pyGPGO: Bayesian Optimization for Python

Abstract

Bayesian optimization has risen over the last few years as a very attractive method to optimize expensive to evaluate, black box, derivative-free and possibly noisy functions (Shahriari et al. 2016). This framework uses surrogate models, such as the likes of a Gaussian Process (Rasmussen and Williams 2004) which describe a prior belief over the possible objective functions in order to approximate them. The procedure itself is inherently sequential: our function is first evaluated a few times, a surrogate model is then fit with this information, which will later suggest the next point to be evaluated according to a predefined acquisition function. These strategies typically aim to balance exploitation and exploration, that is, areas where the posterior mean or variance of our surrogate model are high respectively. These strategies have recently grabbed the attention of machine learning researchers over simpler black-box optimization strategies, such as grid search or random search (Bergstra James and Bengio Yoshua 2012). It is specially interesting in areas such as automatic machine-learning hyperparameter optimization (Snoek, Larochelle, and Adams 2012), A/B testing (Chapelle and Li 2011) or recommender systems (Vanchinathan et al. 2014), among others. Furthermore, the framework is entirely modular; there are many choices a user could take regarding the design of the optimization procedure: choice of surrogate model, covariance function, acquisition function behaviour or hyperparameter treatment, to name a few. Here we present pyGPGO , an open-source Python package for Bayesian Optimization, which embraces this modularity in its design. While additional Python packages exist for the same purpose, either they are restricted for non-commercial applications (Snoek 2012), implement a small subset of the features (Yelp 2014), or do not provide a modular interface (team. 2016). pyGPGO on the other hand aims to provide the highest degree of freedom in the design and inference of a Bayesian optimization pipeline, while being feature-wise competitive with other existing software. pyGPGO currently supports: • Different surrogate models: Gaussian Processes, Student-t Processes, Random Forests (& variants) and Gradient Boosting Machines. • Most usual covariance function structures, as well as their derivatives: squared exponential, Matèrn, gamma-exponential, rational-quadratic, exponential-sine and dot-product kernel. • Several acquisition function behaviours: probability of improvement, expected improvement , upper confidence bound and entropy-based, as well as their integrated versions. • Type II maximum-likelihood estimation of covariance hyperparameters. • MCMC sampling for the full-bayesian treatment of hyperparameters (via pyMC3 (Salvatier, Wiecki, and C. 2016))