Ranking In Generalized Linear Bandits

We study the ranking problem in generalized linear bandits. At each time, the learning agent selects an ordered list of items and observes stochastic outcomes. In recommendation systems, displaying an ordered list of the most attractive items is not always optimal as both position and item dependencies result in a complex reward function. A very naive example is the lack of diversity when all the most attractive items are from the same category. We model the position and item dependencies in the ordered list and design UCB and Thompson Sampling type algorithms for this problem. Our work generalizes existing studies in several directions, including position dependencies where position discount is a particular case, and connecting the ranking problem to graph theory.