  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.
