Multivariate Gaussian Network Structure Learning

We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those at the remaining ones under a group penalty. We show that the proposed estimator can be computed by a fast convex optimization algorithm. We show that as the sample size increases, the estimated regression coefficients and the correct graphical structure are correctly estimated with probability tending to one. By extensive simulations, we show the superiority of the proposed method over comparable procedures. We apply the technique on two real datasets. The first one is to identify gene and protein networks showing up in cancer cell lines, and the second one is to reveal the connections among different industries in the US.Comment: 30 pages, 17 figures, 3 table

Inverse optimality of pure proportional navigation guidance for stationary targets

The main contribution of this study is the optimality analysis of the PPNG performed in full generality. The new theoretical findings can explain the result of the former analysis in which the PPNG is derived as the minimum effort solution [5] and also describe a comprehensive design framework including the observability-enhanced guidance laws developed for the dual homing guidance problem. Furthermore, this study provides several examples illustrating how the PPNG with various navigation gain functions can be understood as optimal control solutions

Look-angle-constrained control of arrival time with exact knowledge of time-to-go

The capability to control the time of arrival at a goal position as desired endows a single vehicle or a coalition of many of them with the strategic advantage to perform time-critical missions. Arrival time coordination can be used as an element to solve multi-agent, multidepot routing and task planning problems in cooperative unmanned aerial robots. The tactic known as Salvo, which either designates or synchronizes the impact times across multiple missiles to enhance their collective survivability as well as attack effectiveness, strongly depends on control of arrival time. In principle, control of arrival time is essentially adjustment of the arc length of the vehicle’s flight path through manipulation of the curvature, provided that most vehicles flying in the atmosphere often prefer not to change their speeds excessively. On the other hand, the capability to take measurements of the target with onboard sensors provides a higher degree of autonomy to the vehicle and hence allows a more intelligent behavior. Modern autonomous vehicles acquire information about the designated destination or the surrounding environment with imaging sensors, in particular. An onboard sensor that collects emission or reflection from the target is usually not likely to be omni-directional yet possesses only a finite field-of-regard. The requirement to ensure continuous acquisition of target-originated signals necessitates a measure to keep the information source inside the sensor’s field of view that spans over a solid angle of limited range. That is, a box constraint is imposed on the look angle

FedFwd: Federated Learning without Backpropagation

In federated learning (FL), clients with limited resources can disrupt the training efficiency. A potential solution to this problem is to leverage a new learning procedure that does not rely on backpropagation (BP). We present a novel approach to FL called FedFwd that employs a recent BP-free method by Hinton (2022), namely the Forward Forward algorithm, in the local training process. FedFwd can reduce a significant amount of computations for updating parameters by performing layer-wise local updates, and therefore, there is no need to store all intermediate activation values during training. We conduct various experiments to evaluate FedFwd on standard datasets including MNIST and CIFAR-10, and show that it works competitively to other BP-dependent FL methods.Comment: ICML 2023 Workshop (Federated Learning and Analytics in Practice: Algorithms, Systems, Applications, and Opportunities

Approximation of achievable robustness limit based on sensitivity inversion

Introduction: The sensitivity function, defined as the closed-loop transfer function from the exogenous input to the tracking error, is central to the multi-objective design and analysis of a feedback control system. Its frequency response determines many performance characteristics of the closed-loop system, such as disturbance attenuation, reference tracking, and robustness against uncertainties and noise. It is well known that the nominal sensitivity peak, i.e., the H∞ -norm of the sensitivity function, is a direct measure of stability robustness, because the sensitivity magnitude quantifies both the attenuation of the effect of external disturbances on the closed-loop output and the variations of the closed-loop system with respect to the plant perturbations

Understanding the Effects of Data Parallelism and Sparsity on Neural Network Training

We study two factors in neural network training: data parallelism and sparsity; here, data parallelism means processing training data in parallel using distributed systems (or equivalently increasing batch size), so that training can be accelerated; for sparsity, we refer to pruning parameters in a neural network model, so as to reduce computational and memory cost. Despite their promising benefits, however, understanding of their effects on neural network training remains elusive. In this work, we first measure these effects rigorously by conducting extensive experiments while tuning all metaparameters involved in the optimization. As a result, we find across various workloads of data set, network model, and optimization algorithm that there exists a general scaling trend between batch size and number of training steps to convergence for the effect of data parallelism, and further, difficulty of training under sparsity. Then, we develop a theoretical analysis based on the convergence properties of stochastic gradient methods and smoothness of the optimization landscape, which illustrates the observed phenomena precisely and generally, establishing a better account of the effects of data parallelism and sparsity on neural network training.Comment: ICLR 202

Analysis of guidance laws with non-monotonic line-of-sight rate convergence

This study presents analyses of guidance laws that involve non-monotonic convergence in heading error from a new perspective based on an advanced stability concept. Pure proportional navigation with range-varying navigation gain is considered, and the gain condition to guarantee asymptotic convergence to the collision course is investigated while allowing the heading error to exhibit patterns that involve intermediate diversion. The extended stability criterion considered in this study allows local increase of the function in some finite intervals, which is less conservative than the standard stability theorem. The existing guidance laws involving intentional modulation of the heading error as well as the design of the navigation gain are discussed with respect to the new stability criterion

Analytic approach to impact time guidance with look angle constraint using exact time-to-go solution

This paper proposes an analytic approach for impact time control guidance laws against stationary targets using biased proportional navigation. The proposed guidance scheme realizes the impact time control in two different ways: the first approach directly uses the exact time-to-go error to satisfy both the impact time control and the field-of-view constraint, while the second approach adopts a look angle tracking law to indirectly control the impact time, with the reference profile of the look angle generated using the exact time-to-go solution. The stability properties of the proposed guidance laws are discussed, and numerical simulations are carried out to evaluate their performance in terms of accuracy and efficiency