms with different mutation operators and estimate the lower bounds of the EHT. Furthermore, we study the EHT on the NAS-Bench-101 problem, and the results demonstrate the validity of the proposed method. To the best of our knowledge, this work is the first attempt to establish a theoretical foundation for ENAS algorithms.

翻译：基于进化计算的神经架构搜索（ENAS）是一种自动化设计深度神经网络架构的流行技术。尽管其应用具有开创性，但目前尚无针对ENAS的理论研究。期望命中时间（EHT）是最重要的理论问题之一，因为它暗示了平均计算时间复杂度。本文提出了一种融合理论与实验的通用方法，用于估计ENAS算法的EHT，该方法包括通用配置、搜索空间划分、转移概率估计、种群分布拟合以及命中时间分析。通过利用所提出的方法，我们考虑了采用不同变异算子的（$\lambda$+$\lambda$）-ENAS算法，并估计了EHT的下界。此外，我们研究了NAS-Bench-101问题上的EHT，结果证明了所提方法的有效性。据我们所知，这项工作是首次尝试为ENAS算法建立理论基础。