# Leveraging Trust for Joint Multi-Objective and Multi-Fidelity Optimization

arXiv: https://arxiv.org/abs/2112.13901 · HTML: https://mlsanity.com/paper/2112.13901/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 62 references that are in the map.
- First posted on arXiv 27 Dec 2021.

## Builds on (most cited first, 15 of 15)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets](https://mlsanity.com/paper/1605.07079/) (2016)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Practical Multi-fidelity Bayesian Optimization for Hyperparameter Tuning](https://mlsanity.com/paper/1903.04703/) (2019)
- [Multi-objective Bayesian Optimization using Pareto-frontier Entropy](https://mlsanity.com/paper/1906.00127/) (2019)
- [Multi-Fidelity Bayesian Optimization via Deep Neural Networks](https://mlsanity.com/paper/2007.03117/) (2020)
- [A Bayesian approach to constrained single- and multi-objective optimization](https://mlsanity.com/paper/1510.00503/) (2015)
- [The Multi-fidelity Multi-armed Bandit](https://mlsanity.com/paper/1610.09726/) (2016)
- [Multi-Fidelity Multi-Objective Bayesian Optimization: An Output Space Entropy Search Approach](https://mlsanity.com/paper/2011.01542/) (2020)
- [Scalarizing Functions in Bayesian Multiobjective Optimization](https://mlsanity.com/paper/1904.05760/) (2019)
- [Practical Bayesian Optimization for Variable Cost Objectives](https://mlsanity.com/paper/1703.04335/) (2017)
- [Using Distance Correlation for Efficient Bayesian Optimization](https://mlsanity.com/paper/2102.08993/) (2021)

## Built on by (most cited first, 7 of 7)

- [Multi-fidelity Gaussian process surrogate modeling for regression problems in physics](https://mlsanity.com/paper/2404.11965/) (2024)
- [Interactive Multi-Objective Probabilistic Preference Learning with Soft and Hard Bounds](https://mlsanity.com/paper/2506.21887/) (2025)
- [Multi-Objective Multi-Fidelity Bayesian Optimization with Causal Priors](https://mlsanity.com/paper/2602.00788/) (2026)
- [Long-run Behaviour of Multi-fidelity Bayesian Optimisation](https://mlsanity.com/paper/2312.12633/) (2023)
- [Multi-fidelity Bayesian Data-Driven Design of Energy Absorbing Spinodoid Cellular Structures](https://mlsanity.com/paper/2507.22079/) (2025)
- [Multi-objective Hyperparameter Optimization in the Age of Deep Learning](https://mlsanity.com/paper/2511.08371/) (2025)
- [SMOG: Scalable Meta-Learning for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2601.22131/) (2026)

## Abstract (arXiv)

In the pursuit of efficient optimization of expensive-to-evaluate systems, this paper investigates a novel approach to Bayesian multi-objective and multi-fidelity (MOMF) optimization. Traditional optimization methods, while effective, often encounter prohibitively high costs in multi-dimensional optimizations of one or more objectives. Multi-fidelity approaches offer potential remedies by utilizing multiple, less costly information sources, such as low-resolution simulations. However, integrating these two strategies presents a significant challenge. We suggest the innovative use of a trust metric to support simultaneous optimization of multiple objectives and data sources. Our method modifies a multi-objective optimization policy to incorporate the trust gain per evaluation cost as one objective in a Pareto optimization problem, enabling simultaneous MOMF at lower costs. We present and compare two MOMF optimization methods: a holistic approach selecting both the input parameters and the trust parameter jointly, and a sequential approach for benchmarking. Through benchmarks on synthetic test functions, our approach is shown to yield significant cost reductions - up to an order of magnitude compared to pure multi-objective optimization. Furthermore, we find that joint optimization of the trust and objective domains outperforms addressing them in sequential manner. We validate our results using the use case of optimizing laser-plasma acceleration simulations, demonstrating our method's potential in Pareto optimization of high-cost black-box functions. Implementing these methods in existing Bayesian frameworks is simple, and they can be readily extended to batch optimization. With their capability to handle various continuous or discrete fidelity dimensions, our techniques offer broad applicability in solving simulation problems in fields such as plasma physics and fluid dynamics.