# Bayesian Optimization for Function Compositions with Applications to Dynamic Pricing

arXiv: https://arxiv.org/abs/2303.11954 · HTML: https://mlsanity.com/paper/2303.11954/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 21 Mar 2023.

## Builds on (most cited first, 7 of 7)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Efficiency of minimizing compositions of convex functions and smooth maps](https://mlsanity.com/paper/1605.00125/) (2016)
- [Tight Complexity Bounds for Optimizing Composite Objectives](https://mlsanity.com/paper/1605.08003/) (2016)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Bayesian Optimization with Machine Learning Algorithms Towards Anomaly Detection](https://mlsanity.com/paper/2008.02327/) (2020)
- [MOCCA: mirrored convex/concave optimization for nonconvex composite functions](https://mlsanity.com/paper/1510.08842/) (2015)

## Built on by (most cited first, 3 of 3)

- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [Practical First-Order Bayesian Optimization Algorithms](https://mlsanity.com/paper/2306.10815/) (2023)
- [Bayesian Optimization for Dynamic Pricing and Learning](https://mlsanity.com/paper/2510.12447/) (2025)

## Abstract (arXiv)

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.