Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processes
This work addresses a bottleneck in Bayesian optimization for researchers and practitioners by enhancing batch efficiency, though it is incremental as it builds on existing sampling methods.
The paper tackles the challenge of selecting diverse and informative batches of evaluation points in batched Bayesian optimization by introducing DPP-BBO, a framework using Determinantal Point Processes to diversify sampling, resulting in tighter regret bounds and improved performance in experiments.
In Bayesian Optimization (BO) we study black-box function optimization with noisy point evaluations and Bayesian priors. Convergence of BO can be greatly sped up by batching, where multiple evaluations of the black-box function are performed in a single round. The main difficulty in this setting is to propose at the same time diverse and informative batches of evaluation points. In this work, we introduce DPP-Batch Bayesian Optimization (DPP-BBO), a universal framework for inducing batch diversity in sampling based BO by leveraging the repulsive properties of Determinantal Point Processes (DPP) to naturally diversify the batch sampling procedure. We illustrate this framework by formulating DPP-Thompson Sampling (DPP-TS) as a variant of the popular Thompson Sampling (TS) algorithm and introducing a Markov Chain Monte Carlo procedure to sample from it. We then prove novel Bayesian simple regret bounds for both classical batched TS as well as our counterpart DPP-TS, with the latter bound being tighter. Our real-world, as well as synthetic, experiments demonstrate improved performance of DPP-BBO over classical batching methods with Gaussian process and Cox process models.