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We present a new efficient hybrid parameter estimation method based on the idea, that if nonlinear dynamic models are stated in terms of a system of equations that is linear in terms of the parameters, then regularized ordinary least…
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…
Factor Analysis is a widely used modeling technique for stationary time series which achieves dimensionality reduction by revealing a hidden low-rank plus sparse structure of the covariance matrix. Such an idea of parsimonious modeling has…
We develop a new approach to robust adaptive beamforming in the presence of signal steering vector errors. Since the signal steering vector is known imprecisely, its presumed (prior) value is used to find a more accurate estimate of the…
We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
In this paper we focus on the development of new methods suitable for efficient and reliable coarse-graining of {\it non-equilibrium} molecular systems. In this context, we propose error estimation and controlled-fidelity model reduction…
This letter proposes a new method for joint state and parameter estimation in uncertain dynamical systems. We exploit the partial errors-in-variables (PEIV) principle and formulate a regression problem in the sense of weighted total least…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
Many modern statistical estimation problems are defined by three major components: a statistical model that postulates the dependence of an output variable on the input features; a loss function measuring the error between the observed…
An inexact accelerated stochastic Alternating Direction Method of Multipliers (AS-ADMM) scheme is developed for solving structured separable convex optimization problems with linear constraints. The objective function is the sum of a…
Unrolled computation graphs arise in many scenarios, including training RNNs, tuning hyperparameters through unrolled optimization, and training learned optimizers. Current approaches to optimizing parameters in such computation graphs…
The paper presents a robust parameter learning methodology for identification of nonlinear dynamical system from data while satisfying safety and stability constraints in the context of learning from demonstration (LfD) methods. Extreme…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…
This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…
In this paper, we consider the problem of empirical risk minimization (ERM) of smooth, strongly convex loss functions using iterative gradient-based methods. A major goal of this literature has been to compare different algorithms, such as…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…