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A search engine recommends to the user a list of web pages. The user examinesthis list, from the first page to the last, and clicks on all attractive pagesuntil the user is satisfied. This behavior of the user can be described by thedependent click model (DCM). We propose DCM bandits, an online learning variantof the DCM where the goal is to maximize the probability of recommendingsatisfactory items, such as web pages. The main challenge of our learningproblem is that we do not observe which attractive item is satisfactory. Wepropose a computationally-efficient learning algorithm for solving our problem,dcmKL-UCB; derive gap-dependent upper bounds on its regret under reasonableassumptions; and also prove a matching lower bound up to logarithmic factors.We evaluate our algorithm on synthetic and real-world problems, and show thatit performs well even when our model is misspecified. This work presents thefirst practical and regret-optimal online algorithm for learning to rank withmultiple clicks in a cascade-like click model.

DCM Bandits: Learning to Rank with Multiple Clicks