Thompson Sampling for Multi-Objective Linear Contextual Bandit
This addresses the challenge of optimizing conflicting objectives in bandit settings for applications like recommendation systems, representing a novel algorithmic contribution rather than an incremental improvement.
The paper tackled the multi-objective linear contextual bandit problem by proposing MOL-TS, the first Thompson Sampling algorithm with Pareto regret guarantees, achieving a worst-case regret bound of O~(d^{3/2}√T) and demonstrating improved performance in experiments.
We study the multi-objective linear contextual bandit problem, where multiple possible conflicting objectives must be optimized simultaneously. We propose \texttt{MOL-TS}, the \textit{first} Thompson Sampling algorithm with Pareto regret guarantees for this problem. Unlike standard approaches that compute an empirical Pareto front each round, \texttt{MOL-TS} samples parameters across objectives and efficiently selects an arm from a novel \emph{effective Pareto front}, which accounts for repeated selections over time. Our analysis shows that \texttt{MOL-TS} achieves a worst-case Pareto regret bound of $\widetilde{O}(d^{3/2}\sqrt{T})$, 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.