Analysis of Expected Hitting Time for Designing Evolutionary Neural Architecture Search Algorithms

Evolutionary computation-based neural architecture search (ENAS) is a popular technique for automating architecture design of deep neural networks. In recent years, various ENAS algorithms have been proposed and shown promising performance on diverse real-world applications. In contrast to these groundbreaking applications, there is no theoretical guideline for assigning a reasonable running time (mainly affected by the generation number, population size, and evolution operator) given both the anticipated performance and acceptable computation budget on ENAS problems. The expected hitting time (EHT), which refers to the average generations, is considered to analyze the running time of ENAS algorithms. This paper proposes a general framework for estimating the EHT of ENAS algorithms, which includes common configuration, search space partition, transition probability estimation, and hitting time analysis. By exploiting the proposed framework, we consider the so-called ($\lambda$+$\lambda$)-ENAS algorithms with different mutation operators and manage to estimate the lower bounds of the EHT {which are critical for the algorithm to find the global optimum}. Furthermore, we study the theoretical results on the NAS-Bench-101 architecture searching problem, and the results show that the one-bit mutation with "bit-based fair mutation" strategy needs less time than the "offspring-based fair mutation" strategy, and the bitwise mutation operator needs less time than the $q$-bit mutation operator. To the best of our knowledge, this is the first work focusing on the theory of ENAS, and the above observation will be substantially helpful in designing efficient ENAS algorithms.