Multi-User Contextual Cascading Bandits for Personalized Recommendation

We introduce a Multi-User Contextual Cascading Bandit model, a new combinatorial bandit framework that captures realistic online advertising scenarios where multiple users interact with sequentially displayed items simultaneously. Unlike classical contextual bandits, MCCB integrates three key structural elements: (i) cascading feedback based on sequential arm exposure, (ii) parallel context sessions enabling selective exploration, and (iii) heterogeneous arm-level rewards. We first propose Upper Confidence Bound with Backward Planning (UCBBP), a UCB-style algorithm tailored to this setting, and prove that it achieves a regret bound of $\widetilde{O}(\sqrt{THN})$ over $T$ episodes, $H$ session steps, and $N$ contexts per episode. Motivated by the fact that many users interact with the system simultaneously, we introduce a second algorithm, termed Active Upper Confidence Bound with Backward Planning (AUCBBP), which shows a strict efficiency improvement in context scaling, i.e., user scaling, with a regret bound of $\widetilde{O}(\sqrt{T+HN})$. We validate our theoretical findings via numerical experiments, demonstrating the empirical effectiveness of both algorithms under various settings.