Approximation-Aware Bayesian Optimization

Natalie Maus, Kyurae Kim, David Eriksson, Geoff Pleiss, John Patrick Cunningham, Jacob R. Gardner

Keywords: Bayesian optimization, variational inference, Gaussian processes, utility maximization, expected improvement, knowledge gradient, black-box optimization

Abstract: High-dimensional Bayesian optimization (BO) tasks such as molecular design often require $>10,$$000$ function evaluations before obtaining meaningful results. While methods like sparse variational Gaussian processes (SVGPs) reduce computational requirements in these settings, the underlying approximations result in suboptimal data acquisitions that slow the progress of optimization. In this paper we modify SVGPs to better align with the goals of BO: targeting informed data acquisition over global posterior fidelity. Using the framework of utility-calibrated variational inference (Lacoste–Julien et al., 2011), we unify GP approximation and data acquisition into a joint optimization problem, thereby ensuring optimal decisions under a limited computational budget. Our approach can be used with any decision-theoretic acquisition function and is readily compatible with trust region methods like TuRBO (Eriksson et al., 2019). We derive efficient joint objectives for the expected improvement (EI) and knowledge gradient (KG) acquisition functions in both the standard and batch BO settings. On a variety of recent high dimensional benchmark tasks in control and molecular design, our approach significantly outperforms standard SVGPs and is capable of achieving comparable rewards with up to $10\times$ fewer function evaluations.

Primary Area: Probabilistic methods (for example: variational inference, Gaussian processes)

Submission Number: 12818