A First Step Towards Runtime Analysis of Evolutionary Neural Architecture Search

Evolutionary neural architecture search (ENAS) employs evolutionary algorithms to find high-performing neural architectures automatically, and has achieved great success. However, compared to the empirical success, its rigorous theoretical analysis has yet to be touched. This work goes preliminary steps toward the mathematical runtime analysis of ENAS. In particular, we define a binary classification problem UNIFORM, and formulate an explicit fitness function to represent the relationship between neural architecture and classification accuracy. Furthermore, we consider (1+1)-ENAS algorithm with mutation to optimize the neural architecture, and obtain the following runtime bounds: 1) the one-bit mutation finds the optimum in an expected runtime of $O(n)$ and $\Omega(\log n)$; 2) the multi-bit mutation finds the optimum in an expected runtime of $\Theta(n)$. These theoretical results show that one-bit and multi-bit mutations achieve nearly the same performance on UNIFORM. We provide insight into the choices of mutation in the ENAS community: although multi-bit mutation can change the step size to prevent a local trap, this may not always improve runtime. Empirical results also verify the equivalence of these two mutation operators. This work begins the runtime analysis of ENAS, laying the foundation for further theoretical studies to guide the design of ENAS.

Efficient Evaluation Methods for Neural Architecture Search: A Survey

Neural Architecture Search (NAS) has received increasing attention because of its exceptional merits in automating the design of Deep Neural Network (DNN) architectures. However, the performance evaluation process, as a key part of NAS, often requires training a large number of DNNs. This inevitably causes NAS computationally expensive. In past years, many Efficient Evaluation Methods (EEMs) have been proposed to address this critical issue. In this paper, we comprehensively survey these EEMs published up to date, and provide a detailed analysis to motivate the further development of this research direction. Specifically, we divide the existing EEMs into four categories based on the number of DNNs trained for constructing these EEMs. The categorization can reflect the degree of efficiency in principle, which can in turn help quickly grasp the methodological features. In surveying each category, we further discuss the design principles and analyze the strength and weaknesses to clarify the landscape of existing EEMs, thus making easily understanding the research trends of EEMs. Furthermore, we also discuss the current challenges and issues to identify future research directions in this emerging topic. To the best of our knowledge, this is the first work that extensively and systematically surveys the EEMs of NAS.

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.