# Cost-aware Multi-objective Bayesian optimisation

arXiv: https://arxiv.org/abs/1909.03600 · HTML: https://mlsanity.com/paper/1909.03600/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2019.

## Built on by (most cited first, 8 of 8)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [A Nonmyopic Approach to Cost-Constrained Bayesian Optimization](https://mlsanity.com/paper/2106.06079/) (2021)
- [Movement Penalized Bayesian Optimization with Application to Wind Energy Systems](https://mlsanity.com/paper/2210.08087/) (2022)
- [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)
- [Learning with a Budget: Identifying the Best Arm with Resource Constraints](https://mlsanity.com/paper/2602.24146/) (2026)

## Abstract (arXiv)

The notion of expense in Bayesian optimisation generally refers to the uniformly expensive cost of function evaluations over the whole search space. However, in some scenarios, the cost of evaluation for black-box objective functions is non-uniform since different inputs from search space may incur different costs for function evaluations. We introduce a cost-aware multi-objective Bayesian optimisation with non-uniform evaluation cost over objective functions by defining cost-aware constraints over the search space. The cost-aware constraints are a sorted tuple of indexes that demonstrate the ordering of dimensions of the search space based on the user's prior knowledge about their cost of usage. We formulate a new multi-objective Bayesian optimisation acquisition function with detailed analysis of the convergence that incorporates this cost-aware constraints while optimising the objective functions. We demonstrate our algorithm based on synthetic and real-world problems in hyperparameter tuning of neural networks and random forests.