Batch Bayesian Optimization via Particle Gradient Flows
This addresses the computational bottleneck in batch Bayesian optimization for researchers and practitioners dealing with expensive black-box functions, though it appears incremental as it builds on existing multipoint expected improvement methods.
The paper tackles the challenge of solving the non-convex acquisition function optimization in batch Bayesian optimization by reformulating it as a convex problem over probability measures and using gradient flows, demonstrating efficacy on benchmark functions with comparisons to state-of-the-art methods.
Bayesian Optimisation (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the uncertainty in that surrogate through Bayesian inference. Objective evaluations are sequentially determined by maximising an acquisition function at each step. However, this ancilliary optimisation problem can be highly non-trivial to solve, due to the non-convexity of the acquisition function, particularly in the case of batch Bayesian optimisation, where multiple points are selected in every step. In this work we reformulate batch BO as an optimisation problem over the space of probability measures. We construct a new acquisition function based on multipoint expected improvement which is convex over the space of probability measures. Practical schemes for solving this `inner' optimisation problem arise naturally as gradient flows of this objective function. We demonstrate the efficacy of this new method on different benchmark functions and compare with state-of-the-art batch BO methods.