# Multi-fidelity Gaussian Process Bandit Optimisation

arXiv: https://arxiv.org/abs/1603.06288 · HTML: https://mlsanity.com/paper/1603.06288/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2016.

## Built on by (most cited first, 30 of 31)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [On the Importance of Hyperparameter Optimization for Model-based Reinforcement Learning](https://mlsanity.com/paper/2102.13651/) (2021)
- [Optimal Order Simple Regret for Gaussian Process Bandits](https://mlsanity.com/paper/2108.09262/) (2021)
- [Neural Contextual Bandits without Regret](https://mlsanity.com/paper/2107.03144/) (2021)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [NAS-Bench-x11 and the Power of Learning Curves](https://mlsanity.com/paper/2111.03602/) (2021)
- [Sample Efficient Preference Alignment in LLMs via Active Exploration](https://mlsanity.com/paper/2312.00267/) (2023)
- [Multi-Fidelity Active Learning with GFlowNets](https://mlsanity.com/paper/2306.11715/) (2023)
- [Improved Regret Bounds for Gaussian Process Upper Confidence Bound in Bayesian Optimization](https://mlsanity.com/paper/2506.01393/) (2025)
- [Optimal Multi-Fidelity Best-Arm Identification](https://mlsanity.com/paper/2406.03033/) (2024)
- [JUMBO: Scalable Multi-task Bayesian Optimization using Offline Data](https://mlsanity.com/paper/2106.00942/) (2021)
- [Multi-Fidelity Methods for Optimization: A Survey](https://mlsanity.com/paper/2402.09638/) (2024)
- [Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization](https://mlsanity.com/paper/2109.09261/) (2021)
- [Kernelized Offline Contextual Dueling Bandits](https://mlsanity.com/paper/2307.11288/) (2023)
- [Active Cost-aware Labeling of Streaming Data](https://mlsanity.com/paper/2304.06808/) (2023)
- [Certified Multi-Fidelity Zeroth-Order Optimization](https://mlsanity.com/paper/2308.00978/) (2023)
- [Towards Leveraging AutoML for Sustainable Deep Learning: A Multi-Objective HPO Approach on Deep Shift Neural Networks](https://mlsanity.com/paper/2404.01965/) (2024)
- [Deep Gaussian Process-based Multi-fidelity Bayesian Optimization for Simulated Chemical Reactors](https://mlsanity.com/paper/2210.17213/) (2022)
- [MISO-wiLDCosts: Multi Information Source Optimization with Location Dependent Costs](https://mlsanity.com/paper/2102.04951/) (2021)
- [Truncating Trajectories in Monte Carlo Reinforcement Learning](https://mlsanity.com/paper/2305.04361/) (2023)
- [Derivation of Output Correlation Inferences for Multi-Output (aka Multi-Task) Gaussian Process](https://mlsanity.com/paper/2501.07964/) (2025)
- [An experimental survey and Perspective View on Meta-Learning for Automated Algorithms Selection and Parametrization](https://mlsanity.com/paper/2504.06207/) (2025)
- [Multi-stage Bayesian optimisation for dynamic decision-making in self-driving labs](https://mlsanity.com/paper/2512.15483/) (2025)
- [Incentive-Aware Multi-Fidelity Optimization for Generative Advertising in Large Language Models](https://mlsanity.com/paper/2604.06263/) (2026)
- [Adaptive multi-fidelity optimization with fast learning rates](https://mlsanity.com/paper/2604.16239/) (2026)
- [A physics-informed Bayesian optimization method for rapid development of electrical machines](https://mlsanity.com/paper/2503.00420/) (2025)
- [Beyond Static Bias: Adaptive Multi-Fidelity Bandits with Improving Proxies](https://mlsanity.com/paper/2605.08558/) (2026)
- [Leveraging AutoML for Sustainable Deep Learning: A Multi-Objective HPO Approach on Deep Shift Neural Networks](https://mlsanity.com/paper/2606.23208/) (2026)
- [Optimization of time-consuming experimental conditions using pseudo-experimental data guided by adaptive polynomial regression](https://mlsanity.com/paper/2607.22238/) (2026)
- [When May a Model Replace the Experiment? Audits, Licenses, and the Price of Trust in Surrogate-Driven Design](https://mlsanity.com/paper/2608.01378/) (2026)

## Abstract (arXiv)

In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function f. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of f in a small but promising region and speedily identify the optimum. We formalise this task as a multi-fidelity bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour, and achieves better regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.