PreprintCC BY 4.0arXiv
The Geometry of Multitask Learning: Sharp Rates for Shared Subspace Estimation
Abstract
Learning a shared subspace in multitask learning is an important statistical problem, yet exact rates remain poorly understood in many of the formal settings considered in the literature. To address this gap, which arises from limitations of existing upper-bound techniques, we propose a general multitask lemma. The lemma provides sufficient conditions for fast subspace estimation in generic multitask settings, in the form of geometric conditions on the task regression functions and their estimators. We subsequently show that the multitask lemma yields sharp minimax rates---previously unknown---for linear regression and classification in the regimes considered, and rates matching up to logarithmic factors for additive-noise regression.
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BibTeX
@misc{cai2026geometry,
title = {{The Geometry of Multitask Learning: Sharp Rates for Shared Subspace Estimation}},
author = {Tony Cai and Abhinav Chakraborty and Samory Kpotufe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40713},
eprint = {2610.40713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40713},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Geometry of Multitask Learning: Sharp Rates for Shared Subspace Estimation
AU - Tony Cai
AU - Abhinav Chakraborty
AU - Samory Kpotufe
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40713
UR - https://arxiv.org/abs/2610.40713
AB - Learning a shared subspace in multitask learning is an important statistical problem, yet exact rates remain poorly understood in many of the formal settings considered in the literature. To address this gap, which arises from limitations of existing upper-bound techniques, we propose a general multitask lemma. The lemma provides sufficient conditions for fast subspace estimation in generic multitask settings, in the form of geometric conditions on the task regression functions and their estimators. We subsequently show that the multitask lemma yields sharp minimax rates---previously unknown---for linear regression and classification in the regimes considered, and rates matching up to logarithmic factors for additive-noise regression.
ER -