\section{Conclusions}
\label{section:conclusions}

We proposed three algorithms \slateglincb, \slateglincbts, \slateglincbtsfixed\ for the slate bandit problem with logistic rewards. While the first two work in both the contextual and non-contextual settings, the third is designed for the non-contextual setting. All our algorithms perform explore-exploit at the slot level, making their average per round time complexity logarithmic in the number of candidate slates. By building on algorithms from \cite{Faury2022}, the average time per round is also logarithmic in the number of rounds $T$. As a result, our algorithms run much faster than state of the art logistic bandit algorithms (having $2^{\Omega(N)}$ per round time complexity). We also show that under a popular diversity assumption (Assumption \ref{assumption: diversity}), which we also empirically validate, \slateglincb\ and \slateglincbtsfixed\ achieve $\kappa$ independent  $\tilde{O}(\sqrt T)$ regret, making them both optimal and computationally efficient. 
