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Bayesian Optimization (BO) is used to find the global optima of black boxfunctions. In this work, we propose a practical BO method of functioncompositions where the form of the composition is known but the constituentfunctions are expensive to evaluate. By assuming an independent Gaussianprocess (GP) model for each of the constituent black-box function, we proposeExpected Improvement (EI) and Upper Confidence Bound (UCB) based BO algorithmsand demonstrate their ability to outperform not just vanilla BO but also thecurrent state-of-art algorithms. We demonstrate a novel application of theproposed methods to dynamic pricing in revenue management when the underlyingdemand function is expensive to evaluate.

Bayesian Optimization for Function Compositions with Applications to Dynamic Pricing