Portfolio Allocation for Bayesian Optimization

Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model's estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm's performance.Comment: This revision contains an updated the performance bound and other minor text change

Bayesian Optimization in Machine Learning

Bayesian optimization has risen over the last few years as a very attractive approach to find the optimum of noisy, expensive to evaluate, and possibly black-box functions. One of the fields where these functions are common is in machine-learning, where one typically has to fit a particular model by minimizing a specified form of loss. In this Master s thesis we first focus on reviewing the most recent literature on Gaussian Processes as well as Bayesian optimiza- tion methods, then we benchmark said methods against several real case machine-learning scenarios and lastly we provide open source software that will allow researchers to apply these strategies in other problems

High-dimensional Bayesian optimization with intrinsically low-dimensional response surfaces

Bayesian optimization is a powerful technique for the optimization of expensive black-box functions. It is used in a wide range of applications such as in drug and material design and training of machine learning models, e.g. large deep networks. We propose to extend this approach to high-dimensional settings, that is where the number of parameters to be optimized exceeds 10--20. In this thesis, we scale Bayesian optimization by exploiting different types of projections and the intrinsic low-dimensionality assumption of the objective function. We reformulate the problem in a low-dimensional subspace and learn a response surface and maximize an acquisition function in this low-dimensional projection. Contributions include i) a probabilistic model for axis-aligned projections, such as the quantile-Gaussian process and ii) a probabilistic model for learning a feature space by means of manifold Gaussian processes. In the latter contribution, we propose to learn a low-dimensional feature space jointly with (a) the response surface and (b) a reconstruction mapping. Finally, we present empirical results against well-known baselines in high-dimensional Bayesian optimization and provide possible directions for future research in this field.Open Acces