Two-step Lookahead Bayesian Optimization with Inequality Constraints
This addresses the challenge of efficient constrained optimization for researchers and practitioners in fields like engineering and design, where constraints are common, and is incremental by building on prior non-myopic methods but extending them to constrained settings.
The paper tackles the problem of computationally expensive non-myopic Bayesian optimization for constrained problems by proposing a two-step lookahead acquisition function (2-OPT-C) with a novel gradient estimator, resulting in query efficiency improvements of 2x or more, and up to 10x in some cases, over previous methods.
Recent advances in computationally efficient non-myopic Bayesian optimization (BO) improve query efficiency over traditional myopic methods like expected improvement while only modestly increasing computational cost. These advances have been largely limited, however, to unconstrained optimization. For constrained optimization, the few existing non-myopic BO methods require heavy computation. For instance, one existing non-myopic constrained BO method [Lam and Willcox, 2017] relies on computationally expensive unreliable brute-force derivative-free optimization of a Monte Carlo rollout acquisition function. Methods that use the reparameterization trick for more efficient derivative-based optimization of non-myopic acquisition functions in the unconstrained setting, like sample average approximation and infinitesimal perturbation analysis, do not extend: constraints introduce discontinuities in the sampled acquisition function surface that hinder its optimization. Moreover, we argue here that being non-myopic is even more important in constrained problems because fear of violating constraints pushes myopic methods away from sampling the boundary between feasible and infeasible regions, slowing the discovery of optimal solutions with tight constraints. In this paper, we propose a computationally efficient two-step lookahead constrained Bayesian optimization acquisition function (2-OPT-C) supporting both sequential and batch settings. To enable fast acquisition function optimization, we develop a novel likelihood-ratio-based unbiased estimator of the gradient of the two-step optimal acquisition function that does not use the reparameterization trick. In numerical experiments, 2-OPT-C typically improves query efficiency by 2x or more over previous methods, and in some cases by 10x or more.