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pyGPGO: Bayesian Optimization for Python |
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4 September 2017 |
paper.bib |
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 [@Shahriari2016]. This framework uses surrogate models, such as the likes of a Gaussian Process [@Rasmussen2004] 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 [@Bergstra2012]. It is specially interesting in areas such as automatic machine-learning hyperparameter optimization [@Snoek2012], A/B testing [@Chapelle2011] or recommender systems [@Vanchinathan2014], 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 [@SpearmintSnoek2012], implement a small subset of the features [@yelpmoe], or do not provide a modular interface [@scikitoptimize]. 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[@Salvatier2016])
pyGPGO is MIT-licensed and can be retrieved from both GitHub and PyPI, with extensive documentation available at ReadTheDocs. pyGPGO is built on top of other well known packages of the Python scientific ecosystem as dependencies, such as numpy, scikit-learn, pyMC3 and theano.
pyGPGO is an ongoing project, and as such there are several improvements that will be tackled in the near future:
- Support for linear combinations of covariance functions, with automatic gradient computation.
- Support for more diverse acquisition functions, such as Predictive Entropy Search [@Hernandez-Lobato2014].
- A class for constrained Bayesian Optimization is planned for the near future. [@Gardner2014]