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We study ``selective'' or ``conditional'' classification problems under an agnostic setting. Classification tasks commonly focus on modeling the relationship between features and categories that captures the vast majority of data. In…

Machine Learning · Computer Science 2025-02-04 Jizhou Huang , Brendan Juba

The current paper studies the problem of agnostic $Q$-learning with function approximation in deterministic systems where the optimal $Q$-function is approximable by a function in the class $\mathcal{F}$ with approximation error $\delta \ge…

Machine Learning · Computer Science 2020-02-18 Simon S. Du , Jason D. Lee , Gaurav Mahajan , Ruosong Wang

We study the complexity of learning real-valued Multi-Index Models (MIMs) under the Gaussian distribution. A $K$-MIM is a function $f:\mathbb{R}^d\to \mathbb{R}$ that depends only on the projection of its input onto a $K$-dimensional…

Machine Learning · Computer Science 2025-05-28 Ilias Diakonikolas , Giannis Iakovidis , Daniel M. Kane , Lisheng Ren

Classical results in statistical learning typically consider two extreme data-generating models: i.i.d. instances from an unknown distribution, or fully adversarial instances, often much more challenging statistically. To bridge the gap…

Machine Learning · Statistics 2025-06-13 Moïse Blanchard

We focus on the task of learning a single index model $\sigma(w^\star \cdot x)$ with respect to the isotropic Gaussian distribution in $d$ dimensions. Prior work has shown that the sample complexity of learning $w^\star$ is governed by the…

Machine Learning · Computer Science 2023-05-19 Alex Damian , Eshaan Nichani , Rong Ge , Jason D. Lee

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal…

Machine Learning · Computer Science 2023-03-14 Aravind Gollakota , Adam R. Klivans , Konstantinos Stavropoulos , Arsen Vasilyan

We study the algorithmic task of testably learning general Massart halfspaces under the Gaussian distribution. In the testable learning setting, the aim is the design of a tester-learner pair satisfying the following properties: (1) if the…

Data Structures and Algorithms · Computer Science 2026-02-27 Ilias Diakonikolas , Giannis Iakovidis , Daniel M. Kane , Sihan Liu

The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by…

Data Structures and Algorithms · Computer Science 2025-10-22 Sophie Huiberts , Yin Tat Lee , Xinzhi Zhang

Using quantum algorithms, we obtain, for accuracy $\epsilon>0$ and confidence $1-\delta,0<\delta<1,$ a new sample complexity upper bound of $O((\mbox{log}(\frac{1}{\delta}))/\epsilon)$ as $\epsilon,\delta\rightarrow 0$ for a general…

Quantum Physics · Physics 2024-04-22 Daniel Z. Zanger

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

Many popular learning algorithms (E.g. Regression, Fourier-Transform based algorithms, Kernel SVM and Kernel ridge regression) operate by reducing the problem to a convex optimization problem over a vector space of functions. These methods…

Machine Learning · Computer Science 2014-05-13 Amit Daniely , Nati Linial , Shai Shalev-Shwartz

We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent agnostic PAC model, with a focus on $L_p$ perturbations. We give a computationally efficient learning algorithm and…

Machine Learning · Computer Science 2020-07-31 Ilias Diakonikolas , Daniel M. Kane , Pasin Manurangsi

We study active learning of homogeneous $s$-sparse halfspaces in $\mathbb{R}^d$ under the setting where the unlabeled data distribution is isotropic log-concave and each label is flipped with probability at most $\eta$ for a parameter $\eta…

Machine Learning · Computer Science 2021-08-16 Chicheng Zhang , Jie Shen , Pranjal Awasthi

We study the task of learning Multi-Index Models (MIMs) with label noise under the Gaussian distribution. A $K$-MIM is any function $f$ that only depends on a $K$-dimensional subspace. We focus on well-behaved MIMs with finite ranges that…

Machine Learning · Computer Science 2025-04-15 Ilias Diakonikolas , Giannis Iakovidis , Daniel M. Kane , Nikos Zarifis

We provide sample complexity upper bounds for agnostically learning multivariate Gaussians under the constraint of approximate differential privacy. These are the first finite sample upper bounds for general Gaussians which do not impose…

Machine Learning · Statistics 2020-10-21 Ishaq Aden-Ali , Hassan Ashtiani , Gautam Kamath

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Machine Learning · Computer Science 2024-09-17 Haihan Zhang , Yuanshi Liu , Qianwen Chen , Cong Fang

We study the efficient PAC learnability of halfspaces in the presence of Tsybakov noise. In the Tsybakov noise model, each label is independently flipped with some probability which is controlled by an adversary. This noise model…

Machine Learning · Computer Science 2020-06-12 Ilias Diakonikolas , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

We consider the problem of distribution-free learning for Boolean function classes in the PAC and agnostic models. Generalizing a beautiful work of Malach and Shalev-Shwartz (2022) that gave tight correlational SQ (CSQ) lower bounds for…

Data Structures and Algorithms · Computer Science 2023-08-25 Aravind Gollakota , Sushrut Karmalkar , Adam Klivans

We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…

Machine Learning · Statistics 2025-06-03 El Mehdi Saad , Wei-Cheng Lee , Francesco Orabona

Motivated by the study of $Q$-learning algorithms in reinforcement learning, we study a class of stochastic approximation procedures based on operators that satisfy monotonicity and quasi-contractivity conditions with respect to an…

Machine Learning · Computer Science 2019-06-25 Martin J. Wainwright