Bayesian optimization

Bayesian optimization is a sequential design strategyfor global optimization of black-box functions that doesn't require derivatives. Bayesian optimization is a sequential design strategyfor global optimization of black-box functions that doesn't require derivatives. The term is generally attributed to Jonas Mockus and is coined in his work from a series of publications on global optimization in the 1970s and 1980s. Since the objective function is unknown, the Bayesian strategy is to treat it as a random function and place a prior over it.The prior captures beliefs about the behaviour of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the posterior distribution over the objective function. The posterior distribution, in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines the next query point. Examples of acquisition functions include probability of improvement, expected improvement, Bayesian expected losses, upper confidence bounds (UCB), Thompson sampling and hybrids of these. They all trade-off exploration and exploitation so as to minimize the number of function queries. As such, Bayesian optimization is well suited for functions that are expensive to evaluate.