# Vector Optimization with Gaussian Process Bandits

arXiv: https://arxiv.org/abs/2412.02484 · HTML: https://mlsanity.com/paper/2412.02484/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 80 references that are in the map.
- First posted on arXiv 3 Dec 2024.

## Builds on (most cited first, 22 of 22)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Predictive Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1511.05467/) (2015)
- [Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraints](https://mlsanity.com/paper/2009.01721/) (2020)
- [Multi-objective Bayesian Optimization using Pareto-frontier Entropy](https://mlsanity.com/paper/1906.00127/) (2019)
- [No-Regret Bayesian Optimization with Unknown Hyperparameters](https://mlsanity.com/paper/1901.03357/) (2019)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Preference Exploration for Efficient Bayesian Optimization with Multiple Outcomes](https://mlsanity.com/paper/2203.11382/) (2022)
- [Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction](https://mlsanity.com/paper/1310.0732/) (2013)
- [Multi-Attribute Bayesian Optimization With Interactive Preference Learning](https://mlsanity.com/paper/1911.05934/) (2019)
- [Multi-objective Bayesian optimisation with preferences over objectives](https://mlsanity.com/paper/1902.04228/) (2019)
- [Fair and Green Hyperparameter Optimization via Multi-objective and Multiple Information Source Bayesian Optimization](https://mlsanity.com/paper/2205.08835/) (2022)
- [Safe Active Learning for Multi-Output Gaussian Processes](https://mlsanity.com/paper/2203.14849/) (2022)
- [Learning Inconsistent Preferences with Gaussian Processes](https://mlsanity.com/paper/2006.03847/) (2020)
- [Vector Optimization with Stochastic Bandit Feedback](https://mlsanity.com/paper/2110.12311/) (2021)
- [Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds Logarithmically Closer to Optimal](https://mlsanity.com/paper/2410.10384/) (2024)
- [Preference-Aware Constrained Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2303.13034/) (2023)
- [Set optimization - a rather short introduction](https://mlsanity.com/paper/1404.5928/) (2014)
- [On Preference Learning Based on Sequential Bayesian Optimization with Pairwise Comparison](https://mlsanity.com/paper/2103.13192/) (2021)
- [Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method](https://mlsanity.com/paper/2207.03842/) (2022)

## Abstract (arXiv)

We study black-box vector optimization with Gaussian process bandits, where there is an incomplete order relation on objective vectors described by a polyhedral convex cone. Existing black-box vector optimization approaches either suffer from high sample complexity or lack theoretical guarantees. We propose Vector Optimization with Gaussian Process (VOGP), an adaptive elimination algorithm that identifies Pareto optimal solutions sample efficiently by exploiting the smoothness of the objective function. We establish theoretical guarantees, deriving information gain-based and kernel-specific sample complexity bounds. Finally, we conduct a thorough empirical evaluation of VOGP and compare it with the state-of-the-art multi-objective and vector optimization algorithms on several real-world and synthetic datasets, emphasizing VOGP's efficiency (e.g., ~18× lower sample complexity on average). We also provide heuristic adaptations of VOGP for cases where the design space is continuous and where the Gaussian process model lacks access to the true kernel hyperparameters. This work opens a new frontier in sample-efficient multi-objective black-box optimization by incorporating preference structures while maintaining theoretical guarantees and practical efficiency.