# qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson sampling

arXiv: https://arxiv.org/abs/2310.15788 · HTML: https://mlsanity.com/paper/2310.15788/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 75 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Builds on (most cited first, 26 of 26)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [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)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1511.05467/) (2015)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Input Warping for Bayesian Optimization of Non-stationary Functions](https://mlsanity.com/paper/1402.0929/) (2014)
- [Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization](https://mlsanity.com/paper/2006.04655/) (2020)
- [Multi-objective Bayesian Optimization using Pareto-frontier Entropy](https://mlsanity.com/paper/1906.00127/) (2019)
- [Joint Entropy Search for Maximally-Informed Bayesian Optimization](https://mlsanity.com/paper/2206.04771/) (2022)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Active Learning for Deep Gaussian Process Surrogates](https://mlsanity.com/paper/2012.08015/) (2020)
- [BoTorch: A Framework for Efficient Monte-Carlo Bayesian Optimization](https://mlsanity.com/paper/1910.06403/) (2019)
- [Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms](https://mlsanity.com/paper/1904.12672/) (2019)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [Triangulation candidates for Bayesian optimization](https://mlsanity.com/paper/2112.07457/) (2021)
- [A Box Decomposition Algorithm to Compute the Hypervolume Indicator](https://mlsanity.com/paper/1510.01963/) (2015)
- [Contour Location for Reliability in Airfoil Simulation Experiments using Deep Gaussian Processes](https://mlsanity.com/paper/2308.04420/) (2023)

## Built on by (most cited first, 11 of 11)

- [Multi-Objective Bayesian Optimization for Networked Black-Box Systems: A Path to Greener Profits and Smarter Designs](https://mlsanity.com/paper/2502.14121/) (2025)
- [On Regret Bounds of Thompson Sampling for Bayesian Optimization](https://mlsanity.com/paper/2603.09276/) (2026)
- [SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion](https://mlsanity.com/paper/2509.21058/) (2025)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [Adaptive Candidate Point Thompson Sampling for High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2604.08891/) (2026)
- [REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis](https://mlsanity.com/paper/2606.13245/) (2026)
- [Multifidelity Cross-validation](https://mlsanity.com/paper/2407.01495/) (2024)
- [Multi-Objective Bayesian Optimization via Adaptive varepsilon-Constraints Decomposition](https://mlsanity.com/paper/2604.15959/) (2026)
- [A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification](https://mlsanity.com/paper/2606.28871/) (2026)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)
- [Learning What to Evaluate: Correlation-Aware Decoupling for Multiobjective Bayesian Optimization](https://mlsanity.com/paper/2609.32632/) (2026)

## Abstract (arXiv)

Classical evolutionary approaches for multiobjective optimization are quite accurate but incur a lot of queries to the objectives; this can be prohibitive when objectives are expensive oracles. A sample-efficient approach to solving multiobjective optimization is via Gaussian process (GP) surrogates and Bayesian optimization (BO). Multiobjective Bayesian optimization (MOBO) involves the construction of an acquisition function which is optimized to acquire new observation candidates sequentially. This ``inner'' optimization can be hard due to various reasons: acquisition functions being nonconvex, nondifferentiable and/or unavailable in analytical form; batch sampling usually exacerbates these problems and the success of MOBO heavily relies on this inner optimization. This, ultimately, affects their sample efficiency. To overcome these challenges, we propose a Thompson sampling (TS) based approach (qtextttPOTS). Whereas TS chooses candidates according to the probability that they are optimal, qtextttPOTS chooses candidates according to the probability that they are Pareto optimal. Instead of a hard acquisition function optimization, qtextttPOTS~ solves a cheap multiobjective optimization on the GP posteriors with evolutionary approaches. This way we get the best of both worlds: accuracy of evolutionary approaches and sample-efficiency of MOBO. New candidates are chosen on the posterior GP Pareto frontier according to a maximin distance criterion. qtextttPOTS~ is endowed with theoretical guarantees, a natural exploration-exploitation trade-off, and superior empirical performance.