# Cost-aware Bayesian Optimization

arXiv: https://arxiv.org/abs/2003.10870 · HTML: https://mlsanity.com/paper/2003.10870/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2020.

## Built on by (most cited first, 30 of 42)

- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [πBO: Augmenting Acquisition Functions with User Beliefs for Bayesian Optimization](https://mlsanity.com/paper/2204.11051/) (2022)
- [A Nonmyopic Approach to Cost-Constrained Bayesian Optimization](https://mlsanity.com/paper/2106.06079/) (2021)
- [Multi-Step Budgeted Bayesian Optimization with Unknown Evaluation Costs](https://mlsanity.com/paper/2111.06537/) (2021)
- [Evolve Cost-aware Acquisition Functions Using Large Language Models](https://mlsanity.com/paper/2404.16906/) (2024)
- [Cost-aware Bayesian Optimization via the Pandora's Box Gittins Index](https://mlsanity.com/paper/2406.20062/) (2024)
- [HiFo-Prompt: Prompting with Hindsight and Foresight for LLM-based Automatic Heuristic Design](https://mlsanity.com/paper/2508.13333/) (2025)
- [Language-Based Bayesian Optimization Research Assistant (BORA)](https://mlsanity.com/paper/2501.16224/) (2025)
- [SnAKe: Bayesian Optimization with Pathwise Exploration](https://mlsanity.com/paper/2202.00060/) (2022)
- [Fair and Green Hyperparameter Optimization via Multi-objective and Multiple Information Source Bayesian Optimization](https://mlsanity.com/paper/2205.08835/) (2022)
- [Generalizing Bayesian Optimization with Decision-theoretic Entropies](https://mlsanity.com/paper/2210.01383/) (2022)
- [VABO: Violation-Aware Bayesian Optimization for Closed-Loop Control Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2110.07479/) (2021)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [Data Mixture Optimization: A Multi-fidelity Multi-scale Bayesian Framework](https://mlsanity.com/paper/2503.21023/) (2025)
- [Non-smooth Bayesian Optimization in Tuning Problems](https://mlsanity.com/paper/2109.07563/) (2021)
- [Bayesian Optimization Over Iterative Learners with Structured Responses: A Budget-aware Planning Approach](https://mlsanity.com/paper/2206.12708/) (2022)
- [Efficient Evaluation of Multi-Task Robot Policies With Active Experiment Selection](https://mlsanity.com/paper/2502.09829/) (2025)
- [Violation-Aware Contextual Bayesian Optimization for Controller Performance Optimization with Unmodeled Constraints](https://mlsanity.com/paper/2301.12099/) (2023)
- [Multi-Fidelity Methods for Optimization: A Survey](https://mlsanity.com/paper/2402.09638/) (2024)
- [SANE: Strategic Autonomous Non-Smooth Exploration for Multiple Optima Discovery in Multi-modal and Non-differentiable Black-box Functions](https://mlsanity.com/paper/2409.12295/) (2024)
- [Cost-aware simulation-based inference](https://mlsanity.com/paper/2410.07930/) (2024)
- [Cost-aware Stopping for Bayesian Optimization](https://mlsanity.com/paper/2507.12453/) (2025)
- [Best Arm Identification with Resource Constraints](https://mlsanity.com/paper/2402.19090/) (2024)
- [Cost-Sensitive Multi-Fidelity Bayesian Optimization with Transfer of Learning Curve Extrapolation](https://mlsanity.com/paper/2405.17918/) (2024)
- [Cost-Sensitive Freeze-thaw Bayesian Optimization for Efficient Hyperparameter Tuning](https://mlsanity.com/paper/2510.21379/) (2025)
- [Constrained Bayesian Experimental Design via Online Planning](https://mlsanity.com/paper/2605.26990/) (2026)
- [MISO-wiLDCosts: Multi Information Source Optimization with Location Dependent Costs](https://mlsanity.com/paper/2102.04951/) (2021)
- [Indirect Query Bayesian Optimization with Integrated Feedback](https://mlsanity.com/paper/2412.13559/) (2024)

## Abstract (arXiv)

Bayesian optimization (BO) is a class of global optimization algorithms, suitable for minimizing an expensive objective function in as few function evaluations as possible. While BO budgets are typically given in iterations, this implicitly measures convergence in terms of iteration count and assumes each evaluation has identical cost. In practice, evaluation costs may vary in different regions of the search space. For example, the cost of neural network training increases quadratically with layer size, which is a typical hyperparameter. Cost-aware BO measures convergence with alternative cost metrics such as time, energy, or money, for which vanilla BO methods are unsuited. We introduce Cost Apportioned BO (CArBO), which attempts to minimize an objective function in as little cost as possible. CArBO combines a cost-effective initial design with a cost-cooled optimization phase which depreciates a learned cost model as iterations proceed. On a set of 20 black-box function optimization problems we show that, given the same cost budget, CArBO finds significantly better hyperparameter configurations than competing methods.