Global optimization of graph acquisition functions for neural architecture search

TL;DR

This paper introduces explicit optimization formulations for graph input spaces in neural architecture search, enabling more effective graph Bayesian optimization by addressing the complexity of discrete graph search spaces.

Contribution

It proposes novel explicit optimization formulations for graph spaces in NAS, with theoretical proofs and practical algorithms for improved graph BO performance.

Findings

Efficiently finds optimal architectures on NAS benchmarks.

Theoretically proven to be equivalent representations of graph space.

Outperforms existing methods in several NAS tasks.

Abstract

Graph Bayesian optimization (BO) has shown potential as a powerful and data-efficient tool for neural architecture search (NAS). Most existing graph BO works focus on developing graph surrogates models, i.e., metrics of networks and/or different kernels to quantify the similarity between networks. However, the acquisition optimization, as a discrete optimization task over graph structures, is not well studied due to the complexity of formulating the graph search space and acquisition functions. This paper presents explicit optimization formulations for graph input space including properties such as reachability and shortest paths, which are used later to formulate graph kernels and the acquisition function. We theoretically prove that the proposed encoding is an equivalent representation of the graph space and provide restrictions for the NAS domain with either node or edge labels. Numerical results over several NAS benchmarks show that our method efficiently finds the optimal architecture for most cases, highlighting its efficacy.