Related papers: Training L1-Regularized Models with Orthant-Wise P…

Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…

$L_0$-smoothness, which has been pivotal to advancing decentralized optimization theory, is often fairly restrictive for modern tasks like deep learning. The recent advent of relaxed $(L_0,L_1)$-smoothness condition enables improved…

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of…

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster…

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…

We study gradient descent (GD) with a constant stepsize for $\ell_2$-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective,…

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

Many applications in data analysis rely on the decomposition of a data matrix into a low-rank and a sparse component. Existing methods that tackle this task use the nuclear norm and L1-cost functions as convex relaxations of the rank…

Online mirror descent (OMD) and dual averaging (DA) -- two fundamental algorithms for online convex optimization -- are known to have very similar (and sometimes identical) performance guarantees when used with a fixed learning rate. Under…

Fine-tuning pretrained models has become a standard approach to adapting pretrained knowledge to improve the accuracy on new sparse, imbalance datasets. However, issues arise when optimization falls into a collapsed state, where the model…

In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of…

Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive…

Orthogonal Gradient Descent (OGD) has emerged as a powerful method for continual learning. However, its Euclidean projections do not leverage the underlying information-geometric structure of the problem, which can lead to suboptimal…

Over the past decade, learning a dictionary from input images for sparse modeling has been one of the topics which receive most research attention in image processing and compressed sensing. Most existing dictionary learning methods…

Low-Rank Adaptation (LoRA) fine-tunes large models by learning low-rank updates on top of frozen weights, dramatically reducing trainable parameters and memory. However, there is still a gap between full training with low-rank projections…

Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…

In this paper, we consider the problem of joint delay-Doppler estimation of moving targets in a passive radar that makes use of orthogonal frequency-division multiplexing (OFDM) communication signals. A compressed sensing algorithm is…

Ordinary differential equations (ODEs) are widely used to characterize the dynamics of complex systems in real applications. In this article, we propose a novel joint estimation approach for generalized sparse additive ODEs where…

In this report, we study decentralized stochastic optimization to minimize a sum of smooth and strongly convex cost functions when the functions are distributed over a directed network of nodes. In contrast to the existing work, we use…

For high dimensional sparse linear regression problems, we propose a sequential convex relaxation algorithm (iSCRA-TL1) by solving inexactly a sequence of truncated $\ell_1$-norm regularized minimization problems, in which the working index…