# Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method

arXiv: https://arxiv.org/abs/2207.03842 · HTML: https://mlsanity.com/paper/2207.03842/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 8 Jul 2022.

## Builds on (most cited first, 8 of 8)

- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/1609.01051/) (2016)
- [A Bayesian approach to constrained single- and multi-objective optimization](https://mlsanity.com/paper/1510.00503/) (2015)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [Improved Max-value Entropy Search for Multi-objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2011.01150/) (2020)
- [Adaptive Batching for Gaussian Process Surrogates with Application in Noisy Level Set Estimation](https://mlsanity.com/paper/2003.08579/) (2020)
- [The Informational Approach to Global Optimization in presence of very noisy evaluation results. Application to the optimization of renewable energy integration strategies](https://mlsanity.com/paper/1506.04493/) (2015)

## Built on by (most cited first, 1 of 1)

- [Vector Optimization with Gaussian Process Bandits](https://mlsanity.com/paper/2412.02484/) (2024)

## Abstract (arXiv)

This article focuses on the multi-objective optimization of stochastic simulators with high output variance, where the input space is finite and the objective functions are expensive to evaluate. We rely on Bayesian optimization algorithms, which use probabilistic models to make predictions about the functions to be optimized. The proposed approach is an extension of the Pareto Active Learning (PAL) algorithm for the estimation of Pareto-optimal solutions that makes it suitable for the stochastic setting. We named it Pareto Active Learning for Stochastic Simulators (PALS). The performance of PALS is assessed through numerical experiments over a set of bi-dimensional, bi-objective test problems. PALS exhibits superior performance when compared to other scalarization-based and random-search approaches.