Combinatorial Reinforcement Learning with Preference Feedback

In this paper, we consider combinatorial reinforcement learning with preference feedback, where a learning agent sequentially offers an action--an assortment of multiple items to--a user, whose preference feedback follows a multinomial logistic (MNL) model. This framework allows us to model real-world scenarios, particularly those involving long-term user engagement, such as in recommender systems and online advertising. However, this framework faces two main challenges: (1) the unknown value of each item, unlike traditional MNL bandits that only address single-step preference feedback, and (2) the difficulty of ensuring optimism while maintaining tractable assortment selection in the combinatorial action space with unknown values. In this paper, we assume a contextual MNL preference model, where the mean utilities are linear, and the value of each item is approximated by a general function. We propose an algorithm, MNL-VQL, that addresses these challenges, making it both computationally and statistically efficient. As a special case, for linear MDPs (with the MNL preference feedback), we establish the first regret lower bound in this framework and show that MNL-VQL achieves nearly minimax-optimal regret. To the best of our knowledge, this is the first work to provide statistical guarantees in combinatorial RL with preference feedback.