# A Robust Multi-Objective Bayesian Optimization Framework Considering Input Uncertainty

arXiv: https://arxiv.org/abs/2202.12848 · HTML: https://mlsanity.com/paper/2202.12848/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 41 references that are in the map.
- First posted on arXiv 25 Feb 2022.

## Builds on (most cited first, 7 of 7)

- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/1609.01051/) (2016)
- [Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms](https://mlsanity.com/paper/1904.12672/) (2019)
- [Noisy-Input Entropy Search for Efficient Robust Bayesian Optimization](https://mlsanity.com/paper/2002.02820/) (2020)
- [Mean-Variance Analysis in Bayesian Optimization under Uncertainty](https://mlsanity.com/paper/2009.08166/) (2020)

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

- [Return of the Latent Space COWBOYS: Re-thinking the use of VAEs for Bayesian Optimisation of Structured Spaces](https://mlsanity.com/paper/2507.03910/) (2025)
- [Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlow](https://mlsanity.com/paper/2302.08436/) (2023)
- [PF2ES: Parallel Feasible Pareto Frontier Entropy Search for Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2204.05411/) (2022)
- [Bounding Box-based Multi-objective Bayesian Optimization of Risk Measures under Input Uncertainty](https://mlsanity.com/paper/2301.11588/) (2023)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [Bayesian Optimization Framework for Efficient Fleet Design in Autonomous Multi-Robot Exploration](https://mlsanity.com/paper/2408.11751/) (2024)
- [Maximizing Reliability with Bayesian Optimization](https://mlsanity.com/paper/2602.02432/) (2026)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)

## Abstract (arXiv)

Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty into account to find a set of robust solutions. While this is an active topic in single-objective Bayesian optimization, it is less investigated in the multi-objective case. We introduce a novel Bayesian optimization framework to efficiently perform multi-objective optimization considering input uncertainty. We propose a robust Gaussian Process model to infer the Bayes risk criterion to quantify robustness, and we develop a two-stage Bayesian optimization process to search for a robust Pareto frontier. The complete framework supports various distributions of the input uncertainty and takes full advantage of parallel computing. We demonstrate the effectiveness of the framework through numerical benchmarks.