  We introduce a novel framework of combinatorial multi-armed bandits (CMAB)
with multivariant and probabilistically triggering arms (CMAB-MT), where the
outcome of each arm is a $d$-dimensional multivariant random variable and the
feedback follows a general arm triggering process. Compared with existing CMAB
works, CMAB-MT not only enhances the modeling power but also allows improved
results by leveraging distinct statistical properties for multivariant random
variables. For CMAB-MT, we propose a general 1-norm multivariant and triggering
probability-modulated smoothness condition, and an optimistic CUCB-MT algorithm
built upon this condition. Our framework can include many important problems as
applications, such as episodic reinforcement learning (RL) and probabilistic
maximum coverage for goods distribution, all of which meet the above smoothness
condition and achieve matching or improved regret bounds compared to existing
works. Through our new framework, we build the first connection between the
episodic RL and CMAB literature, by offering a new angle to solve the episodic
RL through the lens of CMAB, which may encourage more interactions between
these two important directions.
