Bayesian Optimization for Function Compositions with Applications to Dynamic Pricing
This work addresses the problem of efficient optimization in complex, expensive function compositions for researchers and practitioners in fields like revenue management, though it is incremental as it builds on existing Bayesian Optimization frameworks.
The paper tackles optimizing expensive-to-evaluate black-box functions with known compositional structures by proposing Bayesian Optimization methods using independent Gaussian processes, achieving superior performance over state-of-the-art algorithms. It applies this to dynamic pricing, where demand functions are costly to evaluate, demonstrating practical utility.
Bayesian Optimization (BO) is used to find the global optima of black box functions. In this work, we propose a practical BO method of function compositions where the form of the composition is known but the constituent functions are expensive to evaluate. By assuming an independent Gaussian process (GP) model for each of the constituent black-box function, we propose Expected Improvement (EI) and Upper Confidence Bound (UCB) based BO algorithms and demonstrate their ability to outperform not just vanilla BO but also the current state-of-art algorithms. We demonstrate a novel application of the proposed methods to dynamic pricing in revenue management when the underlying demand function is expensive to evaluate.