Batch Bayesian optimization using multi-scale search

Abstract

Hyperparameters are crucial to many machine learning algorithms. Conventional methods like grid search can be expensive when tuning hyperparameters of a complex model, for example, deep neural networks. Recently, Bayesian optimization has become popular in the machine learning community as an efficient tool for tuning hyperparameters. Bayesian optimization is a global optimization technique that is well suited for optimizing expensive black-box functions. Traditionally Bayesian optimization operates sequentially with one recommendation per trial. However, often a batch of recommendations can be simultaneously evaluated. Current batch Bayesian methods are mostly heuristic based and none have considered heteroscedastic nature of the unknown objective functions. This paper proposes a new batch Bayesian optimization method using a multi-scale search strategy. A batch of recommendations is constructed by searching for optimal recommendations across objective functions using alternate smoothness assumptions. Theoretical analysis shows that the proposed batch improves the regret bound of the sequential method by an order of K, where K is the batch size. We show the effectiveness of our techniques by minimizing three benchmark global optimization test functions and tuning the hyperparameters of two machine learning algorithms.