Related papers: A black box method for solving the complex exponen…
In this letter, we consider the problem of recovering an unknown sparse signal from noisy linear measurements, using an enhanced version of the popular Elastic-Net (EN) method. We modify the EN by adding a box-constraint, and we call it the…
Importance sampling is widely used in machine learning and statistics, but its power is limited by the restriction of using simple proposals for which the importance weights can be tractably calculated. We address this problem by studying…
Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…
Matrix ellipsoids provide a standard framework for representing bounded uncertainties in data-driven control. Since noise models for sequential observations are naturally represented as the Minkowski sum of multiple matrix ellipsoids,…
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…
We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing…
We describe two quantum algorithms to approximate the mean value of a black-box function. The first algorithm is novel and asymptotically optimal while the second is a variation on an earlier algorithm due to Aharonov. Both algorithms have…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…
We study the problem of Trajectory Optimization (TO) for a general class of stiff and constrained dynamic systems. We establish a set of mild assumptions, under which we show that TO converges numerically stably to a locally optimal and…
High-probability analysis of stochastic first-order optimization methods under mild assumptions on the noise has been gaining a lot of attention in recent years. Typically, gradient clipping is one of the key algorithmic ingredients to…
An adaptation of Response Surface Methodology (RSM) when the covariate is of high or infinite dimensional is proposed, providing a tool for black-box optimization in this context. We combine dimension reduction techniques with classical…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
We consider the distributed version of the Multiple Knapsack Problem (MKP), where $m$ items are to be distributed amongst $n$ processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff…
In this paper, we consider a semi-linear stochastic strongly damped wave equation driven by additive Gaussian noise. Following a semigroup framework, we establish existence, uniqueness and space-time regularity of a mild solution to such…
In this paper, we consider a new problem of portfolio optimization using stochastic information. In a setting where there is some uncertainty, we ask how to best select $k$ potential solutions, with the goal of optimizing the value of the…
This paper presents a Newton-based stochastic extremum-seeking control method for real-time optimization in multi-input systems with distinct input delays. It combines predictor-based feedback and Hessian inverse estimation via stochastic…
The numerical evaluation of statistics plays a crucial role in statistical physics and its applied fields. It is possible to evaluate the statistics for a stochastic differential equation with Gaussian white noise via the corresponding…
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…