Title: Neural Architecture Search with Bayesian Optimisation and Optimal Transport,
Abstract: Bayesian Optimisation (BO) refers to a class of methods for global
optimisation of a function $f$ which is only accessible via point evaluations.
It is typically used in settings where $f$ is expensive to evaluate. A common
use case for BO in machine learning is model selection, where it is not
possible to analytically model the generalisation performance of a statistical
model, and we resort to noisy and expensive training and validation procedures
to choose the best model. Conventional BO methods have focused on Euclidean and
categorical domains, which, in the context of model selection, only permits
tuning scalar hyper-parameters of machine learning algorithms. However, with
the surge of interest in deep learning, there is an increasing demand to tune
neural network \emph{architectures}. In this work, we develop NASBOT, a
Gaussian process based BO framework for neural architecture search. To
accomplish this, we develop a distance metric in the space of neural network
architectures which can be computed efficiently via an optimal transport
program. This distance might be of independent interest to the deep learning
community as it may find applications outside of BO. We demonstrate that NASBOT
outperforms other alternatives for architecture search in several cross
validation based model selection tasks on multi-layer perceptrons and
convolutional neural networks.