Enforcing safety is a key aspect of many problems pertaining to sequential decision making under uncertainty, which require the decisions made at every step to be both informative of the optimal decision and also safe. For example, we value both efficacy and comfort in medical therapy, and efficiency and safety in robotic control. We consider this problem of optimizing an unknown utility function with absolute feedback or preference feedback subject to unknown safety constraints. We develop an efficient safe Bayesian optimization algorithm, StageOpt, that separates safe region expansion and utility function maximization into two distinct stages. Compared to existing approaches which interleave between expansion and optimization, we show that StageOpt is more efficient and naturally applicable to a broader class of problems. We provide theoretical guarantees for both the satisfaction of safety constraints as well as convergence to the optimal utility value. We evaluate StageOpt on both a variety of synthetic experiments, as well as in clinical practice. We demonstrate that StageOpt is more effective than existing safe optimization approaches, and is able to safely and effectively optimize spinal cord stimulation therapy in our clinical experiments.

A major challenge in Bayesian Optimization is the boundary issue where an algorithm spends too many evaluations near the boundary of its search space. In this paper, we propose BOCK, Bayesian Optimization with Cylindrical Kernels, whose basic idea is to transform the ball geometry of the search space using a cylindrical transformation. Because of the transformed geometry, the Gaussian Process-based surrogate model spends less budget searching near the boundary, while concentrating its efforts relatively more near the center of the search region, where we expect the solution to be located. We evaluate BOCK extensively, showing that it is not only more accurate and efficient, but it also scales successfully to problems with a dimensionality as high as 500. We show that the better accuracy and scalability of BOCK even allows optimizing modestly sized neural network layers, as well as neural network hyperparameters.

Modern deep learning methods are very sensitive to many hyperparameters, and, due to the long training times of state-of-the-art models, vanilla Bayesian hyperparameter optimization is typically computationally infeasible. On the other hand, bandit-based configuration evaluation approaches based on random search lack guidance and do not converge to the best configurations as quickly. Here, we propose to combine the benefits of both Bayesian optimization and bandit-based methods, in order to achieve the best of both worlds: strong anytime performance and fast convergence to optimal configurations. We propose a new practical state-of-the-art hyperparameter optimization method, which consistently outperforms both Bayesian optimization and Hyperbandon a wide range of problem types, including high-dimensional toy functions, support vector machines, feed-forward neural networks, Bayesian neural networks, deep reinforcement learning, and convolutional neural networks. Our method is robust and versatile, while at the same time being conceptually simple and easy to implement.

The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly evalu-ations pose challenges for current techniques in discrete optimization and machine learning, and critically require new algorithmic ideas (NIPS BayesOpt 2017). This article proposes, to the best of our knowledge, the first algorithm to overcome these challenges, based on an adaptive, scal able model that identifies useful combinatorial structure even when data is scarce. Our acquisition function pioneers the use of semidefinite programming to achieve efficiency and scalability.Experimental evaluations demonstrate that this algorithm consistently outperforms other methods from combinatorial and Bayesian optimization.