# Robust Multi-Objective Bayesian Optimization Under Input Noise

arXiv: https://arxiv.org/abs/2202.07549 · HTML: https://mlsanity.com/paper/2202.07549/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 94 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 29 of 29)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Maximizing acquisition functions for Bayesian optimization](https://mlsanity.com/paper/1805.10196/) (2018)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [Multi-objective Bayesian Optimization using Pareto-frontier Entropy](https://mlsanity.com/paper/1906.00127/) (2019)
- [Bayesian Optimization of Composite Functions](https://mlsanity.com/paper/1906.01537/) (2019)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Bayesian Optimization with Expensive Integrands](https://mlsanity.com/paper/1803.08661/) (2018)
- [Noisy-Input Entropy Search for Efficient Robust Bayesian Optimization](https://mlsanity.com/paper/2002.02820/) (2020)
- [Value-at-Risk Optimization with Gaussian Processes](https://mlsanity.com/paper/2105.06126/) (2021)
- [Bag of Baselines for Multi-objective Joint Neural Architecture Search and Hyperparameter Optimization](https://mlsanity.com/paper/2105.01015/) (2021)
- [Bayesian optimisation under uncertain inputs](https://mlsanity.com/paper/1902.07908/) (2019)
- [Mean-Variance Analysis in Bayesian Optimization under Uncertainty](https://mlsanity.com/paper/2009.08166/) (2020)
- [Bayesian Quantile and Expectile Optimisation](https://mlsanity.com/paper/2001.04833/) (2020)
- [Latency-Aware Neural Architecture Search with Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2106.11890/) (2021)
- [A Box Decomposition Algorithm to Compute the Hypervolume Indicator](https://mlsanity.com/paper/1510.01963/) (2015)
- [Mixed Strategies for Robust Optimization of Unknown Objectives](https://mlsanity.com/paper/2002.12613/) (2020)
- [Vector-Valued Multivariate Conditional Value-at-Risk](https://mlsanity.com/paper/1708.01324/) (2017)

## Built on by (most cited first, 30 of 37)

- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Pareto Set Learning for Expensive Multi-Objective Optimization](https://mlsanity.com/paper/2210.08495/) (2022)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterization](https://mlsanity.com/paper/2210.10199/) (2022)
- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
- [Collaborative Bayesian Optimization via Wasserstein Barycenters](https://mlsanity.com/paper/2504.10770/) (2025)
- [Bounding Box-based Multi-objective Bayesian Optimization of Risk Measures under Input Uncertainty](https://mlsanity.com/paper/2301.11588/) (2023)
- [Preference-Aware Constrained Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2303.13034/) (2023)
- [Quantum approximate optimization via learning-based adaptive optimization](https://mlsanity.com/paper/2303.14877/) (2023)
- [Robust Bayesian Target Value Optimization](https://mlsanity.com/paper/2301.04344/) (2023)
- [Multi-objective optimisation via the R2 utilities](https://mlsanity.com/paper/2305.11774/) (2023)
- [Artificial Intelligence for the Electron Ion Collider (AI4EIC)](https://mlsanity.com/paper/2307.08593/) (2023)
- [Multi-Scale Graph Learning for Anti-Sparse Downscaling](https://mlsanity.com/paper/2505.01948/) (2025)
- [Efficient and Principled Scientific Discovery through Bayesian Optimization: A Tutorial](https://mlsanity.com/paper/2604.01328/) (2026)
- [Random Pareto front surfaces](https://mlsanity.com/paper/2405.01404/) (2024)
- [Batched Energy-Entropy acquisition for Bayesian Optimization](https://mlsanity.com/paper/2410.08804/) (2024)
- [Learning Explainable Dense Reward Shapes via Bayesian Optimization](https://mlsanity.com/paper/2504.16272/) (2025)
- [FoMEMO: Towards Foundation Models for Expensive Multi-objective Optimization](https://mlsanity.com/paper/2509.03244/) (2025)
- [Safe Continual Reinforcement Learning Methods for Nonstationary Environments. Towards a Survey of the State of the Art](https://mlsanity.com/paper/2601.05152/) (2026)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [Scalarisation-based risk concepts for robust multi-objective optimisation](https://mlsanity.com/paper/2405.10221/) (2024)
- [Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems](https://mlsanity.com/paper/2408.17387/) (2024)
- [Amortized Active Generation of Pareto Sets](https://mlsanity.com/paper/2510.21052/) (2025)
- [Center-Outward q-Dominance: A Sample-Computable Proxy for Strong Stochastic Dominance in Multi-Objective Optimisation](https://mlsanity.com/paper/2511.12545/) (2025)
- [Non-Myopic Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2412.08085/) (2024)
- [Multi-Objective Planning with Contextual Lexicographic Reward Preferences](https://mlsanity.com/paper/2502.10476/) (2025)
- [Multi-Variable Batch Bayesian Optimization in Materials Research: Synthetic Data Analysis of Noise Sensitivity and Problem Landscape Effects](https://mlsanity.com/paper/2504.03943/) (2025)
- [Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control](https://mlsanity.com/paper/2506.19294/) (2025)
- [NOSTRA: A noise-resilient and sparse data framework for trust region based multi objective Bayesian optimization](https://mlsanity.com/paper/2508.16476/) (2025)

## Abstract (arXiv)

Bayesian optimization (BO) is a sample-efficient approach for tuning design parameters to optimize expensive-to-evaluate, black-box performance metrics. In many manufacturing processes, the design parameters are subject to random input noise, resulting in a product that is often less performant than expected. Although BO methods have been proposed for optimizing a single objective under input noise, no existing method addresses the practical scenario where there are multiple objectives that are sensitive to input perturbations. In this work, we propose the first multi-objective BO method that is robust to input noise. We formalize our goal as optimizing the multivariate value-at-risk (MVaR), a risk measure of the uncertain objectives. Since directly optimizing MVaR is computationally infeasible in many settings, we propose a scalable, theoretically-grounded approach for optimizing MVaR using random scalarizations. Empirically, we find that our approach significantly outperforms alternative methods and efficiently identifies optimal robust designs that will satisfy specifications across multiple metrics with high probability.