Cost-aware Cascading Bandits

In this paper, we propose a cost-aware cascading bandits model, a new variant of multi-armed bandits with cascading feedback, by considering the random cost of pulling arms. In each step, the learning agent chooses an {\it ordered} list of items and \congr{examines} them sequentially, until certain stopping condition is satisfied. Our objective is then to maximize the expected {\it net reward} in each step, i.e., the reward obtained in each step minus the total cost incurred in examining the items, by deciding the ordered list of items, as well as when to stop examination. We study both the offline and online settings, depending on whether the state and cost statistics of the items are known beforehand. For the offline setting, we show that the Unit Cost Ranking with Threshold 1 (UCR-T1) policy is optimal. For the online setting, we propose a Cost-aware Cascading Upper Confidence Bound (CC-UCB) algorithm, and show that the cumulative regret scales in $O(\log T)$. We also provide a lower bound for all $\alpha$-consistent policies, which scales in $\Omega(\log T)$ and matches our upper bound. The performance of the CC-UCB algorithm is evaluated with both synthetic and real-world data.