# Bayesian Optimization of Expensive Nested Grey-Box Functions

arXiv: https://arxiv.org/abs/2306.05150 · HTML: https://mlsanity.com/paper/2306.05150/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 8 Jun 2023.

## Builds on (most cited first, 21 of 21)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Practical Multi-fidelity Bayesian Optimization for Hyperparameter Tuning](https://mlsanity.com/paper/1903.04703/) (2019)
- [What Doubling Tricks Can and Can't Do for Multi-Armed Bandits](https://mlsanity.com/paper/1803.06971/) (2018)
- [Constrained Efficient Global Optimization of Expensive Black-box Functions](https://mlsanity.com/paper/2211.00162/) (2022)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [Model-based Causal Bayesian Optimization](https://mlsanity.com/paper/2211.10257/) (2022)
- [Bayesian Optimization with Expensive Integrands](https://mlsanity.com/paper/1803.08661/) (2018)
- [Dynamic Causal Bayesian Optimization](https://mlsanity.com/paper/2110.13891/) (2021)
- [VABO: Violation-Aware Bayesian Optimization for Closed-Loop Control Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2110.07479/) (2021)
- [Lower Bounds on the Worst-Case Complexity of Efficient Global Optimization](https://mlsanity.com/paper/2209.09655/) (2022)
- [Violation-Aware Contextual Bayesian Optimization for Controller Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2301.12099/) (2023)
- [No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximations](https://mlsanity.com/paper/2305.03824/) (2023)
- [Constrained Causal Bayesian Optimization](https://mlsanity.com/paper/2305.20011/) (2023)
- [CONFIG: Constrained Efficient Global Optimization for Closed-Loop Control System Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2211.11822/) (2022)

## Built on by (most cited first, 1 of 1)

- [Data-driven adaptive building thermal controller tuning with constraints: A primal-dual contextual Bayesian optimization approach](https://mlsanity.com/paper/2310.00758/) (2023)

## Abstract (arXiv)

We consider the problem of optimizing a grey-box objective function, i.e., nested function composed of both black-box and white-box functions. A general formulation for such grey-box problems is given, which covers the existing grey-box optimization formulations as special cases. We then design an optimism-driven algorithm to solve it. Under certain regularity assumptions, our algorithm achieves similar regret bound as that for the standard black-box Bayesian optimization algorithm, up to a constant multiplicative term depending on the Lipschitz constants of the functions considered. We further extend our method to the constrained case and discuss special cases. For the commonly used kernel functions, the regret bounds allow us to derive a convergence rate to the optimal solution. Experimental results show that our grey-box optimization method empirically improves the speed of finding the global optimal solution significantly, as compared to the standard black-box optimization algorithm.