Scott Clark

Ian Dewancker, Michael McCourt, Scott Clark

The engineering of machine learning systems is still a nascent field; relying on a seemingly daunting collection of quickly evolving tools and best practices. It is our hope that this guidebook will serve as a useful resource for machine learning practitioners looking to take advantage of Bayesian optimization techniques. We outline four example machine learning problems that can be solved using open source machine learning libraries, and highlight the benefits of using Bayesian optimization in the context of these common machine learning applications.

Jialei Wang, Scott C. Clark, Eric Liu et al.

We consider parallel global optimization of derivative-free expensive-to-evaluate functions, and propose an efficient method based on stochastic approximation for implementing a conceptual Bayesian optimization algorithm proposed by Ginsbourger et al. (2007). At the heart of this algorithm is maximizing the information criterion called the "multi-points expected improvement'', or the q-EI. To accomplish this, we use infinitessimal perturbation analysis (IPA) to construct a stochastic gradient estimator and show that this estimator is unbiased. We also show that the stochastic gradient ascent algorithm using the constructed gradient estimator converges to a stationary point of the q-EI surface, and therefore, as the number of multiple starts of the gradient ascent algorithm and the number of steps for each start grow large, the one-step Bayes optimal set of points is recovered. We show in numerical experiments that our method for maximizing the q-EI is faster than methods based on closed-form evaluation using high-dimensional integration, when considering many parallel function evaluations, and is comparable in speed when considering few. We also show that the resulting one-step Bayes optimal algorithm for parallel global optimization finds high-quality solutions with fewer evaluations than a heuristic based on approximately maximizing the q-EI. A high-quality open source implementation of this algorithm is available in the open source Metrics Optimization Engine (MOE).

Ian Dewancker, Michael McCourt, Scott Clark et al.

Bayesian optimization is an elegant solution to the hyperparameter optimization problem in machine learning. Building a reliable and robust Bayesian optimization service requires careful testing methodology and sound statistical analysis. In this talk we will outline our development of an evaluation framework to rigorously test and measure the impact of changes to the SigOpt optimization service. We present an overview of our evaluation system and discuss how this framework empowers our research engineers to confidently and quickly make changes to our core optimization engine

Ian Dewancker, Michael McCourt, Scott Clark et al.

Empirical analysis serves as an important complement to theoretical analysis for studying practical Bayesian optimization. Often empirical insights expose strengths and weaknesses inaccessible to theoretical analysis. We define two metrics for comparing the performance of Bayesian optimization methods and propose a ranking mechanism for summarizing performance within various genres or strata of test functions. These test functions serve to mimic the complexity of hyperparameter optimization problems, the most prominent application of Bayesian optimization, but with a closed form which allows for rapid evaluation and more predictable behavior. This offers a flexible and efficient way to investigate functions with specific properties of interest, such as oscillatory behavior or an optimum on the domain boundary.