# Dimension-Adaptive Batched Lipschitz Narrowing Without Knowing the Zooming Dimension

arXiv: https://arxiv.org/abs/2609.05214 · HTML: https://mlsanity.com/paper/2609.05214/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 2 references that are in the map.
- First posted on arXiv 4 Sep 2026.

## Builds on (most cited first, 1 of 1)

- [Lipschitz Bandits with Batched Feedback](https://mlsanity.com/paper/2110.09722/) (2021)

## Abstract (arXiv)

The Appropriately Combined Edge-length (ACE) sequence in A-BLiN depends on the zooming dimension dz. This note removes that dependence. The next edge length is selected from the number of cubes that survive the preceding elimination. The resulting Count-Adaptive BLiN algorithm does not use dz or the zooming constant Cz, yet it attains widetildemathcal Od(T(dz+1)/(dz+2)) regret with mathcal Od(loglog T) batches. Together with the adaptive-grid lower bound in Theorem 10 of the original paper, the optimal batch complexity remains Thetad(loglog T) when dz is unknown.