# Thompson Sampling for Multi-Objective Linear Contextual Bandit

arXiv: https://arxiv.org/abs/2512.00930 · HTML: https://mlsanity.com/paper/2512.00930/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 30 Nov 2025.

## Builds on (most cited first, 9 of 9)

- [A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizations](https://mlsanity.com/paper/1805.12168/) (2018)
- [Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization](https://mlsanity.com/paper/2006.04655/) (2020)
- [Multi-objective Contextual Bandit Problem with Similarity Information](https://mlsanity.com/paper/1803.04015/) (2018)
- [Multi-Objective Generalized Linear Bandits](https://mlsanity.com/paper/1905.12879/) (2019)
- [Combinatorial Neural Bandits](https://mlsanity.com/paper/2306.00242/) (2023)
- [Multi-objective Contextual Multi-armed Bandit with a Dominant Objective](https://mlsanity.com/paper/1708.05655/) (2017)
- [Pareto Regret Analyses in Multi-objective Multi-armed Bandit](https://mlsanity.com/paper/2212.00884/) (2022)
- [Optimal Scalarizations for Sublinear Hypervolume Regret](https://mlsanity.com/paper/2307.03288/) (2023)
- [Learning the Pareto Front Using Bootstrapped Observation Samples](https://mlsanity.com/paper/2306.00096/) (2023)

## Built on by (most cited first, 2 of 2)

- [Efficient Online Lexicographic Generalized Low-Rank Matrix Bandits](https://mlsanity.com/paper/2608.04324/) (2026)
- [Few-for-Many Best-Arm Identification in Multi-Objective Bandits](https://mlsanity.com/paper/2610.16840/) (2026)

## Abstract (arXiv)

We study the multi-objective linear contextual bandit problem, where multiple possible conflicting objectives must be optimized simultaneously. We propose textttMOL-TS, the textitfirst Thompson Sampling algorithm with Pareto regret guarantees for this problem. Unlike standard approaches that compute an empirical Pareto front each round, textttMOL-TS samples parameters across objectives and efficiently selects an arm from a novel effective Pareto front, which accounts for repeated selections over time. Our analysis shows that textttMOL-TS achieves a worst-case Pareto regret bound of widetildeO(d3/2√T), where d is the dimension of the feature vectors, T is the total number of rounds, matching the best known order for randomized linear bandit algorithms for single objective. Empirical results confirm the benefits of our proposed approach, demonstrating improved regret minimization and strong multi-objective performance.