Categorized Bandits
This addresses the challenge of optimizing recommendations in e-commerce by leveraging category structures, but it is incremental as it extends existing bandit frameworks with new ordering concepts.
The paper tackles the problem of multi-armed bandits with arms grouped into ordered categories, inspired by e-commerce scenarios where customers prefer items from specific unknown categories, by proving lower bounds and providing algorithms with theoretical guarantees, and validates the model on real data.
We introduce a new stochastic multi-armed bandit setting where arms are grouped inside ``ordered'' categories. The motivating example comes from e-commerce, where a customer typically has a greater appetence for items of a specific well-identified but unknown category than any other one. We introduce three concepts of ordering between categories, inspired by stochastic dominance between random variables, which are gradually weaker so that more and more bandit scenarios satisfy at least one of them. We first prove instance-dependent lower bounds on the cumulative regret for each of these models, indicating how the complexity of the bandit problems increases with the generality of the ordering concept considered. We also provide algorithms that fully leverage the structure of the model with their associated theoretical guarantees. Finally, we have conducted an analysis on real data to highlight that those ordered categories actually exist in practice.