Contextual Combinatorial Bandits with Probabilistically Triggered Arms

We study contextual combinatorial bandits with probabilistically triggered arms (C2MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C2-UCB-T algorithm and propose a novel analysis that achieves an tildeO(d√KT) regret bound, removing a potentially exponentially large factor O(1/pmin), where d is the dimension of contexts, pmin is the minimum positive probability that any arm can be triggered, and batch-size K is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC2-UCB and derive a regret bound tildeO(d√T), which is independent of the batch-size K. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C2MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets.