  We analyze the regret of combinatorial Thompson sampling (CTS) for the
combinatorial multi-armed bandit with probabilistically triggered arms under
the semi-bandit feedback setting. We assume that the learner has access to an
exact optimization oracle but does not know the expected base arm outcomes
beforehand. When the expected reward function is Lipschitz continuous in the
expected base arm outcomes, we derive $O(\sum_{i =1}^m \log T / (p_i
\Delta_i))$ regret bound for CTS, where $m$ denotes the number of base arms,
$p_i$ denotes the minimum non-zero triggering probability of base arm $i$ and
$\Delta_i$ denotes the minimum suboptimality gap of base arm $i$. We also
compare CTS with combinatorial upper confidence bound (CUCB) via numerical
experiments on a cascading bandit problem.
