  The problem of multi-armed bandits (MAB) asks to make sequential decisions
while balancing between exploitation and exploration, and have been
successfully applied to a wide range of practical scenarios. Various algorithms
have been designed to achieve a high reward in a long term. However, its
short-term performance might be rather low, which is injurious in risk
sensitive applications. Building on previous work of conservative bandits, we
bring up a framework of contextual combinatorial conservative bandits. An
algorithm is presented and a regret bound of $\tilde O(d^2+d\sqrt{T})$ is
proven, where $d$ is the dimension of the feature vectors, and $T$ is the total
number of time steps. We further provide an algorithm as well as regret
analysis for the case when the conservative reward is unknown. Experiments are
conducted, and the results validate the effectiveness of our algorithm.
