# Minimax Adaptive Online Nonparametric Regression over Besov Spaces

arXiv: https://arxiv.org/abs/2505.19741 · HTML: https://mlsanity.com/paper/2505.19741/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 48 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 17 of 17)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Coin Betting and Parameter-Free Online Learning](https://mlsanity.com/paper/1602.04128/) (2016)
- [Black-Box Reductions for Parameter-free Online Learning in Banach Spaces](https://mlsanity.com/paper/1802.06293/) (2018)
- [A Second-order Bound with Excess Losses](https://mlsanity.com/paper/1402.2044/) (2014)
- [Lipschitz and Comparator-Norm Adaptivity in Online Learning](https://mlsanity.com/paper/2002.12242/) (2020)
- [Second-order Quantile Methods for Experts and Combinatorial Games](https://mlsanity.com/paper/1502.08009/) (2015)
- [Optimal learning with Bernstein Online Aggregation](https://mlsanity.com/paper/1404.1356/) (2014)
- [A Chaining Algorithm for Online Nonparametric Regression](https://mlsanity.com/paper/1502.07697/) (2015)
- [Online Nonparametric Regression with General Loss Functions](https://mlsanity.com/paper/1501.06598/) (2015)
- [Second-Order Kernel Online Convex Optimization with Adaptive Sketching](https://mlsanity.com/paper/1706.04892/) (2017)
- [Efficient online learning with kernels for adversarial large scale problems](https://mlsanity.com/paper/1902.09917/) (2019)
- [Unconstrained Dynamic Regret via Sparse Coding](https://mlsanity.com/paper/2301.13349/) (2023)
- [Locally-Adaptive Nonparametric Online Learning](https://mlsanity.com/paper/2002.01882/) (2020)
- [Online nonparametric regression with Sobolev kernels](https://mlsanity.com/paper/2102.03594/) (2021)
- [Near-optimal learning with average H"older smoothness](https://mlsanity.com/paper/2302.06005/) (2023)
- [Efficient Agnostic Learning with Average Smoothness](https://mlsanity.com/paper/2309.17016/) (2023)
- [Minimax-optimal and Locally-adaptive Online Nonparametric Regression](https://mlsanity.com/paper/2410.03363/) (2024)

## Built on by (most cited first, 1 of 1)

- [High-Probability Minimax Adaptive Estimation in Besov Spaces via Online-to-Batch](https://mlsanity.com/paper/2602.11747/) (2026)

## Abstract (arXiv)

We study online adversarial regression with convex losses against a rich class of continuous yet highly irregular prediction rules, modeled by Besov spaces Bpqs with general parameters 1 ≤ p,q ≤ ∞ and smoothness s > tfracdp. 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 Bpqs. 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.