Contextual Slate GLM Bandits with Limited Adaptivity

2026-06-30

AI Summary

This work addresses the problem of contextual slate combinatorial online decision-making, where at each round one item is selected from each of $N$ groups and a reward governed by a generalized linear model (GLM) is observed. Under limited adaptivity constraints, the paper proposes two efficient algorithms: a batched variant, B-SlateGLinCB, and a rare-switching variant, RS-SlateGLinCB. Both algorithms rely solely on historical data or infrequent parameter updates, achieving— for the first time in this setting—regret bounds independent of the nonlinearity parameter $\kappa$, while reducing computational complexity to polynomial in $N$, thereby overcoming the exponential blowup of the slate space. Theoretical regret bounds are $O(N d^{3/2} \sqrt{T})$ and $O(N d \sqrt{T})$, respectively. Experiments demonstrate that both methods significantly outperform existing low-adaptivity baselines, closely matching the performance of the fully adaptive Slate-GLM-OFU, and exhibit strong empirical results in large-model context example selection tasks.

Abstract

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, where each item is represented by a $d$-dimensional feature vector. The learner then 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 settings: (a) Batched and (b) Rarely-Switching. For the batched setting, we introduce B-SlateGLinCB, which partitions the time horizon into $\mathcal{O}(\log\log T)$ 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 $\mathcal{O}(Nd\log T)$ parameter updates. Under a diversity assumption on the item sequences, we prove that B-SlateGLinCB and RS-SlateGLinCB achieve regret bounds of $\mathcal{O}(Nd^{3/2}\sqrt{T})$ and $\mathcal{O}(Nd\sqrt{T})$, respectively. Notably, both bounds are independent of the non-linearity parameter $κ$ 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 $2^{Ω(N)}$ possible slates. Simulations show our algorithms outperform existing baselines with limited adaptivity 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.

Problem

• contextual slate bandits
• generalized linear models
• limited adaptivity
• regret minimization
• combinatorial selection

Innovation

• Contextual Slate Bandits
• Generalized Linear Models
• Limited Adaptivity
• Batched Learning
• Rarely-Switching Algorithms