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Adaptive Time Synchronization in Time Sensitive-Wireless Sensor Networks Based on stochastic gradient algorithms Framework

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CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2025年第3期142卷 2585-2616页

作者： Abdul-Rashid, Ramadan Rahman, Mohd Amiruddin Abd Chan, Kar Tim Sangaiah, Arun Kumar Univ Putra Malaysia UPM Fac Sci Dept Phys Serdang 43400 Malaysia Natl Yunlin Univ Sci & Technol YunTech Int Grad Sch Artificial Intelligence Touliu 64002 Taiwan Sunway Univ Petaling Jaya 47500 Selangor Malaysia Chandigarh Univ Grahuan 140413 Punjab India

This study proposes a novel time-synchronization protocol inspired by stochastic gradient algorithms. The clock model of each network node in this synchronizer is configured as a generic adaptive filter where different stochastic gradient algorithms can be adopted for adaptive clock frequency adjustments. The study analyzes the pairwise synchronization behavior of the protocol and proves the generalized convergence of the synchronization error and clock frequency. A novel closed-form expression is also derived for a generalized asymptotic error variance steady state. Steady and convergence analyses are then presented for the synchronization, with frequency adaptations done using least mean square (LMS), the Newton search, the gradient descent (GraDes), the normalized LMS (N-LMS), and the Sign-Data LMS algorithms. Results obtained from real-time experiments showed a better performance of our protocols as compared to the Average Proportional-Integral Synchronization Protocol (AvgPISync) regarding the impact of quantization error on synchronization accuracy, precision, and convergence time. This generalized approach to time synchronization allows flexibility in selecting a suitable protocol for different wireless sensor network applications.

关键词： Wireless sensor network time synchronization stochastic gradient algorithm multi-hop

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A stochastic gradient-based two-step sparse identification algorithm for multivariate ARX systems

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Control Theory and Technology 2024年第2期22卷 213-221页

作者： Yanxin Fu Wenxiao Zhao Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing100049China

We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.

关键词： ARX system stochastic gradient algorithm Sparse identification Support recovery Parameter estimation Strong consistency

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A stochastic multiple gradient descent algorithm

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第3期271卷 808-817页

作者： Mercier, Quentin Poirion, Fabrice Desideri, Jean-Antoine Univ Paris Saclay ONERA DMAS Onera French Aerosp Lab 29 Ave Div Leclerc F-92320 Chatillon France INRIA 2004 Route Lucioles F-06902 Valbonne France

In this article, we propose a new method for multiobjective optimization problems in which the objective functions are expressed as expectations of random functions. The present method is based on an extension of the classical stochastic gradient algorithm and a deterministic multiobjective algorithm, the Multiple gradient Descent algorithm (MGDA). In MGDA a descent direction common to all specified objective functions is identified through a result of convex geometry. The use of this common descent vector and the Pareto stationarity definition into the stochastic gradient algorithm makes the algorithm able to solve multiobjective problems. The mean square and almost sure convergence of this new algorithm are proven considering the classical stochastic gradient algorithm hypothesis. The algorithm efficiency is illustrated on a set of benchmarks with diverse complexity and assessed in comparison with two classical algorithms (NSGA-II, DMS) coupled with a Monte Carlo expectation estimator. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Multiple objective programming Multiobjective stochastic optimization stochastic gradient algorithm Multiple gradient descent algorithm Common descent vector

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Langevin Dynamics for Adaptive Inverse Reinforcement Learning of stochastic gradient algorithms

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JOURNAL OF MACHINE LEARNING RESEARCH 2021年第1期22卷 1-49页

作者： Krishnamurthy, Vikram Yin, George Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA Univ Connecticut Dept Math Storrs CT 06269 USA

Inverse reinforcement learning (IRL) aims to estimate the reward function of optimizing agents by observing their response (estimates or actions). This paper considers IRL when noisy estimates of the gradient of a reward function generated by multiple stochastic gradient agents are observed. We present a generalized Langevin dynamics algorithm to estimate the reward function R(theta);specifically, the resulting Langevin algorithm asymptotically generates samples from the distribution proportional to exp(R(theta)). The proposed adaptive IRL algorithms use kernel-based passive learning schemes. We also construct multi-kernel passive Langevin algorithms for IRL which are suitable for high dimensional data and achieve variance reduction. The performance of the proposed IRL algorithms are illustrated on examples in adaptive Bayesian learning, logistic regression (high dimensional problem) and constrained Markov decision processes. We prove weak convergence of the proposed IRL algorithms using martingale averaging methods. We also analyze the tracking performance of the IRL algorithms in non-stationary environments where the utility function R(theta) has a hyper-parameter that jump changes over time as a slow Markov chain which is not known to the inverse learner. In this case, martingale averaging yields a Markov switched diffusion limit as the asymptotic behavior of the IRL algorithm.

关键词： passive learning stochastic gradient algorithm inverse reinforcement learning weak convergence martingale averaging theory Langevin dynamics stochastic sampling inverse Bayesian learning Constrained Markov Decision process logistic regression variance reduction Bernstein von-Mises theorem Markov chain hyper-parameter

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Averaged stochastic gradient algorithms for adaptive blind multiuser detection in DS/CDMA systems

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IEEE TRANSACTIONS ON COMMUNICATIONS 2000年第1期48卷 125-134页

作者： Krishnamurthy, V Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3052 Australia

In this paper, we present a blind adaptive gradient (BAG) algorithm for code-aided suppression of multiple-access interference (MAI) and narrow-band interference (NBI) in direct-sequence/code-division multiple-access (DS/CDMA) systems. This BAG algorithm is based on the concept of accelerating the convergence of a stochastic gradient algorithm by averaging, This ingenious concept of averaging was invented by Polyak-this paper examines its application to blind multiuser detection and NBI suppression in DS/CDMA systems, We prove that BAG has identical convergence and tracking properties to recursive least squares (RLS) but has a computational cost similar to the least mean squares (LMS) algorithm-i.e., an order of magnitude lower computational cost than RLS, Simulations are used to compare our averaged gradient algorithm with the blind RLS and LMS schemes.

关键词： averaging blind multiuser detection DS/CDMA narrow-band interference suppression spread spectrum stochastic gradient algorithm

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L^p and almost sure rates of convergence of averaged stochastic gradient algorithms: locally strongly convex objective

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ESAIM-PROBABILITY AND STATISTICS 2019年第1期23卷 841-873页

作者： Godichon-Baggioni, Antoine Univ Paul Sabatier Inst Math Toulouse Toulouse France

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are efficient candidates. Indeed, (1) they do not need too much computational efforts, (2) they do not need to store all the data, which is crucial when we deal with big data, (3) they allow to simply update the estimates, which is important when data arrive sequentially. The aim of this work is to give asymptotic and non asymptotic rates of convergence of stochastic gradient estimates as well as of their averaged versions when the function we would like to minimize is only locally strongly convex.

关键词： stochastic optimization stochastic gradient algorithm averaging Robust statistics

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Multikernel Passive stochastic gradient algorithms and Transfer Learning

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第4期67卷 1792-1805页

作者： Krishnamurthy, Vikram Yin, George Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA Univ Connecticut Dept Math Storrs CT 06269 USA

This article develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated. Classical passive stochastic gradient algorithms use a kernel that approximates a Dirac delta to weigh the gradients based on how far they are evaluated from the desired point. In this article, we construct a multikernel passive stochastic gradient algorithm. The algorithm performs substantially better in high dimensional problems and incorporates variance reduction. We analyze the weak convergence of the multikernel algorithm and its rate of convergence. In numerical examples, we study the multikernel version of the passive least mean squares algorithm for transfer learning to compare the performance with the classical passive version.

关键词： Convergence Approximation algorithms Kernel Noise measurement Transfer learning Monte Carlo methods Ordinary differential equations Bernstein von-Mises theorem passive least mean squares (LMS) stochastic gradient algorithm stochastic sampling transfer learning variance reduction weak convergence

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Online estimation of the asymptotic variance for averaged stochastic gradient algorithms

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2019年 203卷 1-19页

作者： Godichon-Baggioni, Antoine Univ Paul Sabatier Inst Math Toulouse F-31000 Toulouse France

stochastic gradient algorithms are more and more studied since they can deal efficiently and online with large samples in high dimensional spaces. In this paper, we first establish a Central Limit Theorem for these estimates as well as for their averaged version in general Hilbert spaces. Moreover, since having the asymptotic normality of estimates is often unusable without an estimation of the asymptotic variance, we introduce a new recursive algorithm for estimating this last one, and we establish its almost sure rate of convergence as well as its rate of convergence in quadratic mean. Finally, two examples consisting in estimating the parameters of the logistic regression and estimating geometric quantiles are given. (C) 2019 Elsevier B.V. All rights reserved.

关键词： stochastic gradient algorithm Averaging Central Limit Theorem Asymptotic variance

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Langevin dynamics for adaptive inverse reinforcement learning of stochastic gradient algorithms

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2021年第1期22卷 5372-5420页

作者： Vikram Krishnamurthy George Yin School of Electrical and Computer Engineering Cornell University Ithaca NY Department of Mathematics University of Connecticut Storrs CT

Inverse reinforcement learning (IRL) aims to estimate the reward function of optimizing agents by observing their response (estimates or actions). This paper considers IRL when noisy estimates of the gradient of a reward function generated by multiple stochastic gradient agents are observed. We present a generalized Langevin dynamics algorithm to estimate the reward function R(θ); specifically, the resulting Langevin algorithm asymptotically generates samples from the distribution proportional to exp(R(θ)). The proposed adaptive IRL algorithms use kernel-based passive learning schemes. We also construct multi-kernel passive Langevin algorithms for IRL which are suitable for high dimensional data and achieve variance reduction. The performance of the proposed IRL algorithms are illustrated on examples in adaptive Bayesian learning, logistic regression (high dimensional problem) and constrained Markov decision processes. We prove weak convergence of the proposed IRL algorithms using martingale averaging methods. We also analyze the tracking performance of the IRL algorithms in non-stationary environments where the utility function R(θ) has a hyper-parameter that jump changes over time as a slow Markov chain which is not known to the inverse learner. In this case, martingale averaging yields a Markov switched diffusion limit as the asymptotic behavior of the IRL algorithm.

关键词： passive learning stochastic gradient algorithm inverse reinforcement learning weak convergence martingale averaging theory Langevin dynamics stochastic sampling inverse Bayesian learning constrained Markov decision process logistic regression variance reduction Bernstein von-Mises theorem Markov chain hyper-parameter

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A stochastic gradient METHOD WITH MESH REFINEMENT FOR PDE-CONSTRAINED OPTIMIZATION UNDER UNCERTAINTY

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2020年第5期42卷 A2750-A2772页

作者： Geiersbach, Caroline Wollner, Winnifried Weierstrass Inst D-10117 Berlin Germany Tech Univ Darmstadt Fachbereich Math D-64293 Darmstadt Germany

Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth tracking-type functional subject to a linear partial differential equation with random coefficients and box constraints. The approach we take is based on stochastic approximation where, in place of a true gradient, a stochastic gradient is chosen using one sample from a known probability distribution. Feasibility is maintained by performing a projection at each iteration. In the application of this method to PDE-constrained optimization under uncertainty, new challenges arise. We observe the discretization error made by approximating the stochastic gradient using finite elements. Analyzing the interplay between PDE discretization and stochastic error, we develop a mesh refinement strategy coupled with decreasing step sizes. Additionally, we develop a mesh refinement strategy for the modified algorithm using iterate averaging and larger step sizes. The effectiveness of the approach is demonstrated numerically for different random field choices.

关键词： stochastic approximation stochastic gradient algorithm random elliptic PDEs as constraints PDE-constrained optimization under uncertainty optimization in Hilbert spaces discretization error

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