Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimization
Authors: Joshua E. Hammond, Tyler A. Soderstrom, Brian A. Korgel, Michael Baldea
Organizations: McKetta Department of Chemical Engineering, The University of Texas at Austin, 200 E. Dean Keaton St. Stop C0400, Austin, Texas 78712, USA · ExxonMobil Technology and Engineering, 22777 Springwoods Village Pkwy, Spring, Texas 77389, USA · Energy Institute, The University of Texas at Austin, 2304 Whitis Ave. Stop C2400, Austin, Texas 78712, USA · Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 E. 24th Street, POB 4.102, Stop C0200, Austin, Texas 78712, USA
We consider grey-box optimization problems where the decision variables naturally partition into black-box variables (as arguments to an expensive black-box function) and white-box variables, governed by a set of explicit, closed-form equations that also depend on the output of the black-box function. We exploit this separability through a bilevel reformulation: an outer Bayesian optimization (BO) to optimize the scalar objective as a function of black-box variables alone, while an inner problem solves the white-box subproblem via global optimization. The Gaussian process surrogate used in BO is therefore defined rather than and white-box constraints are satisfied exactly whenever the inner optimizer converges to a feasible point---without penalty functions, chance constraints, or moment approximations. On a suite of 13 benchmark problems, bilevel BO achieves lower regret, with fewer iterations and wall clock time. This advantage is robust to initialization set size, exploration parameters, and inner-solver choice.