Related papers: Stochastic Adaptive Optimization with Unreliable I…

Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…

Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…

In this paper, we investigate accelerated first-order methods for smooth convex optimization problems under inexact information on the gradient of the objective. The noise in the gradient is considered to be additive with two possibilities:…

We extend traditional complexity analyses of trust-region methods for unconstrained, possibly nonconvex, optimization. Whereas most complexity analyses assume uniform boundedness of the model Hessians, we work with potentially unbounded…

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…

In this paper we focus on the problem of assigning uncertainties to single-point predictions generated by a deterministic model that outputs a continuous variable. This problem applies to any state-of-the-art physics or engineering models…

Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain…

We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the…

With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same…

Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…

We study the robustness of accelerated first-order algorithms to stochastic uncertainties in gradient evaluation. Specifically, for unconstrained, smooth, strongly convex optimization problems, we examine the mean-squared error in the…

This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes…

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…

This paper proposes a framework to study the convergence of stochastic optimization and learning algorithms. The framework is modeled over the different challenges that these algorithms pose, such as (i) the presence of random additive…

Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search…

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…

This paper proposes an Adaptive Learning Model Predictive Control strategy for uncertain constrained linear systems performing iterative tasks. The additive uncertainty is modeled as the sum of a bounded process noise and an unknown…

We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…