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We study the complexity of smoothed agnostic learning of halfspaces on $\{\pm 1\}^n$ under uniform marginals in the model of~\cite{KM25}, where each input coordinate is independently flipped with probability $\sigma \in (0, {1}/{2})$. We…

Machine Learning · Computer Science 2026-05-14 Tim Sinen

We derive approximation bounds for learning single neuron models using thresholded gradient descent when both the labels and the covariates are possibly corrupted adversarially. We assume the data follows the model $y =…

Machine Learning · Statistics 2024-09-06 Arvind Rathnashyam , Alex Gittens

This paper considers the problem of learning a single ReLU neuron with squared loss (a.k.a., ReLU regression) in the overparameterized regime, where the input dimension can exceed the number of samples. We analyze a Perceptron-type…

Machine Learning · Computer Science 2023-06-27 Jingfeng Wu , Difan Zou , Zixiang Chen , Vladimir Braverman , Quanquan Gu , Sham M. Kakade

Motivated by the resurgence of neural networks in being able to solve complex learning tasks we undertake a study of high depth networks using ReLU gates which implement the function $x \mapsto \max\{0,x\}$. We try to understand the role of…

Computational Complexity · Computer Science 2017-11-10 Anirbit Mukherjee , Amitabh Basu

We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable dataset. The classifier is described by a nonlinear ReLU model and the objective function adopts the exponential…

Machine Learning · Computer Science 2018-10-17 Tengyu Xu , Yi Zhou , Kaiyi Ji , Yingbin Liang

Boosting is a key method in statistical learning, allowing for converting weak learners into strong ones. While well studied in the realizable case, the statistical properties of weak-to-strong learning remain less understood in the…

Machine Learning · Computer Science 2026-01-01 Arthur da Cunha , Mikael Møller Høgsgaard , Andrea Paudice , Yuxin Sun

We describe an algorithm that learns two-layer residual units using rectified linear unit (ReLU) activation: suppose the input $\mathbf{x}$ is from a distribution with support space $\mathbb{R}^d$ and the ground-truth generative model is a…

Machine Learning · Computer Science 2022-12-13 Zhunxuan Wang , Linyun He , Chunchuan Lyu , Shay B. Cohen

We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and…

Machine Learning · Computer Science 2018-03-01 Simon S. Du , Jason D. Lee , Yuandong Tian

We study the overparametrization bounds required for the global convergence of stochastic gradient descent algorithm for a class of one hidden layer feed-forward neural networks, considering most of the activation functions used in…

Machine Learning · Computer Science 2022-11-17 Bartłomiej Polaczyk , Jacek Cyranka

Gradient boosting algorithms construct a regression predictor using a linear combination of ``base learners''. Boosting also offers an approach to obtaining robust non-parametric regression estimators that are scalable to applications with…

Methodology · Statistics 2020-08-11 Xiaomeng Ju , Matías Salibián-Barrera

Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such…

Machine Learning · Computer Science 2025-11-25 Yiwen Kou , Raghu Meka

Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing…

Machine Learning · Computer Science 2019-12-16 Yunwen Lei , Ting Hu , Guiying Li , Ke Tang

Policy gradient methods in reinforcement learning update policy parameters by taking steps in the direction of an estimated gradient of policy value. In this paper, we consider the statistically efficient estimation of policy gradients from…

Machine Learning · Statistics 2020-02-21 Nathan Kallus , Masatoshi Uehara

Quantile regression is the task of estimating a specified percentile response, such as the median, from a collection of known covariates. We study quantile regression with rectified linear unit (ReLU) neural networks as the chosen model…

Statistics Theory · Mathematics 2020-12-21 Oscar Hernan Madrid Padilla , Wesley Tansey , Yanzhen Chen

We study the problem of agnostically learning halfspaces under the Gaussian distribution. Our main result is the {\em first proper} learning algorithm for this problem whose sample complexity and computational complexity qualitatively match…

Machine Learning · Computer Science 2021-02-11 Ilias Diakonikolas , Daniel M. Kane , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(\mathbf{x},y)$ from an unknown distribution on $\mathbb{R}^n \times \{ \pm 1\}$, whose marginal distribution on…

Machine Learning · Computer Science 2023-02-14 Ilias Diakonikolas , Daniel M. Kane , Lisheng Ren

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…

Statistics Theory · Mathematics 2009-09-09 Jean-Yves Audibert

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

Statistics Theory · Mathematics 2008-03-04 Jean-Yves Audibert

Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…

Machine Learning · Computer Science 2020-07-09 Adithya M. Devraj , Sean P. Meyn

Recent works explore deep learning's success by examining functions or data with hierarchical structure. To study the learning complexity of functions with hierarchical structure, we study the noise stability of functions with tree…

Probability · Mathematics 2025-09-30 Rupert Li , Elchanan Mossel