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The problem of stochastic convex optimization with bandit feedback (in the learning community) or without knowledge of gradients (in the optimization community) has received much attention in recent years, in the form of algorithms and…

Machine Learning · Computer Science 2013-04-30 Ohad Shamir

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…

Machine Learning · Computer Science 2012-04-23 Francis Bach , Rodolphe Jenatton , Julien Mairal , Guillaume Obozinski

An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the…

Machine Learning · Computer Science 2020-08-06 Yuheng Bu , Shaofeng Zou , Venugopal V. Veeravalli

The study of random Fourier series, linear combinations of trigonometric functions whose coefficients are independent (in our case Gaussian) random variables with polynomially bounded means and standard deviations, dates back to Norbert…

Spectral Theory · Mathematics 2023-01-10 Ethan Sussman

We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number of training examples. The time complexity of our…

Optimization and Control · Mathematics 2017-04-26 Naman Agarwal , Zeyuan Allen-Zhu , Brian Bullins , Elad Hazan , Tengyu Ma

A problem of bounding the generalization error of a classifier f in H, where H is a "base" class of functions (classifiers), is considered. This problem frequently occurs in computer learning, where efficient algorithms of combining simple…

Probability · Mathematics 2007-06-13 Vladimir Koltchinskii , Dmitry Panchenko , Fernando Lozano

We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…

Statistics Theory · Mathematics 2018-04-04 Sara van de Geer

Self-supervised learning attempts to learn representations from un-labeled data; it does so via a loss function that encourages the embedding of a point to be close to that of its augmentations. This simple idea performs remarkably well,…

Machine Learning · Computer Science 2026-01-30 Parikshit Bansal , Ali Kavis , Sujay Sanghavi

The online meta-learning framework is designed for the continual lifelong learning setting. It bridges two fields: meta-learning which tries to extract prior knowledge from past tasks for fast learning of future tasks, and online-learning…

Machine Learning · Computer Science 2020-02-20 Zhenxun Zhuang , Yunlong Wang , Kezi Yu , Songtao Lu

Consider the sequential optimization of an expensive to evaluate and possibly non-convex objective function $f$ from noisy feedback, that can be considered as a continuum-armed bandit problem. Upper bounds on the regret performance of…

Machine Learning · Statistics 2021-03-11 Sattar Vakili , Kia Khezeli , Victor Picheny

The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…

Optimization and Control · Mathematics 2019-10-24 Brian Swenson , Anirudh Sridhar , H. Vincent Poor

We extend the notion of minimax fairness in supervised learning problems to its natural conclusion: lexicographic minimax fairness (or lexifairness for short). Informally, given a collection of demographic groups of interest, minimax…

Machine Learning · Computer Science 2021-02-18 Emily Diana , Wesley Gill , Ira Globus-Harris , Michael Kearns , Aaron Roth , Saeed Sharifi-Malvajerdi

For a class $F$ of complex-valued functions on a set $D$, we denote by $g_n(F)$ its sampling numbers, i.e., the minimal worst-case error on $F$, measured in $L_2$, that can be achieved with a recovery algorithm based on $n$ function…

Numerical Analysis · Mathematics 2023-05-15 Matthieu Dolbeault , David Krieg , Mario Ullrich

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…

Statistics Theory · Mathematics 2020-07-27 T. Tony Cai , Tengyuan Liang , Alexander Rakhlin

In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…

Optimization and Control · Mathematics 2024-12-13 Getachew K. Befekadu

This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the…

Information Theory · Computer Science 2016-11-03 Hugo Reboredo , Francesco Renna , Robert Calderbank , Miguel R. D. Rodrigues

This paper addresses the meta-learning problem in sparse linear regression with infinite tasks. We assume that the learner can access several similar tasks. The goal of the learner is to transfer knowledge from the prior tasks to a similar…

Machine Learning · Computer Science 2021-02-19 Zhanyu Wang , Jean Honorio

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

The gauge function, closely related to the atomic norm, measures the complexity of a statistical model, and has found broad applications in machine learning and statistical signal processing. In a high-dimensional learning problem, the…

Optimization and Control · Mathematics 2022-03-11 Armin Eftekhari , Peyman Mohajerin Esfahani

Sensor calibration is an indispensable task in any networked cyberphysical system. In this paper, we consider a sensor network plagued with offset errors, measuring a rank-1 signal subspace, where each sensor collects measurements under a…

Signal Processing · Electrical Eng. & Systems 2023-12-14 Raj Thilak Rajan