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)\\) <span style=\"font-size: 1rem;\">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\u00a0\u00a0parameter 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})\\)\u00a0and \\(O(Nd\\sqrt{T})\\), respectively. Notably, both bounds are independent of the non-linearity parameter \\(\\kappa\\)\u00a0that is typically found to scale the regret of GLM bandit algorithms. Our algorithms are computationally efficient, requiring only \\(\\text{poly}(N)\\)\u00a0time per round despite \\(2^{\\OmesdfsdfN)}\\)\u00a0possible 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.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
We investigate the contextual slate bandit problem with generalized linear rewards under limited adaptivity. At each round, the learner is presented with 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). 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