Distributional Learning

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Period ending 2026-09-21

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229 papers

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Proper Agnostic Learning of Functions of Halfspaces under Gaussian Marginals
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Sample Complexity of Transfer Learning: An Optimal Transport Approach
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Statistical Limits and Efficient Algorithms for Differentially Private Federated Learning
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May 13, 2026Huan Wang, Jun Shen, Haoran Li +6Heterogeneous Federated Learning Federated Learning
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May 4, 2026Ahmad Dabaja, Rachid El-AzouziHeterogeneous Federated Learning Federated Learning

May 26, 2026 · cs.DSJ/K move · Enter open · S save

Proper Agnostic Learning of Functions of Halfspaces under Gaussian Marginals

Sergei Tikhonov, Arsen Vasilyan

UT Austin

We study the problem of computationally efficient proper agnostic learning of multidimensional concept classes under the Gaussian distribution. In this setting, given i.i.d. labeled samples from an unknown distribution over

\mathbb{R}^d \times \{\pm 1\}

whose marginal on

\mathbb{R}^d

is Gaussian, the goal is to output a hypothesis from a target class

\mathcal{F}

whose 0-1 loss is within

ε

of that of the best classifier in

\mathcal{F}

. We give the first efficient proper agnostic learning algorithm for arbitrary Boolean functions of

K

halfspaces under Gaussian marginals. Our algorithm runs in time

d^{O(K^2 \log(1/ε)/ε^2)} + (K/ε)^{O(K^3/ε^{2.5})}

. Prior to our work, the only known algorithm for

K \geq 2

was brute-force search, with run-time exponential in

d

. Moreover, the dependence of our run-time on the dimension

d

matches that of the best known improper learning algorithm, namely

d^{\widetilde{O}(K^2/ε^2)}

. For the special case of a single halfspace (

K=1

), the best previous run-time was

d^{O(1/ε^4)} + (1/ε)^{O(1/ε^6)}

. Our algorithm improves this to

d^{O(1/ε^2)} + (1/ε)^{O(1/ε^{2.5})}

. Once again, the dependence on

d

matches that of the best known improper algorithm, namely

d^{O(1/ε^2)}

. Furthermore, the dependence of our run-time on the dimension

d

is essentially optimal in the statistical query model.

Optimal Sample Complexity Binary Classification Distributional Learning 3D Gaussian Splatting

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