1,720,970 research outputs found
Centralized and distributed online learning for sparse time-varying optimization
Full text linkThe development of online algorithms to track time-varying systems has drawn a lot of attention in the last years, in particular in the framework of online convex optimization. Meanwhile, sparse time-varying optimization has emerged as a powerful tool to deal with widespread applications, ranging from dynamic compressed sensing to parsimonious system identification. In most of the literature on sparse time-varying problems, some prior information on the system's evolution is assumed to be available. In contrast, in this paper, we propose an online learning approach, which does not employ a given model and is suitable for adversarial frameworks. Specifically, we develop centralized and distributed algorithms, and we theoretically analyze them in terms of dynamic regret, in an online learning perspective. Further, we propose numerical experiments that illustrate their practical effectiveness
Fast sparse optimization via adaptive shrinkage
Full text linkThe need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm is a valuable method to solve Lasso, which is particularly appreciated for its ease of implementation. Nevertheless, it converges slowly. In this paper, we develop a proximal method, based on logarithmic regularization, which turns out to be an iterative shrinkage-thresholding algorithm with adaptive shrinkage hyperparameter. This adaptivity substantially enhances the trajectory of the algorithm, in a way that yields faster convergence, while keeping the simplicity of the original method. Our contribution is twofold: on the one hand, we derive and analyze the proposed algorithm; on the other hand, we validate its fast convergence via numerical experiments and we discuss the performance with respect to state-of-the-art algorithms
A non-convex adaptive regularization approach to binary optimization
Full text linkBinary optimization is a long-time problem ubiquitous in many engineering applications, e.g., automatic control, cyber-physical systems and machine learning. From a mathematical viewpoint, binary optimization is an NP-hard problem, to solve which one can find some suboptimal strategies in the literature. Among the most popular approaches, semidefinite relaxation has attracted much attention in the last years. In contrast, this work proposes and analyzes a non-convex regularization approach, through which we obtain a relaxed problem whose global minimum corresponds to the true binary solution of the original problem. Moreover, because the problem is non-convex, we propose an adaptive regularization that promotes the descent towards the global minimum. We provide both theoretical results that characterize the proposed model and numerical experiments that prove its effectiveness with respect to state-of-the-art methods
A New Framework for Constrained Optimization via Feedback Control of Lagrange Multipliers
Full text linkThe continuous-time analysis of iterative algorithms for optimization has a long-standing history. This work introduces a novel framework for equality-constrained optimization based on control theory. The central concept is to design a feedback control system in which the Lagrange multipliers serve as the control inputs while the output represents the constraints. This system converges to a stationary point of the constrained optimization problem through suitable regulation. Concerning the Lagrange multipliers, we explore two control laws: proportional-integral control and feedback linearization. These choices lead to a variety of different methods. We rigorously develop the related algorithms, analyze their convergence theoretically, and present several numerical experiments that demonstrate their effectiveness compared to the state-of-the-art approaches
Direct data-driven controller design from bounded errors-in-variables measurements
Full text linkThe work focuses on direct data-driven controller design using input-output measurements corrupted by bounded additive noise. The main goal is to tackle the data-driven model reference control problem. To this end, we employ a set-membership framework and define the feasible controller parameter set, i.e., the set of parameters consistent with the noise bounds and the model-matching condition. We determine the controller parameters as the Chebyshev center of this set. We also provide a data-driven condition that is sufficient for establishing stability. This condition is also robust against the presence of bounded noise. The approach utilizes polynomial optimization and achieves global optimality via semidefinite relaxation techniques. A simulation example demonstrates the effectiveness of the proposed approach
Lasso-based state estimation for cyber-physical systems under sensor attacks
Full text linkThe development of algorithms for secure state estimation in vulnerable cyber-physical systems has been gaining attention in the last years. A consolidated assumption is that an adversary can tamper a relatively small number of sensors. In the literature, block-sparsity methods exploit this prior information to recover the attack locations and the state of the system. In this paper, we propose an alternative, Lasso-based approach and we analyse its effectiveness. In particular, we theoretically derive conditions that guarantee successful attack/state recovery, independently of established time sparsity patterns. Furthermore, we develop a sparse state observer, by starting from the iterative soft thresholding algorithm for Lasso, to perform online estimation. Through several numerical experiments, we compare the proposed methods to the state-of-the-art algorithms
Sparse linear regression with compressed and low-precision data via concave quadratic programming
Full text linkWe consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different k-sparse solutions may be present in the feasible set, and the classical `1 approach may be unsuccessful. For this motivation, we propose a non-convex quadratic programming method, which exploits prior information on the magnitude of the non-zero parameters. This results in a more efficient support recovery.
We provide sufficient conditions for successful recovery and numerical simulations to illustrate the practical feasibility of the proposed method
Solar wind spectral analysis in heliosheath from Voyager 2 data
No full textThe solar wind is a supersonic flow of magnetized plasma. It is time-dependent on all scales and expands with distance. The flow has fluctuations on a broad range of scales and frequencies. This fluctuations are not just convected outward but show energy cascades among the different scales. The solar wind turbulence peculiar phenomenology has been comprehensively reviewed by Tu and Marsch [11] and Bruno and Carbone [2]. As the distance from the sun increases, the available data on plasma and magnetic field become increasingly scarce. At distance of the order of 1 astronomic unit (AU), several measurement have been performed by various crafts, but, nowadays, only the Voyager spacecrafts can measure data in the heliosheath, the outermost layer in heliosphere where the solar wind is slowed by the pressure of the interstellar gas, and only the Voyager 2 craft can measure both plasma and magnetic fields (Voyager 1 can measure only the magnetic field, and Pioneer 10 and 11 has ceased communications). Taken together, the Voyager 1 and 2 probes have collected over 11 year of data in the heliosheath. The Voyager plasma experiment observes plasma currents in the energy/charge range 10 – 5950 eV /q using four modulated-grid Faraday cup detectors [1]. The observed currents are fit to convected isotropic proton Maxwellian distributions to derive the parameters (velocity, density, and temperature) used in this work. Magnetic field and plasma data are taken the COHO web site and MIT Space Plasma Group repository. Several studies have been done in order to extend the existing models to make them consistent with the energetic particles and magnetic fields measured in the heliosheath, but so far an exhaustive explanation has not yet been obtained. In particular, the differences between the energetic particle intensity variations seen by the two crafts are unexplained. The electron intensity measured by Voyager 2 varies steeper by a factor of 10 in a single year, while the same quantity from Voyager 1 changes gradually over time.[7] A possible explanation can be the presence of bubble of turbulence that travels in the heliosheat. Therefore, a characterization of turbulence and its intermittency is necessary to explain this phenomenology. The aim of this work is to provide the first spectral analysis of heliosheath solar wind, trying to characterize the plasma turbulence in that region by estimating the spectral slopes. A first result is represented in figure 2, where it can be seen that the low frequency spectral slope is lower when the electron intensity is low. In order to compute spectra, signal reconstruction techniques are mandatory: at distance over 80 AU, available data are very spotty. For the plasma velocity, there are 97% of missings due to unsteadiness in the signals, see 1, the most important of which are: tracking gaps due to the V2 location and due to limited deep space network availability; interference from other instruments; possible errors in the measurement chain (from the Faraday cups up to the data acquisition system and the signal shipping to Earth); the temporal sequence of the nuclear propulsion used to control the Voyager trajectory and to assist in several critical repositionings of the craft. For data recovery, we mainly use two different methods. The first method used is based on the correlation computation [8] that allows to reconstruct correlations and use it to compute spectra. Better results can be achieved implementing the maximum likelihood reconstruction by Rybicki and Press [10] based on a minimum-variance recovery with a stochastic component. The second methods comes from the Compress Sensing, a recent technique widely used in telecommunications, that provides the reconstruction of the signal from a sparse dataset [3], by using sparse Fourier matrices [9]. The methods used have been previously tested on 1979 data and on synthetic fluid turbulent fields. Results were in good agreement with the literature, and allows to compute largest spectra of solar wind at 5 AU, with frequencies ranging from 10-7 to 10-2 Hz [4, 5, 6]
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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