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On landscape of lagrangian function and stochastic search for constrained nonconvex optimization

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arXiv 2018年

作者： Chen, Zhehui Li, Xingguo Yang, Lin F. Haupt, Jarvis Zhao, Tuo School of Industrial and Systems Engineering Georgia Institute of Technology Department of Electrical and Computer Engineering University of Minnesota Operation Research and Financial Engineering Department Princeton University

We study constrained nonconvex optimization problems in machine learning, signal processing, and stochastic control. It is well-known that these problems can be rewritten to a minimax problem in a Lagrangian form. However, due to the lack of convexity, their landscape is not well understood and how to find the stable equilibria of the Lagrangian function is still unknown. To bridge the gap, we study the landscape of the Lagrangian function. Further, we define a special class of Lagrangian functions. They enjoy two properties: *** are either stable or unstable (Formal definition in Section 2);*** equilibria correspond to the global optima of the original problem. We show that a generalized eigenvalue (GEV) problem, including canonical correlation analysis and other problems, belongs to the class. Specifically, we characterize its stable and unstable equilibria by leveraging an invariant group and symmetric property (more details in Section 3). Motivated by these neat geometric structures, we propose a simple, efficient, and stochastic primal-dual algorithm solving the online GEV problem. Theoretically, we provide sufficient conditions, based on whichwe establish an asymptotic convergence rate and obtain the first sample complexity result for the online GEV problem by diffusion approximations, which are widely used in applied probability and stochastic control. Numerical results are provided to support our theory. Copyright © 2018, The Authors. All rights reserved.

关键词： Lagrange multipliers

Single photonic perceptron based on a soliton crystal Kerr microcomb for high-speed, scalable, optical neural networks

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arXiv 2020年

作者： Xu, Xingyuan Tan, Mengxi Corcoran, Bill Wu, Jiayang Nguyen, Thach G. Boes, Andreas Chu, Sai T. Little, Brent E. Morandotti, Roberto Mitchell, Arnan Hicks, Damien G. Moss, David J. Optical Sciences Centre for Micro-Photonics Swinburne University of Technology HawthornVIC3122 Australia Department of Electrical and Computer Systems Engineering Monash University ClaytonVIC3800 Australia School of Engineering RMIT University MelbourneVIC3001 Australia Department of Physics and Material Science City University of Hong Kong Tat Chee Avenue Hong Kong Hong Kong Xi’an Institute of Optics and Precision Mechanics Precision Mechanics of CAS Xi’an China INRS-Énergie Matériaux et Télécommunications 1650 Boulevard Lionel-Boulet VarennesQCJ3X 1S2 Canada Bioinformatics Division Walter & Eliza Hall Institute of Medical Research ParkvilleVIC3052 Australia

Optical artificial neural networks (ONNs) — analog computing hardware tailored for machine learning [1, 2] — have significant potential for ultra-high computing speed and energy efficiency [3]. We propose a new approach to architectures for ONNs based on integrated Kerr micro-comb sources [4] that is programmable, highly scalable and capable of reaching ultra-high speeds. We experimentally demonstrate the building block of the ONN — a single neuron perceptron — by mapping synapses onto 49 wavelengths of a micro-comb to achieve a high single-unit throughput of 11.9 Giga-FLOPS at 8 bits per FLOP, corresponding to 95.2 Gbps. We test the perceptron on simple standard benchmark datasets — handwritten-digit recognition and cancer-cell detection — achieving over 90% and 85% accuracy, respectively. This performance is a direct result of the record small wavelength spacing (49GHz) for a coherent integrated microcomb source, which results in an unprecedented number of wavelengths for neuromorphic optics. Finally, we propose an approach to scaling the perceptron to a deep learning network using the same single micro-comb device and standard off-the-shelf telecommunications technology, for high-throughput operation involving full matrix multiplication for applications such as real-time massive data processing for unmanned vehicle and aircraft tracking. Copyright © 2020, The Authors. All rights reserved.

关键词： Energy efficiency

Stochastic Search Methods for Mobile Manipulators ⁎

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Procedia Manufacturing 2018年 17卷 976-984页

作者： Amoako-Frimpong Samuel Yaw Matthew Messina Henry Medeiros Jeremy Marvel Roger Bostelman Department of Electrical and Computer Engineering Marquette University Milwaukee WI 53233 USA Intelligent Systems Division National Institute of Standards and Technology Gaithersburg MD 20899

Mobile manipulators are a potential solution to the increasing need for additional flexibility and mobility in industrial applications. However, they tend to lack the accuracy and precision achieved by fixed manipulators, especially in scenarios where both the manipulator and the autonomous vehicle move simultaneously. This paper analyzes the problem of dynamically evaluating the positioning error of mobile manipulators. In particular, it investigates the use of Bayesian methods to predict the position of the end-effector in the presence of uncertainty propagated from the mobile platform. The precision of the mobile manipulator is evaluated through its ability to intercept retroreflective markers using a photoelectric sensor attached to the end-effector. Compared to a deterministic search approach, we observed improved robustness with comparable search times, thereby enabling effective calibration of the mobile manipulator.

关键词： mobile manipulators calibration search algorithms

Dealing with state estimation in fractional-order systems under artifacts

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arXiv 2018年

作者： Chatterjee, Sarthak Pequito, Sérgio Department of Electrical Computer and Systems Engineering Rensselaer Polytechnic Institute TroyNY12180 United States Department of Industrial and Systems Engineering Rensselaer Polytechnic Institute TroyNY12180 United States

Fractional-order dynamical systems are used to describe processes that exhibit long-term memory with power-law dependence. Notable examples include complex neurophysiological signals such as electroencephalogram (EEG) and blood-oxygen-level dependent (BOLD) signals. When analyzing different neurophysiological signals and other signals with different origin (for example, biological systems), we often find the presence of artifacts, that is, recorded activity that is due to external causes and does not have its origins in the system of interest. In this paper, we consider the problem of estimating the states of a discrete-time fractional-order dynamical system when there are artifacts present in some of the sensor measurements. Specifically, we provide necessary and sufficient conditions that ensure we can retrieve the system states even in the presence of artifacts. We provide a state estimation algorithm that can estimate the states of the system in the presence of artifacts. Finally, we present illustrative examples of our main results using real EEG data. Copyright © 2018, The Authors. All rights reserved.

关键词： Neurophysiology

A comparison of nonsmooth, nonconvex, constrained optimization solvers for the design of time-delay compensators

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arXiv 2018年

作者： Kungurtsev, Vyacheslav Mitchell, Tim Vyhlídal, Tomáš Department of Computer Science Faculty of Electrical Engineering Czech Technical University in Prague Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Department of Instrumentation and Control Engineering Faculty of Mechanical Engineering Czech Institute of Informatics Robotics and Cybernetics Czech Technical University in Prague

We present a detailed set of performance comparisons of two state-of-the-art solvers for the application of designing time-delay compensators, an important problem in the field of robust control. Formulating such robust control mechanics as constrained optimization problems often involves objective and constraint functions that are both nonconvex and nonsmooth, both of which present significant challenges to many solvers and their end-users hoping to obtain good solutions to these problems. In our particular engineering task, the main difficulty in the optimization arises in a nonsmooth and nonconvex stability constraint, which states that the infinite spectrum of zeros of the so-called shaper should remain in the open left half-plane. To perform our evaluation, we make use β-relative minimization profiles, recently introduced visualization tools that are particularly suited for benchmarking solvers on nonsmooth, nonconvex, constrained optimization problems. Furthermore, we also introduce new visualization tools, called Global-Local Profiles, which for a given problem and a fixed computational budget, assess the tradeoffs of distributing the budget over few or many starting points, with the former getting more budget per point and latter less. Copyright © 2018, The Authors. All rights reserved.

关键词： Robust control

Secrecy Outage Analysis Over Fluctuating Two-Ray Fading Channels

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arXiv 2019年

作者： Zhao, Hui Yang, Liang Pan, Gaofeng Alouini, M.-S. Thuwal23955-6900 Saudi Arabia Communication Systems Department EURECOM Sophia Antipolis06410 France College of Computer Science and Electronic Engineering Hunan University Changsha410082 China School of Information and Electronics Beijing Institute of Technology Beijing100081 China Computer Electrical and Mathematical Science and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this letter, we analyze the secrecy outage probability (SOP) over fluctuating two-ray fading channels but with a different definition from the one adopted in [5]. Following the new defined SOP, we derive an analytical closed-form expression for our proposed SOP, as well as an asymptotic formula valid in the high signal-to-noise ratio region of the source to destination link. In the numerical results section, we perform some Monte-Carlo simulations to validate the accuracy of our derived expressions, and also present the probability gap between our proposed SOP and the SOP in [5]. Copyright © 2019, The Authors. All rights reserved.

关键词： Fading channels

Event-Triggered Particle Filtering Via Diffusion Strategies for Distributed Estimation in Autonomous systems

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Event-Triggered Particle Filtering Via Diffusion Strategies ...

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Somayeh Davar Arash Mohammadi Konstantinos N. Plataniotis Concordia Institute for Information Systems Engineering Concordia University Montreal Canada Department of Electrical and Computer Engineering University of Toronto Toronto ON Canada

ISBN: (纸本)9781538646595

The paper is motivated by recent advancements and developments in large, distributed, autonomous, and self-aware systems such as autonomous vehicles and vehicle-to-everything (V2X) technologies, where bandwidth, security, privacy, and/or power considerations limit the number of information transfers between neighbouring agents. In this regard, we propose an event-triggered distributed state estimation via diffusion strategies (ET/DPF), which is a systematic and intuitively pleasing distributed state estimation algorithm that jointly incorporates point and set-valued measurements within the particle filtering framework. In the absence of a measurement form a neighbouring node (i.e., having a set-valued measurement), each local agent/node evaluates the probability that the unknown measurement belongs to the event-triggering set based on its particles which is then used to update the corresponding particle weights. In our Monte Carlo simulations, the proposed ET/DPF outperforms its counterparts in environments with limited bandwidth or/and intermittent connectivity.

关键词： Autonomous and self-aware systems Autonomous Vehicles Event-triggered estimation Particle filtering

EndoSensorFusion: Particle Filtering-Based Multi-sensory Data Fusion with Switching State-Space Model for Endoscopic Capsule Robots

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EndoSensorFusion: Particle Filtering-Based Multi-sensory Dat...

IEEE International Conference on robotics and Automation

作者： Mehmet Turan Yasin Almalioglu Hunter Gilbert Helder Araujo Taylan Cemgil Metin Sitti Physical Intelligence Department Max Planck Institute for Intelligent Systems Germany Computer Engineering Department Bogazici University Turkey Mechanical Engineering Department Louisiana State University Baton Rouge LA USA Institute for Systems and Robotics University of Coimbra Portugal

A reliable, real time, multi-sensor fusion functionality is crucial for localization of actively controlled capsule endoscopy robots, which are an emerging, minimally invasive diagnostic and therapeutic technology for the gastrointestinal (GI) tract. In this study, we propose a novel multi-sensor fusion approach based on a particle filter that incorporates an on-line estimation of sensor reliability and a non-linear kinematic model learned by a recurrent neural network. Our method sequentially estimates the true robot pose from noisy pose observations delivered by multiple sensors. We experimentally test the method using 5 degree-of-freedom (5-DoF) absolute pose measurement by a magnetic localization system and a 6-DoF relative pose measurement by visual odometry. In addition, the proposed method is capable of detecting and handling sensor failures by ignoring corrupted data, providing the robustness expected of a medical device. Detailed analyses and evaluations are presented using ex vivo experiments on a porcine stomach model, proving that our system achieves high translational and rotational accuracies for different types of endoscopic capsule robot trajectories.

关键词： Robot sensing systems Switches Kalman filters Proposals Endoscopes Magnetic resonance imaging

RF and microwave fractional differentiation with transversal filters using a soliton crystal microcomb multiwavelength source

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TechRxiv

TechRxiv 2020年

作者： Tan, Mengxi Xu, Xingyuan Corcoran, Bill Wu, Jiayang Boes, Andreas Nguyen, Thach G. Chu, Sai T. Little, Brent E. Morandotti, Roberto Mitchell, Arnan Moss, David J. Centre for Micro-Photonics Swinburne University of Technology HawthornVIC3122 Australia Department of Electrical and Computer Systems Engineering Monash University ClaytonVIC3800 Australia School of Engineering RMIT University MelbourneVIC3001 Australia Department of Physics City University of Hong Kong Tat Chee Avenue Hong Kong Hong Kong State Key Laboratory of Transient Optics and Photonics Xi'an Institute of Optics and Precision Mechanics Chinese Academy of Science Xi'An China INSR-Énergie Matériaux et Télécommunications 1650 Boulevard Lionel-Boulet VarennesQCJ3X 1S2 Canada Institute of Fundamental and Frontier Sciences University of Electronic Science and Technology of China Chengdu610054 China

We report a photonic radio frequency (RF) fractional differentiator based on an integrated Kerr micro-comb source. The micro-comb source has a free spectral range (FSR) of 49 GHz, generating a large number of comb lines that serve as a high-performance multi-wavelength source for the differentiator. By programming and shaping the comb lines according to calculated tap weights, arbitrary fractional orders ranging from 0.15 to 0.90 are achieved over a broad RF operation bandwidth of 15.49 GHz. We experimentally characterize the frequency-domain RF amplitude and phase response as well as the temporal response with a Gaussian pulse input. The experimental results show good agreement with theory, confirming the effectiveness of our approach towards high-performance fractional differentiators featuring broad processing bandwidth, high reconfigurability, and potentially reduced sized and cost. © 2020, CC BY.

关键词： Frequency domain analysis