# CAGES: Cost-Aware Gradient Entropy Search for Efficient Local Multi-Fidelity Bayesian Optimization

arXiv: https://arxiv.org/abs/2405.07760 · HTML: https://mlsanity.com/paper/2405.07760/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 16 of 16)

- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Multi-Information Source Optimization](https://mlsanity.com/paper/1603.00389/) (2016)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (2019)
- [Bayesian Optimisation over Multiple Continuous and Categorical Inputs](https://mlsanity.com/paper/1906.08878/) (2019)
- [Local policy search with Bayesian optimization](https://mlsanity.com/paper/2106.11899/) (2021)
- [A Latent Variable Approach to Gaussian Process Modeling with Qualitative and Quantitative Factors](https://mlsanity.com/paper/1806.07504/) (2018)
- [Local Bayesian optimization via maximizing probability of descent](https://mlsanity.com/paper/2210.11662/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [The Behavior and Convergence of Local Bayesian Optimization](https://mlsanity.com/paper/2305.15572/) (2023)
- [COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information](https://mlsanity.com/paper/2105.04114/) (2021)
- [Enhancing predictive capabilities in fusion burning plasmas through surrogate-based optimization in core transport solvers](https://mlsanity.com/paper/2312.12610/) (2023)

## Built on by (most cited first, 4 of 4)

- [BayeSQP: Bayesian Optimization through Sequential Quadratic Programming](https://mlsanity.com/paper/2602.03232/) (2026)
- [Rethinking Trust Region Bayesian Optimization in High Dimensions](https://mlsanity.com/paper/2604.22967/) (2026)
- [Local Entropy Search over Descent Sequences for Bayesian Optimization](https://mlsanity.com/paper/2511.19241/) (2025)
- [Local Preferential Bayesian Optimization](https://mlsanity.com/paper/2606.02351/) (2026)

## Abstract (arXiv)

Bayesian optimization (BO) is a popular approach for optimizing expensive-to-evaluate black-box objective functions. An important challenge in BO is its application to high-dimensional search spaces due in large part to the curse of dimensionality. One way to overcome this challenge is to focus on local BO methods that aim to efficiently learn gradients, which have shown strong empirical performance on high-dimensional problems including policy search in reinforcement learning (RL). Current local BO methods assume access to only a single high-fidelity information source whereas, in many problems, one has access to multiple cheaper approximations of the objective. We propose a novel algorithm, Cost-Aware Gradient Entropy Search (CAGES), for local BO of multi-fidelity black-box functions. CAGES makes no assumption about the relationship between different information sources, making it more flexible than other multi-fidelity methods. It also employs a new information-theoretic acquisition function, which enables systematic identification of samples that maximize the information gain about the unknown gradient per evaluation cost. We demonstrate CAGES can achieve significant performance improvements compared to other state-of-the-art methods on synthetic and benchmark RL problems.