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Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…
Pruning has recently been widely adopted to reduce the parameter scale and improve the inference efficiency of Large Language Models (LLMs). Mainstream pruning techniques often rely on uniform layerwise pruning strategies, which can lead to…
The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed. The new method, the…
Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…
Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal…
This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…
3D spatial understanding is essential in real-world applications such as robotics, autonomous vehicles, virtual reality, and medical imaging. Recently, Large Language Models (LLMs), having demonstrated remarkable success across various…
The high cost and data scarcity in scientific exploration have motivated the use of large language models (LLMs) as knowledge-driven components in Bayesian optimization (BO). However, existing approaches typically embed LLMs directly into…
In today's modern era of Big data, computationally efficient and scalable methods are needed to support timely insights and informed decision making. One such method is sub-sampling, where a subset of the Big data is analysed and used as…
Ensuring alignment with human preferences is a crucial characteristic of large language models (LLMs). Presently, the primary alignment methods, RLHF and DPO, require extensive human annotation, which is expensive despite their efficacy.…
Global localization and kidnapping are two challenging problems in robot localization. The popular method, Monte Carlo Localization (MCL) addresses the problem by iteratively updating a set of particles with a "sampling-weighting" loop.…
Decision making algorithms are used in a multitude of different applications. Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
The network Lasso (nLasso) has been proposed recently as an efficient learning algorithm for massive networked data sets (big data over networks). It extends the well-known least absolute shrinkage and selection operator (Lasso) from…
Supervised machine learning often operates on the data-driven paradigm, wherein internal model parameters are autonomously optimized to converge predicted outputs with the ground truth, devoid of explicitly programming rules or a priori…
Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…
In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…