Technology Category
Machine Learning: Online Learning & BanditsSearch and Optimization: Adversarial SearchGame Theory and Economic Paradigms: Adversarial Learning
Minimax Adaptive Online Nonparametric Regression over Besov Spaces
🤖 AI Summary
This paper studies online adversarial regression in Besov spaces $B_{pq}^s$ with unknown smoothness parameters $(s,p,q)$, where $s > d/p$ and $1 le p,q le infty$. To address the challenges posed by spatially heterogeneous and highly irregular function regularity, we propose the first parameter-free adaptive wavelet algorithm, integrating multiresolution analysis, local thresholding estimation, and online convex optimization. Furthermore, we design a spatio-temporal jointly local adaptive mechanism that enables dynamic tracking of non-uniform smoothness—achieved for the first time in this setting. Theoretically, the global variant achieves the minimax-optimal regret bound over $B_{pq}^s$, while the locally adaptive variant significantly outperforms the global approach in heterogeneous environments; its regret bound explicitly reflects regional variations in regularity.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Online adversarial regression in Besov spaces
Adaptive prediction without prior smoothness knowledge
Dynamic tracking of spatially inhomogeneous smoothness
Innovation
Methods, ideas, or system contributions that make the work stand out.
Wavelet-based adaptive online regression algorithm
Minimax-optimal regret without prior parameters
Locally adaptive tracking of spatial inhomogeneity
🔎 Similar Papers
No similar papers found.
💼 Related Jobs
No related jobs found.
