Linear contextual bandits represent a fundamental class of models with numerous real-world applications, and it is critical to developing algorithms that can effectively manage noise with unknown variance, ensuring provable guarantees for both worst-case constant-variance noise and deterministic reward scenarios.

We first prove case (a).

From the learning theory perspective, the learning guarantees of SCO algorithms with known derivatives have been studied in the literature.

The following lemma is standard in the literature, see e.g.

In this paper, we present the first accelerated VI for both the Bellman consistency and optimality operators.

In this paper, we present the first accelerated VI for both the Bellman consistency and optimality operators.