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Mathematics > Statistics Theory

arXiv:2505.19741 (math)
[Submitted on 26 May 2025]

Title:Minimax Adaptive Online Nonparametric Regression over Besov Spaces

Authors:Paul Liautaud (LPSM, SU), Pierre Gaillard (UGA), Olivier Wintenberger (LPSM, SU, ICP)
View a PDF of the paper titled Minimax Adaptive Online Nonparametric Regression over Besov Spaces, by Paul Liautaud (LPSM and 5 other authors
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Abstract:We study online adversarial regression with convex losses against a rich class of continuous yet highly irregular prediction rules, modeled by Besov spaces $B_{pq}^s$ with general parameters $1 \leq p,q \leq \infty$ and smoothness $s > d/p$. We introduce an adaptive wavelet-based algorithm that performs sequential prediction without prior knowledge of $(s,p,q)$, and establish minimax-optimal regret bounds against any comparator in $B_{pq}^s$. We further design a locally adaptive extension capable of dynamically tracking spatially inhomogeneous smoothness. This adaptive mechanism adjusts the resolution of the predictions over both time and space, yielding refined regret bounds in terms of local regularity. Consequently, in heterogeneous environments, our adaptive guarantees can significantly surpass those obtained by standard global methods.
Subjects: Statistics Theory (math.ST); Machine Learning (stat.ML)
Cite as: arXiv:2505.19741 [math.ST]
  (or arXiv:2505.19741v1 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2505.19741
arXiv-issued DOI via DataCite

Submission history

From: Paul Liautaud [view email] [via CCSD proxy]
[v1] Mon, 26 May 2025 09:23:11 UTC (615 KB)
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