Related papers: Beyond Worst-Case Analysis in Private Singular Vec…
We study differentially private (DP) stochastic optimization (SO) with loss functions whose worst-case Lipschitz parameter over all data may be extremely large or infinite. To date, the vast majority of work on DP SO assumes that the loss…
We consider the classical gradient descent algorithm with constant stepsizes, where some error is introduced in the computation of each gradient. More specifically, we assume some relative bound on the inexactness, in the sense that the…
In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discrepancy between forward error (the…
The objective of the matrix selection problem is to select a submatrix $A_{S}\in \mathbb{R}^{n\times k}$ from $A\in \mathbb{R}^{n\times m}$ such that its minimum singular value is maximized. In this paper, we employ the interlacing…
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…
We propose a unifying framework for the automated computer-assisted worst-case analysis of cyclic block coordinate algorithms in the unconstrained smooth convex optimization setup. We compute exact worst-case bounds for the cyclic…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
We show new lower bounds on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer large sets of counting queries. A counting query on a database $D \in (\{0,1\}^d)^n$ has the form "What…
Computing accurate low rank approximations of large matrices is a fundamental data mining task. In many applications however the matrix contains sensitive information about individuals. In such case we would like to release a low rank…
We study the relationship between two desiderata of algorithms in statistical inference and machine learning: differential privacy and robustness to adversarial data corruptions. Their conceptual similarity was first observed by Dwork and…
A wide variety of fundamental data analyses in machine learning, such as linear and logistic regression, require minimizing a convex function defined by the data. Since the data may contain sensitive information about individuals, and these…
Fingerprinting codes are a crucial tool for proving lower bounds in differential privacy. They have been used to prove tight lower bounds for several fundamental questions, especially in the ``low accuracy'' regime. Unlike…
We provide computationally efficient, differentially private algorithms for the classical regression settings of Least Squares Fitting, Binary Regression and Linear Regression with unbounded covariates. Prior to our work, privacy…
In this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions. We propose a new method, called DP-Thresholding, to…
We initiate a systematic study of worst-group risk minimization under $(\epsilon, \delta)$-differential privacy (DP). The goal is to privately find a model that approximately minimizes the maximal risk across $p$ sub-populations (groups)…
The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…
We derive a new lower bound on the success probability of the Pretty Good Measurement (PGM) for worst-case quantum state discrimination among $m$ pure states. Our bound is strictly tighter than the previously known Gram-matrix-based bound…
Bilevel optimization, in which one optimization problem is nested inside another, underlies many machine learning applications with a hierarchical structure -- such as meta-learning and hyperparameter optimization. Such applications often…
Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data…
Differential privacy is a strong mathematical notion of privacy. Still, a prominent challenge when using differential privacy in real data collection is understanding and counteracting the accuracy loss that differential privacy imposes. As…