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Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
This article explores the integration of deep learning models into combinatorial optimization pipelines, specifically targeting NP-hard problems. Traditional exact algorithms for such problems often rely on heuristic criteria to guide the…
We study the convergence rate of first-order methods for rectangular matrix factorization, which is a canonical nonconvex optimization problem. Specifically, given a rank-$r$ matrix $\mathbf{A}\in\mathbb{R}^{m\times n}$, we prove that…
We consider the problem of the optimal trading strategy in the presence of a price predictor, linear trading costs and a quadratic risk control. The solution is known to be a band system, a policy that induces a no-trading zone in the…
We reformulate a class of non-linear stochastic optimal control problems introduced by Todorov (2007) as a Kullback-Leibler (KL) minimization problem. As a result, the optimal control computation reduces to an inference computation and…
This paper proposes a novel mission planning algorithm for autonomous robots that selects an optimal waypoint sequence from a predefined set to maximize total reward while satisfying obstacle avoidance, state, input, derivative, mission…
In this work, we derive the maximum a posteriori (MAP) symbol detector for a multiple-input multiple-output system in the presence of Wiener phase noise due to noisy local oscillators. As in single-antenna systems, the computation of the…
We study harmonic map regression, a nonparametric estimator for manifold-valued responses, that penalizes the empirical Fr\'echet risk by the Dirichlet energy. By connecting penalized regression to the theory of harmonic maps, the estimator…
Unified graph representation learning aims to generate node embeddings, which can be applied to multiple downstream applications of graph analytics. However, existing studies based on graph neural networks and language models either suffer…
Autonomous vehicles (AVs) must share the driving space with other drivers and often employ conservative motion planning strategies to ensure safety. These conservative strategies can negatively impact AV's performance and significantly slow…
This paper introduces a novel neural network-based approach to solving the Monge-Amp\`ere equation with the transport boundary condition, specifically targeted towards optical design applications. We leverage multilayer perceptron networks…
Gradient-based local optimization has been shown to improve results of genetic programming (GP) for symbolic regression. Several state-of-the-art GP implementations use iterative nonlinear least squares (NLS) algorithms such as the…
We have investigated the fluctuations and the higher order susceptibilities of quark number, isospin number, electric charge and strangeness at vanishing chemical potential for 2+1 flavor Polyakov loop extended Nambu--Jona-Lasinio model.…
The problem of finding roots or solutions of a nonlinear partial differential equation may be formulated as the problem of minimizing a sum of squared residuals. One then defines an evolution equation so that in the asymptotic limit a…
The interdiction problem arises in a variety of areas including military logistics, infectious disease control, and counter-terrorism. In the typical formulation of network interdiction, the task of the interdictor is to find a set of edges…
Traffic sign detection is a critical task in the operation of Autonomous Vehicles (AV), as it ensures the safety of all road users. Current DNN-based sign classification systems rely on pixel-level features to detect traffic signs and can…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We explore the behavior of the iterative procedure to obtain the solution to the gap equation of the Nambu-Jona-Lasinio (NLJ) model for arbitrarily large values of the coupling constant and in the presence of a magnetic field and a thermal…
Over the years, reinforcement learning has emerged as a popular approach to develop signal control and vehicle platooning strategies either independently or in a hierarchical way. However, jointly controlling both in real-time to alleviate…
Discrete Optimal Transport problems give rise to very large linear programs (LP) with a particular structure of the constraint matrix. In this paper we present a hybrid algorithm that mixes an interior point method (IPM) and column…