Dimension-Adaptive Batched Lipschitz Narrowing Without Knowing the Zooming Dimension

arXiv:2609.05214v1 Announce Type: new 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(loglog T) batches. Together with the adaptive-grid lower bound in Theorem 10 of the original paper, the optimal batch complexity remains Theta_d(loglog T) when d_z is unknown.

Source: arXiv cs.LG | 2026-09-07