# Multi-Objective Generalized Linear Bandits

arXiv: https://arxiv.org/abs/1905.12879 · HTML: https://mlsanity.com/paper/1905.12879/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 19 of 19)

- [Traversing Pareto Optimal Policies: Provably Efficient Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2407.17466/) (2024)
- [Efficient Algorithms for Generalized Linear Bandits with Heavy-tailed Rewards](https://mlsanity.com/paper/2310.18701/) (2023)
- [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)
- [Preference-based Pure Exploration](https://mlsanity.com/paper/2412.02988/) (2024)
- [Provably Efficient Multi-Objective Bandit Algorithms under Preference-Centric Customization](https://mlsanity.com/paper/2502.13457/) (2025)
- [Demonstration Guided Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2404.03997/) (2024)
- [Best Group Identification in Multi-Objective Bandits](https://mlsanity.com/paper/2505.17869/) (2025)
- [Bandit Pareto Set Identification in a Multi-Output Linear Model](https://mlsanity.com/paper/2507.04255/) (2025)
- [Thompson Sampling for Multi-Objective Linear Contextual Bandit](https://mlsanity.com/paper/2512.00930/) (2025)
- [The Digital Transformation in Health: How AI Can Improve the Performance of Health Systems](https://mlsanity.com/paper/2409.16098/) (2024)
- [Multi-thresholding Good Arm Identification with Bandit Feedback](https://mlsanity.com/paper/2503.10386/) (2025)
- [Stochastic Multi-Objective Multi-Armed Bandits: Regret Definition and Algorithm](https://mlsanity.com/paper/2506.13125/) (2025)
- [Beyond the Lower Bound: Bridging Regret Minimization and Best Arm Identification in Lexicographic Bandits](https://mlsanity.com/paper/2511.05802/) (2025)
- [Center-Outward q-Dominance: A Sample-Computable Proxy for Strong Stochastic Dominance in Multi-Objective Optimisation](https://mlsanity.com/paper/2511.12545/) (2025)
- [Online Pareto-Optimal Decision-Making for Complex Tasks using Active Inference](https://mlsanity.com/paper/2406.11984/) (2024)
- [Provably Efficient Personalized Multi-Objective Bandits with Proactive Conversational Queries](https://mlsanity.com/paper/2606.08410/) (2026)
- [Bayesian Anytime Pareto Set Identification for Multi-Objective Multi-Armed Bandits](https://mlsanity.com/paper/2606.18785/) (2026)
- [Selective Ensemble Based on Preference-Directed Multi-Objective Bandits](https://mlsanity.com/paper/2606.21929/) (2026)

## Abstract (arXiv)

In this paper, we study the multi-objective bandits (MOB) problem, where a learner repeatedly selects one arm to play and then receives a reward vector consisting of multiple objectives. MOB has found many real-world applications as varied as online recommendation and network routing. On the other hand, these applications typically contain contextual information that can guide the learning process which, however, is ignored by most of existing work. To utilize this information, we associate each arm with a context vector and assume the reward follows the generalized linear model (GLM). We adopt the notion of Pareto regret to evaluate the learner's performance and develop a novel algorithm for minimizing it. The essential idea is to apply a variant of the online Newton step to estimate model parameters, based on which we utilize the upper confidence bound (UCB) policy to construct an approximation of the Pareto front, and then uniformly at random choose one arm from the approximate Pareto front. Theoretical analysis shows that the proposed algorithm achieves an tilde O(d√T) Pareto regret, where T is the time horizon and d is the dimension of contexts, which matches the optimal result for single objective contextual bandits problem. Numerical experiments demonstrate the effectiveness of our method.