Runtime Analysis of Evolutionary NAS for Multiclass Classification

TL;DR

This paper provides a theoretical runtime analysis of evolutionary neural architecture search (ENAS) for multiclass classification, establishing bounds and highlighting the efficiency of simple mutation strategies.

Contribution

It introduces a benchmark and analyzes the runtime bounds of (1+1)-ENAS algorithms with different mutations, offering new theoretical insights into ENAS efficiency.

Findings

Expected runtime upper bound: O(rM ln rM)

Expected runtime lower bound: Ω(rM ln M)

Simple one-bit mutation is effective and competitive

Abstract

Evolutionary neural architecture search (ENAS) is a key part of evolutionary machine learning, which commonly utilizes evolutionary algorithms (EAs) to automatically design high-performing deep neural architectures. During past years, various ENAS methods have been proposed with exceptional performance. However, the theory research of ENAS is still in the infant. In this work, we step for the runtime analysis, which is an essential theory aspect of EAs, of ENAS upon multiclass classification problems. Specifically, we first propose a benchmark to lay the groundwork for the analysis. Furthermore, we design a two-level search space, making it suitable for multiclass classification problems and consistent with the common settings of ENAS. Based on both designs, we consider (1+1)-ENAS algorithms with one-bit and bit-wise mutations, and analyze their upper and lower bounds on the expected runtime. We prove that the algorithm using both mutations can find the optimum with the expected runtime upper bound of $O(rM\ln{rM})$ and lower bound of $\Omega(rM\ln{M})$. This suggests that a simple one-bit mutation may be greatly considered, given that most state-of-the-art ENAS methods are laboriously designed with the bit-wise mutation. Empirical studies also support our theoretical proof.