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Multivariate function approximation is a fundamental problem in machine learning. Classic multivariate function approximations rely on hand-crafted basis functions (e.g., polynomial basis and Fourier basis), which limits their approximation…

This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…

Structural pruning techniques are essential for deploying multimodal large language models (MLLMs) across various hardware platforms, from edge devices to cloud servers. However, current pruning methods typically determine optimal…

We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…

Robot motion planning has made vast advances over the past decades, but the challenge remains: robot mobile manipulators struggle to plan long-range whole-body motion in common household environments in real time, because of…

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…

This paper investigates the MaxRS problem in spatial databases. Given a set O of weighted points and a rectangular region r of a given size, the goal of the MaxRS problem is to find a location of r such that the sum of the weights of all…

Efficient multi-hop reasoning requires Large Language Models (LLMs) based agents to acquire high-value external knowledge iteratively. Previous work has explored reinforcement learning (RL) to train LLMs to perform search-based document…

Nuclear-norm regularization plays a vital role in many learning tasks, such as low-rank matrix recovery (MR), and low-rank representation (LRR). Solving this problem directly can be computationally expensive due to the unknown rank of…

Within machine learning, the subfield of Neural Architecture Search (NAS) has recently garnered research attention due to its ability to improve upon human-designed models. However, the computational requirements for finding an exact…

Efficient and biologically plausible alternatives to backpropagation in neural network training remain a challenge due to issues such as high computational complexity and additional assumptions about neural networks, which limit scalability…

We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…

Reinforcement learning (RL) has achieved impressive results across domains, yet learning an optimal policy typically requires extensive interaction data, limiting practical deployment. A common remedy is to leverage priors, such as…

The proximal point algorithm (PPA) has been developed to solve the monotone variational inequality problem. It provides a theoretical foundation for some methods, such as the augmented Lagrangian method (ALM) and the alternating direction…

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

In recent years new deep learning approaches to solve combinatorial optimization problems, in particular NP-hard Vehicle Routing Problems (VRP), have been proposed. The most impactful of these methods are sequential neural construction…

Recent technical advances in collecting spatial data have been increasing the demand for methods to analyze large spatial datasets. The statistical analysis for these types of datasets can provide useful knowledge in various fields.…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…

Neural networks offer high-accuracy solutions to a range of problems, but are costly to run in production systems because of computational and memory requirements during a forward pass. Given a trained network, we propose a techique called…