# Multi-Fidelity Multi-Objective Bayesian Optimization: An Output Space Entropy Search Approach

arXiv: https://arxiv.org/abs/2011.01542 · HTML: https://mlsanity.com/paper/2011.01542/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2020.

## Built on by (most cited first, 22 of 22)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overview](https://mlsanity.com/paper/2206.07438/) (2022)
- [Bayesian Optimization over Hybrid Spaces](https://mlsanity.com/paper/2106.04682/) (2021)
- [Multi-objective Asynchronous Successive Halving](https://mlsanity.com/paper/2106.12639/) (2021)
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- [Fair and Green Hyperparameter Optimization via Multi-objective and Multiple Information Source Bayesian Optimization](https://mlsanity.com/paper/2205.08835/) (2022)
- [Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2110.06980/) (2021)
- [Leveraging Trust for Joint Multi-Objective and Multi-Fidelity Optimization](https://mlsanity.com/paper/2112.13901/) (2021)
- [Preference-Aware Constrained Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2303.13034/) (2023)
- [Bi-level Multi-objective Evolutionary Learning: A Case Study on Multi-task Graph Neural Topology Search](https://mlsanity.com/paper/2302.02565/) (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)
- [Information-theoretic Bayesian Optimization: Survey and Tutorial](https://mlsanity.com/paper/2502.06789/) (2025)
- [Multi-Objective Multi-Fidelity Bayesian Optimization with Causal Priors](https://mlsanity.com/paper/2602.00788/) (2026)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [Multipoint-BAX: A New Approach for Efficiently Tuning Particle Accelerator Emittance via Virtual Objectives](https://mlsanity.com/paper/2209.04587/) (2022)
- [Datasets and Benchmarks for Nanophotonic Structure and Parametric Design Simulations](https://mlsanity.com/paper/2310.19053/) (2023)
- [A Trajectory-Based Bayesian Approach to Multi-Objective Hyperparameter Optimization with Epoch-Aware Trade-Offs](https://mlsanity.com/paper/2405.15303/) (2024)
- [Multi-objective Hyperparameter Optimization in the Age of Deep Learning](https://mlsanity.com/paper/2511.08371/) (2025)
- [Leveraging AutoML for Sustainable Deep Learning: A Multi-Objective HPO Approach on Deep Shift Neural Networks](https://mlsanity.com/paper/2606.23208/) (2026)
- [High-dimensional Multi-objective Bayesian Optimization with Learned Variable Interactions](https://mlsanity.com/paper/2608.11713/) (2026)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)

## Abstract (arXiv)

We study the novel problem of blackbox optimization of multiple objectives via multi-fidelity function evaluations that vary in the amount of resources consumed and their accuracy. The overall goal is to approximate the true Pareto set of solutions by minimizing the resources consumed for function evaluations. For example, in power system design optimization, we need to find designs that trade-off cost, size, efficiency, and thermal tolerance using multi-fidelity simulators for design evaluations. In this paper, we propose a novel approach referred as Multi-Fidelity Output Space Entropy Search for Multi-objective Optimization (MF-OSEMO) to solve this problem. The key idea is to select the sequence of candidate input and fidelity-vector pairs that maximize the information gained about the true Pareto front per unit resource cost. Our experiments on several synthetic and real-world benchmark problems show that MF-OSEMO, with both approximations, significantly improves over the state-of-the-art single-fidelity algorithms for multi-objective optimization.