Batch Bayesian Optimization For Replicable Experimental Design

Zhongxiang Dai, Quoc Phong Nguyen, Sebastian Shenghong Tay, Daisuke Urano, Richalynn Leong, Bryan Kian Hsiang Low, Patrick Jaillet

Keywords: Bayesian optimization, Gaussian processes, AI4Science

TL;DR: Our methods, aimed at experimental design problems with (a) batch evaluations and (b) large and heterogeneous noise, adaptively assign more replications to an input with a larger noise variance and is theoretically grounded and practically effective.

Abstract: Many real-world experimental design problems (a) evaluate multiple experimental conditions in parallel and (b) replicate each condition multiple times due to large and heteroscedastic observation noise. Given a fixed total budget, this naturally induces a trade-off between evaluating more unique conditions while replicating each of them fewer times vs. evaluating fewer unique conditions and replicating each more times. Moreover, in these problems, practitioners may be risk-averse and hence prefer an input with both good average performance and small variability. To tackle both challenges, we propose the Batch Thompson Sampling for Replicable Experimental Design (BTS-RED) framework, which encompasses three algorithms. Our BTS-RED-Known and BTS-RED-Unknown algorithms, for, respectively, known and unknown noise variance, choose the number of replications adaptively rather than deterministically such that an input with a larger noise variance is replicated more times. As a result, despite the noise heteroscedasticity, both algorithms enjoy a theoretical guarantee and are asymptotically no-regret. Our Mean-Var-BTS-RED algorithm aims at risk-averse optimization and is also asymptotically no-regret. We also show the effectiveness of our algorithms in two practical real-world applications: precision agriculture and AutoML.

Submission Number: 11002