Agnostic Learning

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An Agnostic Sample Compression Scheme for Squared Loss of Near-Linear Size in the Fat-Shattering Dimension
Aug 31, 2026Guangjian Zhang, Zhengyi Yang, Xiaoyang WangAgnostic Learning Sample Compression
Two Dimensions Govern Agnostic Multiclass Transductive Learning
Aug 26, 2026Pahan DewasurendraAgnostic Learning Multiclass Classification
Johns Hopkins University
Robust Regression of General ReLUs with Queries
Jun 9, 2026Ilias Diakonikolas, Daniel M. Kane, Mingchen MaReLU Neural Networks Active Learning
University of Wisconsin-Madison · University of California, San Diego
Proper Agnostic Learning of Functions of Halfspaces under Gaussian Marginals
May 26, 2026Sergei Tikhonov, Arsen VasilyanAgnostic Learning Boolean Function Learning
UT Austin
Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals
May 20, 2026Ilias Diakonikolas, Giannis Iakovidis, Mingchen MaAgnostic Learning Multiclass Classification
University of Wisconsin-Madison
Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale
May 13, 2026Shashaank Aiyer, Yishay Mansour, Shay Moran +2Agnostic Learning Statistical Learning Theory
University of Maryland · Tel Aviv University and Google Research · Technion and Google Research +1
Near-Optimal Cryptographic Hardness of Learning With Homogeneous Halfspaces Under Gaussian Marginals
Apr 29, 2026Jizhou Huang, Brendan JubaAgnostic Learning Statistical Learning Theory
Meta · Washington Universtiy in St. Louis
Robust Learning with Optimal Error
Apr 2, 2026Guy BlancAgnostic Learning Robust Classification
Stanford
Agnostic learning in (almost) optimal time via Gaussian surface area
Mar 6, 2026Lucas Pesenti, Lucas Slot, Manuel WiedmerAgnostic Learning Statistical Learning Theory
ETH Zurich · University of Amsterdam
Smoothed Analysis for Learning Concepts with Low Intrinsic Dimension
Jul 1, 2024Gautam Chandrasekaran, Adam Klivans, Vasilis Kontonis +2Agnostic Learning Margin-Based Learning
a University of Texas at Austin · b University of California, Los Angeles

Aug 31, 2026J/K move · Enter open · S save

An Agnostic Sample Compression Scheme for Squared Loss of Near-Linear Size in the Fat-Shattering Dimension

Guangjian Zhang, Zhengyi Yang, Xiaoyang Wang

Agnostic Learning Sample Compression Empirical Risk Minimization

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We study the squared-loss sample compression question posed by Attias, Hanneke, Kontorovich, and Sadigurschi in their ICML 2024 paper. For every nonempty class

\mathcal{F}\subseteq[0,1]^{\mathcal{X}}

and accuracy

0<α\le1

with

d=\operatorname{fat}(\mathcal{F},c'α)<\infty

, where

c'>0

is universal, we prove the existence of a deterministic agnostic scheme of total size

O(d\log^3(2/α))

. Its code contains original labeled observations and auxiliary bits, and its reconstruction has empirical loss at most

α

above the infimum over

\mathcal{F}

on every finite sample. This establishes the polylogarithmic formulation in Section 5 of arXiv:1810.01864v2. The construction approximates a near-optimal internal target by a fixed-step boosting ensemble and takes its equal-weight median. Average loss permits an accuracy-dependent number of rounds, so the entire ensemble can be retained without dual-dimension sparsification. Quantized target constraints and round-membership bits determine the reconstructed function exactly. We also prove that, when retained observations must come from the sample, a fixed class of fat-shattering dimension one requires total size

Ω(\log(1/α))

. With observations and auxiliary bits charged together, this rules out the proceedings version's log-free formulation under its original-example restriction. The framework extends to average power loss at scale

α/p