A Gentle Introduction to Bayesian Optimization

Bayesian optimization is a sample efficient sequential global optimization method for black-box, expensive and multi-extremal functions. It generates, and keeps updated, a probabilistic surrogate model of the objective function, depending on the performed evaluations, and optimizes an acquisition function to choose a new point to evaluate. The acquisition function deals with the exploration-exploitation dilemma depending on surrogate's predictive mean and uncertainty. Many alternatives are available offering different trade-off mechanisms; different options are also possible for the probabilistic surrogate model: Gaussian Process regression is best suited for optimization over continuous search spaces while other approaches, such as Random Forests or Gaussian Prcesses with ah-hoc kernels, deal with complex search spaces spanned by nominal, numeric and conditional variables. This tutorial offers an introduction to these topics and a discussion on available tools, real-life applications, and recent advances, such as unknown constraints, multi-information sources and cost-awareness, and multi-objective optimization.