Duc‐Toan Nguyen

Duc Toan Nguyen, Eric C. Chi

Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.\@ (2019) introduced a minimum-volume NMF for the identifiable recovery of rank-deficient matrices in the presence of noise. The performance of their formulation, however, requires the selection of a tuning parameter whose optimal value depends on the unknown noise level. In this work, we propose an alternative formulation of minimum-volume NMF inspired by the square-root lasso and its tuning-free properties. Our formulation also requires the selection of a tuning parameter, but its optimal value does not depend on the noise level. To fit our NMF model, we propose a majorization-minimization (MM) algorithm that comes with global convergence guarantees. We show empirically that the optimal choice of our tuning parameter is insensitive to the noise level in the data.

Duc Toan Nguyen, Trang H. Tran, Lam M. Nguyen

In this paper, we propose Adjusted Shuffling SARAH, a novel algorithm that integrates shuffling techniques with the well-known variance-reduced algorithm SARAH while dynamically adjusting the stochastic gradient weights in each update to enhance exploration. Our method achieves the best-known gradient complexity for shuffling variance reduction methods in a strongly convex setting. This result applies to any shuffling technique, which narrows the gap in the complexity analysis of variance reduction methods between uniform sampling and shuffling data. Furthermore, we introduce Inexact Adjusted Reshuffling SARAH, an inexact variant of Adjusted Shuffling SARAH that eliminates the need for full-batch gradient computations. This algorithm retains the same linear convergence rate as Adjusted Shuffling SARAH while showing an advantage in total complexity when the sample size is very large.

Marcello Balduccini, William C. Regli, Duc N. Nguyen

Traditional AI reasoning techniques have been used successfully in many domains, including logistics, scheduling and game playing. This paper is part of a project aimed at investigating how such techniques can be extended to coordinate teams of unmanned aerial vehicles (UAVs) in dynamic environments. Specifically challenging are real-world environments where UAVs and other network-enabled devices must communicate to coordinate -- and communication actions are neither reliable nor free. Such network-centric environments are common in military, public safety and commercial applications, yet most research (even multi-agent planning) usually takes communications among distributed agents as a given. We address this challenge by developing an agent architecture and reasoning algorithms based on Answer Set Programming (ASP). Although ASP has been used successfully in a number of applications, to the best of our knowledge this is the first practical application of a complete ASP-based agent architecture. It is also the first practical application of ASP involving a combination of centralized reasoning, decentralized reasoning, execution monitoring, and reasoning about network communications.

Marcello Balduccini, William C. Regli, Duc N. Nguyen

Traditional AI reasoning techniques have been used successfully in many domains, including logistics, scheduling and game playing. This paper is part of a project aimed at investigating how such techniques can be extended to coordinate teams of unmanned aerial vehicles (UAVs) in dynamic environments. Specifically challenging are real-world environments where UAVs and other network-enabled devices must communicate to coordinate---and communication actions are neither reliable nor free. Such network-centric environments are common in military, public safety and commercial applications, yet most research (even multi-agent planning) usually takes communications among distributed agents as a given. We address this challenge by developing an agent architecture and reasoning algorithms based on Answer Set Programming (ASP). ASP has been chosen for this task because it enables high flexibility of representation, both of knowledge and of reasoning tasks. Although ASP has been used successfully in a number of applications, and ASP-based architectures have been studied for about a decade, to the best of our knowledge this is the first practical application of a complete ASP-based agent architecture. It is also the first practical application of ASP involving a combination of centralized reasoning, decentralized reasoning, execution monitoring, and reasoning about network communications. This work has been empirically validated using a distributed network-centric software evaluation testbed and the results provide guidance to designers in how to understand and control intelligent systems that operate in these environments.