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Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration,…

Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…

The curve-based lane representation is a popular approach in many lane detection methods, as it allows for the representation of lanes as a whole object and maximizes the use of holistic information about the lanes. However, the curves…

Recent advancements in 3D Gaussian Splatting (3DGS) have greatly influenced neural fields, as it enables high-fidelity rendering with impressive visual quality. However, 3DGS has difficulty accurately representing surfaces. In contrast,…

In this work, we propose a stochastic gradient descent (SGD) framework to design data-driven policy gradient descent algorithms for the linear quadratic regulator problem. Two alternative schemes are considered to estimate the policy…

Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics,…

There is an increased interest in building data analytics frameworks with advanced algebraic capabilities both in industry and academia. Many of these frameworks, e.g., TensorFlow and BIDMach, implement their compute-intensive primitives in…

Deep learning networks are typically trained by Stochastic Gradient Descent (SGD) methods that iteratively improve the model parameters by estimating a gradient on a very small fraction of the training data. A major roadblock faced when…

3D Gaussian Splatting has emerged as an alternative 3D representation for novel view synthesis, benefiting from its high-quality rendering results and real-time rendering speed. However, the 3D Gaussians learned by 3D-GS have ambiguous…

Visual tracking fundamentally involves regressing the state of the target in each frame of a video. Despite significant progress, existing regression-based trackers still tend to experience failures and inaccuracies. To enhance the…

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…

Level of Detail (LoD) is a fundamental technique in real-time computer graphics for managing the rendering costs of complex scenes while preserving visual fidelity. Traditionally, LoD is implemented using discrete levels (DLoD), where…

The training of machine learning models is typically carried out using some form of gradient descent, often with great success. However, non-asymptotic analyses of first-order optimization algorithms typically employ a gradient smoothness…

We study the proximal gradient descent (PGD) method for $\ell^{0}$ sparse approximation problem as well as its accelerated optimization with randomized algorithms in this paper. We first offer theoretical analysis of PGD showing the bounded…

To increase the interpretability and prediction accuracy of the Machine Learning (ML) models, visualization of ML models is a key part of the ML process. Decision Trees (DTs) are essential in machine learning (ML) because they are used to…

This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function…

We consider the problem of minimizing a convex function over a closed convex set, with Projected Gradient Descent (PGD). We propose a fully parameter-free version of AdaGrad, which is adaptive to the distance between the initialization and…

Stochastic gradient descent (SGD) and projected stochastic gradient descent (PSGD) are scalable algorithms to compute model parameters in unconstrained and constrained optimization problems. In comparison with SGD, PSGD forces its iterative…

The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…