Batch Selection for Parallelisation of Bayesian Quadrature

TL;DR

This paper introduces batch selection methods for Bayesian Quadrature, enabling parallel sampling to reduce computation time in probabilistic numerical integration, especially for expensive-to-evaluate integrands.

Contribution

It extends Bayesian Quadrature with batch selection techniques inspired by Bayesian Optimization, allowing parallel sampling and improving efficiency over traditional serial methods.

Findings

Batch methods significantly reduce computation time.

Parallel sampling maintains accuracy comparable to serial approaches.

Applicable to expensive integrand evaluations.

Abstract

Integration over non-negative integrands is a central problem in machine learning (e.g. for model averaging, (hyper-)parameter marginalisation, and computing posterior predictive distributions). Bayesian Quadrature is a probabilistic numerical integration technique that performs promisingly when compared to traditional Markov Chain Monte Carlo methods. However, in contrast to easily-parallelised MCMC methods, Bayesian Quadrature methods have, thus far, been essentially serial in nature, selecting a single point to sample at each step of the algorithm. We deliver methods to select batches of points at each step, based upon those recently presented in the Batch Bayesian Optimisation literature. Such parallelisation significantly reduces computation time, especially when the integrand is expensive to sample.