Contextual dueling bandits, where a learner compares two options based on context and receives feedback indicating which was preferred, extends classic dueling bandits by incorporating contextual information for decision-making and preference learning. Several algorithms based on the upper confidence bound (UCB) have been proposed for linear contextual dueling bandits. However, no algorithm based on posterior sampling has been developed in this setting, despite the empirical success observed in traditional contextual bandits. In this paper, we propose a Thompson sampling algorithm, named FGTS.CDB, for linear contextual dueling bandits. At the core of our algorithm is a new Feel-Good exploration term specifically tailored for dueling bandits. This term leverages the independence of the two selected arms, thereby avoiding a cross term in the analysis. We show that our algorithm achieves nearly minimax-optimal regret, i.e., $\tilde{\mathcal{O}}(d\sqrt T)$, where $d$ is the model dimension and $T$ is the time horizon. Finally, we evaluate our algorithm on synthetic data and observe that FGTS.CDB outperforms existing algorithms by a large margin.

提出了适用于线性上下文对抗性对决带的一种名为FGTS.CDB的汤普森抽样算法，最小化遗憾，并在合成数据上证明比现有算法表现优秀。

上下文决斗赌徒的良好感知汤普森抽样