No-Regret Bayesian Optimization with Unknown Hyperparameters

Understand

Bayesian optimization (BO) based on Gaussian process models is a powerful paradigm to optimize black-box functions that are expensive to evaluate.

• While several BO algorithms provably converge to the global optimum of the unknown function, they assume that the hyperparameters of the kernel are known in advance.
• This is not the case in practice and misspecification often causes these algorithms to converge to poor local optima.
• In this paper, we present the first BO algorithm that is provably no-regret and converges to the optimum without knowledge of the hyperparameters.