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Evolutionary computation-based neural architecture search (ENAS) is a populartechnique for automating architecture design of deep neural networks. In recentyears, various ENAS algorithms have been proposed and shown promisingperformance on diverse real-world applications. In contrast to thesegroundbreaking applications, there is no theoretical guideline for assigning areasonable running time (mainly affected by the generation number, populationsize, and evolution operator) given both the anticipated performance andacceptable computation budget on ENAS problems. The expected hitting time(EHT), which refers to the average generations, is considered to analyze therunning time of ENAS algorithms. This paper proposes a general framework forestimating the EHT of ENAS algorithms, which includes common configuration,search space partition, transition probability estimation, and hitting timeanalysis. By exploiting the proposed framework, we consider the so-called($\lambda$+$\lambda$)-ENAS algorithms with different mutation operators andmanage to estimate the lower bounds of the EHT {which are critical for thealgorithm to find the global optimum}. Furthermore, we study the theoreticalresults on the NAS-Bench-101 architecture searching problem, and the resultsshow that the one-bit mutation with "bit-based fair mutation" strategy needsless time than the "offspring-based fair mutation" strategy, and the bitwisemutation operator needs less time than the $q$-bit mutation operator. To thebest of our knowledge, this is the first work focusing on the theory of ENAS,and the above observation will be substantially helpful in designing efficientENAS algorithms.

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