Contextual Slate GLM Bandits with Limited Adaptivity

We investigate the contextual slate bandit problem with generalized linear rewards under limited adaptivity. At each round, the learner is presented with $N$ sets of items and constructs a slate by selecting one item per set; the resulting slate yields a scalar reward sampled from a Generalized Linear Model (GLM). We propose algorithms under two limited-adaptivity paradigms: (a) batched and (b) rarely-switching settings. For the batched setting, we introduce B-SlateGLinCB, which partitions the time horizon into $O(\log\log T)$ batches such that each batch's policy relies only on data from previous batches. For the rarely-switching setting, we propose RS-SlateGLinCB, which adaptively performs only $O(d\log T)$ parameter updates. Under a diversity assumption on the item sequences, we prove that B-SlateGLinCB and RS-SlateGLinCB achieve regret bounds of $O(Nd^{3/2}\sqrt{T})$ and $O(Nd\sqrt{T})$, respectively. Notably, both bounds are independent of the non-linearity parameter $\kappa$ that is typically found to scale the regret of GLM bandit algorithms. Our algorithms are computationally efficient, requiring only $\text{poly}(N)$ time per round despite $2^{\Omega(N)}$ possible slates. Simulations show our algorithms outperform existing batched baselines and remain competitive with Slate-GLM-OFU, a fully adaptive state-of-the-art algorithm. Notably, a slightly modified B-SlateGLinCB empirically matches this baseline. Finally, we demonstrate strong performance in a practical in-context example selection task for language models.