Contextual Combinatorial Cascading Bandits

Abstract

We propose the contextual combinatorial cascading bandits, a combinatorial online learning game, where at each time step a learning agent is given a set of contextual information, then selects a list of items, and observes stochastic outcomes of a prefix in the selected items by some stopping criterion. In online recommendation, the stopping criterion might be the first item a user selects; in network routing, the stopping criterion might be the first edge blocked in a path. We consider position discounts in the list order, so that the agent’s reward is discounted depending on the position where the stopping criterion is met. We design a UCB-type algorithm, C^3-UCB, for this problem, prove an n-step regret bound \tildeO(\sqrt{n}) in the general setting, and give finer analysis for two special cases. Our work generalizes existing studies in several directions, including contextual information, position discounts, and a more general cascading bandit model. Experiments on synthetic and real datasets demonstrate the advantage of involving contextual information and position discounts.