Home Page




Editorial Board

Special Issues

Open Source Software

Proceedings (PMLR)

Transactions (TMLR)




Frequently Asked Questions

Contact Us

RSS Feed

Distributionally Ambiguous Optimization for Batch Bayesian Optimization

Nikitas Rontsis, Michael A. Osborne, Paul J. Goulart; 21(149):1−26, 2020.


We propose a novel, theoretically-grounded, acquisition function for Batch Bayesian Optimization informed by insights from distributionally ambiguous optimization. Our acquisition function is a lower bound on the well-known Expected Improvement function, which requires evaluation of a Gaussian expectation over a multivariate piecewise affine function. Our bound is computed instead by evaluating the best-case expectation over all probability distributions consistent with the same mean and variance as the original Gaussian distribution. Unlike alternative approaches, including Expected Improvement, our proposed acquisition function avoids multi-dimensional integrations entirely, and can be computed exactly - even on large batch sizes - as the solution of a tractable convex optimization problem. Our suggested acquisition function can also be optimized efficiently, since first and second derivative information can be calculated inexpensively as by-products of the acquisition function calculation itself. We derive various novel theorems that ground our work theoretically and we demonstrate superior performance via simple motivating examples, benchmark functions and real-world problems.

[abs][pdf][bib]        [code]
© JMLR 2020. (edit, beta)