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arXiv · 2609.05214

Dimension-Adaptive Batched Lipschitz Narrowing Without Knowing the Zooming Dimension

Yasong Feng
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Abstract

The Appropriately Combined Edge-length (ACE) sequence in A-BLiN depends on the zooming dimension $d_z$. 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 $d_z$ or the zooming constant $C_z$, yet it attains $\widetilde{\mathcal O}_d(T^{(d_z+1)/(d_z+2)})$ regret with $\mathcal O_d(\log\log T)$ batches. Together with the adaptive-grid lower bound in Theorem 10 of the original paper, the optimal batch complexity remains $Θ_d(\log\log T)$ when $d_z$ is unknown.

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Yasong Feng. 2026-09-04. Dimension-Adaptive Batched Lipschitz Narrowing Without Knowing the Zooming Dimension. https://arxiv.org/abs/2609.05214

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