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Algorithmic stability is a central notion in learning theory that quantifies the sensitivity of an algorithm to small changes in the training data. If a learning algorithm satisfies certain stability properties, this leads to many important…

Machine Learning · Statistics 2025-04-01 Yuetian Luo , Rina Foygel Barber

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…

Statistical Mechanics · Physics 2015-03-13 Fabrizio Altarelli , Alfredo Braunstein , Abolfazl Ramezanpour , Riccardo Zecchina

We propose an approach to construction of robust non-Euclidean iterative algorithms for convex composite stochastic optimization based on truncation of stochastic gradients. For such algorithms, we establish sub-Gaussian confidence bounds…

Statistics Theory · Mathematics 2019-07-08 Anatoli Juditsky , Alexander Nazin , Arkadi Nemirovsky , Alexandre Tsybakov

We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…

Machine Learning · Statistics 2022-02-24 Nuri Mert Vural , Lu Yu , Krishnakumar Balasubramanian , Stanislav Volgushev , Murat A. Erdogdu

This paper presents a non-manual design engineering method based on heuristic search algorithm to search for candidate agents in the solution space which formed by artificial intelligence agents modeled on the base of bionics.Compared with…

Artificial Intelligence · Computer Science 2018-07-30 Zengkun Li

Optimization over the set of matrices $X$ that satisfy $X^\top B X = I_p$, referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA),…

Machine Learning · Computer Science 2025-11-11 Simon Vary , Pierre Ablin , Bin Gao , P. -A. Absil

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as…

Machine Learning · Statistics 2022-09-13 Yuxin Chen , Jianqing Fan , Cong Ma , Yuling Yan

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

Machine Learning · Statistics 2020-12-25 Yunbei Xu , Assaf Zeevi

In recommendation systems, one is interested in the ranking of the predicted items as opposed to other losses such as the mean squared error. Although a variety of ways to evaluate rankings exist in the literature, here we focus on the Area…

Machine Learning · Statistics 2015-08-26 Charanpal Dhanjal , Romaric Gaudel , Stephan Clemencon

In this paper we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed…

Optimization and Control · Mathematics 2023-10-05 Zifan Wang , Changxin Liu , Thomas Parisini , Michael M. Zavlanos , Karl H. Johansson

When the target of statistical inference is chosen in a data-driven manner, the guarantees provided by classical theories vanish. We propose a solution to the problem of inference after selection by building on the framework of algorithmic…

Statistics Theory · Mathematics 2022-03-16 Tijana Zrnic , Michael I. Jordan

We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…

Optimization and Control · Mathematics 2025-11-25 Katya Scheinberg , Miaolan Xie

Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…

Optimization and Control · Mathematics 2020-07-22 Albert Berahas , Frank E. Curtis , Daniel P. Robinson , Baoyu Zhou

Robust optimization (RO) is a common approach to tractably obtain safeguarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO, based on learning a…

Optimization and Control · Mathematics 2020-03-03 L. Jeff Hong , Zhiyuan Huang , Henry Lam

As machine learning being used increasingly in making high-stakes decisions, an arising challenge is to avoid unfair AI systems that lead to discriminatory decisions for protected population. A direct approach for obtaining a fair…

Machine Learning · Computer Science 2023-02-24 Yao Yao , Qihang Lin , Tianbao Yang

While statistics and machine learning offers numerous methods for ensuring generalization, these methods often fail in the presence of adaptivity---the common practice in which the choice of analysis depends on previous interactions with…

Machine Learning · Computer Science 2018-06-19 Kobbi Nissim , Adam Smith , Thomas Steinke , Uri Stemmer , Jonathan Ullman

Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…

Machine Learning · Computer Science 2025-08-14 Arpit Agarwal , Rohan Ghuge , Viswanath Nagarajan , Zhengjia Zhuo

When looking for a solution, deterministic methods have the enormous advantage that they do find global optima. Unfortunately, they are very CPU-intensive, and are useless on untractable NP-hard problems that would require thousands of…

Neural and Evolutionary Computing · Computer Science 2011-12-20 Pierre Collet , Jean-Philippe Rennard

Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…

Optimization and Control · Mathematics 2021-12-13 Yafei Wang , Bo Pan , Wei Tu , Peng Liu , Bei Jiang , Chao Gao , Wei Lu , Shangling Jui , Linglong Kong

We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…