Contextual Combinatorial Conservative Bandits

Abstract: 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.