Bayesian Optimization with Expensive Integrands

Nonconvex derivative-free time-consuming objectives are often optimized using “black-box” optimization. These approaches assume very little about the objective. While broadly applicable, they typically require more evaluations than methods exploiting problem structure. Often, such actually sum or integral of a larger number functions, each which consumes significant time when evaluated individually. This arises in designing aircraft, choosing parameters ride-sharing dispatch systems, and tuning hyperparameters deep neural networks. We develop novel Bayesian optimization algorithm that leverages this structure to improve performance. Our is average-case optimal by construction single evaluation integrand remains within our budget. Achieving one-step optimality requires solving challenging value information problem, for we provide efficient discretization-free computational method. also prove consistency method both continuum discrete finite domains objective functions sums. In numerical experiments comparing against previous state-of-the-art methods, including those leverage structure, performs as well better across wide range problems offers improvements noisy varies smoothly integrated variables.