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 $\textsc{UNIFORM}$, 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: both the local and global mutations find the optimum in an expected runtime of $\Theta(n)$, where $n$ is the problem size. The theoretical results show that the local and global mutations achieve nearly the same performance on $\textsc{UNIFORM}$. Empirical results also verify the equivalence of these two mutation operators.

翻译：进化神经架构搜索（ENAS）利用进化算法自动寻找高性能神经架构，并已取得巨大成功。然而，相较于其实验上的成功，其严格的理论分析尚未被涉及。本文对ENAS的数学运行时分析进行了初步探索。具体而言，我们定义了一个二分类问题$\textsc{UNIFORM}$，并构建了一个显式适应度函数来表示神经架构与分类精度之间的关系。此外，我们考虑了采用变异操作的(1+1)-ENAS算法来优化神经架构，并得到了以下运行时界限：局部变异和全局变异均能在期望运行时间$\Theta(n)$内找到最优解，其中$n$为问题规模。理论结果表明，局部变异和全局变异在$\textsc{UNIFORM}$问题上性能几乎相同。实验结果也验证了这两种变异操作在性能上的等价性。