Tensor Completion for Efficient and Accurate Hyperparameter Optimisation in Large-Scale Statistical Learning

Hyperparameter optimisation is a prerequisite for state-of-the- art performance in machine learning, with current strategies including Bayesian optimisation, hyperband, and evolutionary methods. While such methods have been shown to improve performance, none of these is designed to explicitly take advantage of the underlying data structure. To this end, we introduce a completely different approach for hyperparameter optimisation, based on low-rank tensor completion. This is achieved by first forming a multi-dimensional tensor which comprises performance scores for different combinations of hyperparameters. Based on the realistic underlying assumption that the so-formed tensor has a low-rank structure, reliable estimates of the unobserved validation scores of combinations of hyper- parameters are next obtained through tensor completion, from only a fraction of the known elements in the tensor. Through extensive experimentation on various datasets and learning models, the proposed method is shown to exhibit competitive or superior performance to state-of-the-art hyperparameter optimisation strategies. Distinctive advantages of the proposed method include its ability to simultaneously handle any hyper- parameter type (kind of optimiser, number of neurons, number of layer, etc.), its relative simplicity compared to competing methods, as well as the ability to suggest multiple optimal combinations of hyperparameters.