REVIEW: Taking the human out of the loop - a review of Bayesian Optimization / by Siobhán Cronin

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016). Shahriari et al. Proceedings of the IEEE

Introduction

  • "Mathematically we are considering the problem of finding a global maximizer (or minimizer) of an unknown objective function f, where X is some design space of interest; ..."
  • "...in global optimization, X is often a compact subset of R^d but the Bayesian optimization framework can be applied to more unusual search spaces that involve categorical or conditional inputs."
  • "The Bayesian posterior represents our updates beliefs - given data - on the likely objective function we are optimizing. Equipped with this probabilistic model, we can sequentially induce acquisition functions that leverage the uncertainty in the posterior to guide exploration."
  • "Intuitively, the acquisition function evaluates the utility of candidate points for the next evaluation of f; therefore x_n+1 is selected by maximizing \alpha_n"
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Nonparametric models

  • "The kernel trick allows us to specify an intuitive similarity between pairs of points, rather than a feature map, which in practice can be hard to define."
  • Common kernels (Matérn)
  • "The marginal likelihood is very useful in learning the hyperparameters. As long as the kernel is differentiable with respect to its hyperparameters, the marginal likelihood can be differentiated and can therefore be optimized."