Related papers: On Robustness in Nonconvex Optimization with Appli…

In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is…

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

Despite tremendous advancements of machine learning models and algorithms in various application domains, they are known to be vulnerable to subtle, natural or intentionally crafted perturbations in future input data, known as adversarial…

We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…

Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…

An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said…

Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…

We study non-rectangular robust Markov decision processes under the average-reward criterion, where the ambiguity set couples transition probabilities across states and the adversary commits to a stationary kernel for the entire horizon. We…

This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…

Recent research shows the susceptibility of machine learning models to adversarial attacks, wherein minor but maliciously chosen perturbations of the input can significantly degrade model performance. In this paper, we theoretically analyse…

In this paper, we leverage an information-theoretic upper bound on the maximum admissible level of noise (MALN) in convex Lipschitz-continuous zeroth-order optimisation to establish corresponding upper bounds for classes of strongly convex…

This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…

Many problems in high-dimensional statistics and optimization involve minimization over nonconvex constraints-for instance, a rank constraint for a matrix estimation problem-but little is known about the theoretical properties of such…

In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…

This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…

Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…

Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz…

We revisit a classical assumption for analyzing stochastic gradient algorithms where the squared norm of the stochastic subgradient (or the variance for smooth problems) is allowed to grow as fast as the squared norm of the optimization…