Related papers: Supervised Descent Method for Solving Nonlinear Le…
Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…
Surveillance scenarios are prone to several problems since they usually involve low-resolution footage, and there is no control of how far the subjects may be from the camera in the first place. This situation is suitable for the…
Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) a simple convex term, and (iii) a concave and continuous term. First, by extending…
By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…
We consider gradient descent like algorithms for Support Vector Machine (SVM) training when the data is in relational form. The gradient of the SVM objective can not be efficiently computed by known techniques as it suffers from the…
Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…
Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a…
This paper introduces a novel Homogeneous Second-order Descent Ascent (HSDA) algorithm for nonconvex-strongly concave minimax optimization problems. At each iteration, HSDA uniquely computes a search direction by solving a homogenized…
Self-supervised real-world image denoising remains a fundamental challenge, arising from the antagonistic trade-off between decorrelating spatially structured noise and preserving high-frequency details. Existing blind-spot network (BSN)…
Image denoising is a classical problem in low level computer vision. Model-based optimization methods and deep learning approaches have been the two main strategies for solving the problem. Model-based optimization methods are flexible for…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
Minimax problems have recently attracted a lot of research interests. A few efforts have been made to solve decentralized nonconvex strongly-concave (NCSC) minimax-structured optimization; however, all of them focus on smooth problems with…
We study a fundamental class of regression models called the second order linear model (SLM). The SLM extends the linear model to high order functional space and has attracted considerable research interest recently. Yet how to efficiently…
This work analyzes the convergence of a class of smoothing-based gradient descent methods when applied to optimization problems. In particular, Gaussian smoothing is employed to define a nonlocal gradient that reduces high-frequency noise,…
We introduce a machine-learning framework to learn the hyperparameter sequence of first-order methods (e.g., the step sizes in gradient descent) to quickly solve parametric convex optimization problems. Our computational architecture…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…
Due to limited size and imperfect of the optical components in a spectrometer, aberration has inevitably been brought into two-dimensional multi-fiber spectrum image in LAMOST, which leads to obvious spacial variation of the point spread…
Most modern learning problems are highly overparameterized, meaning that there are many more parameters than the number of training data points, and as a result, the training loss may have infinitely many global minima (parameter vectors…
We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can…