Title: Efficient and Optimal Strategies for Linear Contextual Bandits with Infrequent Parameter Adjustments

Abstract:

This paper investigates linear contextual bandit problems characterized by infrequent parameter updates. In this setting, the learner integrates reward feedback into its parameter estimates only at a limited number of distinct time steps, despite continuously observing contexts and making sequential action choices. This perspective highlights a crucial practical distinction frequently overlooked in existing literature: many approaches classified as "strictly batched" impose additional constraints on context adaptivity within intervals. Specifically, these methods prevent the action selection policy within an interval from adapting to the sequence of observed contexts and actions occurring during that interval, relying solely on the current round's context.

For linear contextual bandits, we introduce two practical algorithms that require merely $O(\log\log T)$ parameter updates. The first, named BLCE-G, achieves minimax-optimal regret (up to polylogarithmic factors in $T$) across both small-$K$ and large-$K$ scenarios using a static update schedule. The second algorithm, BLCE, eliminates the computationally expensive near G-optimal design step—a major bottleneck in previous strictly batched static-grid methods. Despite this simplification, BLCE maintains minimax-optimal regret and offers the lowest known runtime complexity among optimal algorithms. We also generalize these principles of rare updates and computational efficiency to the domain of generalized linear contextual bandits. Collectively, our findings present statistically optimal solutions that are not only efficient in terms of parameter updates but also practical in computational performance.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC