Batch Bayesian optimisation via density-ratio estimation with guarantees
This work addresses the scalability and efficiency of Bayesian optimization for expensive black-box functions, offering a batch extension with theoretical guarantees, though it builds incrementally on prior BORE methods.
The paper tackles the problem of scaling Bayesian optimization (BO) to batch settings by extending the density-ratio estimation (BORE) approach, which reformulates BO as a probabilistic classifier to avoid explicit priors. It provides theoretical regret guarantees and shows improved performance in experiments against baselines.
Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a theoretical analysis of BORE's regret and an extension of the algorithm with improved uncertainty estimates. We also show that BORE can be naturally extended to a batch optimisation setting by recasting the problem as approximate Bayesian inference. The resulting algorithms come equipped with theoretical performance guarantees and are assessed against other batch and sequential BO baselines in a series of experiments.