Algorithms for slate bandits with non-separable reward functions

In this paper, we study a slate bandit problem where the function that determines the slate-level reward is non-separable: the optimal value of the function cannot be determined by learning the optimal action for each slot. We are mainly concerned with cases where the number of slates is large relative to the time horizon, so that trying each slate as a separate arm in a traditional multi-armed bandit, would not be feasible. Our main contribution is the design of algorithms that still have sub-linear regret with respect to the time horizon, despite the large number of slates. Experimental results on simulated data and real-world data show that our proposed method outperforms popular benchmark bandit algorithms.