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Science China Mathematics 2022年第10期65卷 2151-2170页

作者： Andre Milzarek Xiantao Xiao Zaiwen Wen Michael Ulbrich School of Data Science The Chinese University of Hong KongShenzhenShenzhen 518172China Shenzhen Research Institute of Big Data Shenzhen 518172China Shenzhen Institute of Arti cial Intelligence and Robotics for Society Shenzhen 518172China School of Mathematical Sciences Dalian University of TechnologyDalian 116024China Beijing International Center for Mathematical Research Peking UniversityBeijing 100871China Department of Mathematics Technical University of MunichGarching bei Munchen 85748Germany

In this work,we present probabilistic local convergence results for a stochastic semismooth Newton method for a class of stochastic composite optimization problems involving the sum of smooth nonconvex and nonsmooth convex terms in the objective *** assume that the gradient and Hessian information of the smooth part of the objective function can only be approximated and accessed via calling stochastic firstand second-order *** approach combines stochastic semismooth Newton steps,stochastic proximal gradient steps and a globalization strategy based on growth *** present tail bounds and matrix concentration inequalities for the stochastic oracles that can be utilized to control the approximation errors via appropriately adjusting or increasing the sampling *** standard local assumptions,we prove that the proposed algorithm locally turns into a pure stochastic semismooth Newton method and converges r-linearly or r-superlinearly with high probability.

关键词： nonsmooth stochastic optimization stochastic approximation semismooth Newton method stochastic second-order information local convergence

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A stochastic NEWTON METHOD FOR NONLINEAR EQUATIONS

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Journal of Computational Mathematics 2023年第6期41卷 1192-1221页

作者： Jiani Wang Xiao Wang Liwei Zhang School of Mathematical Sciences Dalian University of TechnologyDalianChina School of Mathematical Sciences University of Chinese Academy of SciencesBeijingChina Peng Cheng Laboratory ShenzhenChina

In this paper,we study a stochastic Newton method for nonlinear equations,whose exact function information is difficult to obtain while only stochastic approximations are *** each iteration of the proposed algorithm,an inexact Newton step is first computed based on stochastic zeroth-and first-order *** encourage the possible reduction of the optimality error,we then take the unit step size if it is acceptable by an inexact Armijo line search ***,a small step size will be taken to help induce desired good *** we investigate convergence properties of the proposed algorithm and obtain the almost sure global convergence under certain *** also explore the computational complexities to find an approximate solution in terms of calls to stochastic zeroth-and first-order oracles,when the proposed algorithm returns a randomly chosen ***,we analyze the local convergence properties of the algorithm and establish the local convergence rate in high *** last we present preliminary numerical tests and the results demonstrate the promising performances of the proposed algorithm.

关键词： Nonlinear equations stochastic approximation Line search Global convergence Computational complexity Local convergence rate

A Symmetric Linearized Alternating Direction Method of Multipliers for a Class of stochastic Optimization Problems

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Journal of Systems Science and Information 2023年第1期11卷 58-77页

作者： Jia HU Qimin HU Networked Supporting Software International S&T Cooperation Base of China Jiangxi Normal UniversityNanchang 330022China

Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related *** 2013,Ouyang et *** the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization *** this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of ***,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration *** ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.

关键词： alternating direction method of multipliers stochastic approximation expected convergence rate and high probability bound convex optimization machine learning

Differentially Private Distributed Parameter Estimation

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Journal of Systems Science & Complexity 2023年第1期36卷 187-204页

作者： WANG Jimin TAN Jianwei ZHANG Ji-Feng School of Automation and Electrical Engineering University of Science and Technology BeijingBeijing 100083China Key Laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Data privacy is an important issue in control systems,especially when datasets contain sensitive information about *** this paper,the authors are concerned with the differentially private distributed parameter estimation problem,that is,we estimate an unknown parameter while protecting the sensitive information of each ***,the authors propose a distributed stochastic approximation estimation algorithm in the form of the differentially private consensus+innovations(DP-CI),and establish the privacy and convergence property of the proposed ***,it is shown that the proposed algorithm asymptotically unbiased converges in mean-square to the unknown parameter while differential privacy-preserving holds for finite number of ***,the exponentially damping step-size and privacy noise for DP-CI algorithm is *** estimate approximately converges to the unknown parameter with an error proportional to the step-size parameter while differential privacy-preserving holds for all *** tradeoff between accuracy and privacy of the algorithm is effectively ***,a simulation example is provided to verify the effectiveness of the proposed algorithm.

关键词： Differential privacy distributed parameter estimation stochastic approximation

Identification of Linear Systems Using Binary Sensors with Random Thresholds

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Journal of Systems Science & Complexity 2024年第3期37卷 907-923页

作者： HUANG Zhiyong SONG Qijiang School of Mathematics Renmin University of ChinaBeijing 100872China School of Mathematics Sino-French InstituteRenmin University of ChinaBeijing 100872China

In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is *** the help of stochastic approximation algorithms with expanding truncations,the authors give the recursive estimates for the parameters of both the linear system and the binary *** reasonable conditions,all constructed estimates are proved to be convergent to the true values with probability one,and the convergence rates are also established.A simulation example is provided to justify the theoretical results.

关键词： α-mixing binary sensor quantized system stochastic approximation stochastic thresh-old strongly consistent system identification

ON CONTROL OF STRONG CONSENSUS FOR NETWORKED AGENTS WITH NOISY OBSERVATIONS

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Journal of Systems Science & Complexity 2012年第1期25卷 1-12页

作者： Haitao FANG Han-Fu CHEN Lei WEN Key Laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

The discrete-time first-order multi-agent networks with communication noises are under consideration. Based on the noisy observations, the consensus control is given for networks with both fixed and time-varying topologies. The states of agents in the resulting closed-loop network are updated by a stochastic approximation （SA） algorithm, and the consensus analysis for networks turns to be the convergence analysis for SA. For networks with fixed topologies, the proposed consensus control leads to consensus of agents with probability one if the graph associated with the network is connected. In the case of time-varying topologies, the similar results are derived if the graph is jointly connected in a fixed time period. Compared with existing results, the networks considered here are in a more general setting under weaker assumptions and the strong consensus is established by a simpler proof.

关键词： Consensus control multi-agent networks stochastic approximation strong consensus.

Distributed regression estimation with incomplete data in multi-agent networks

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Science China(Information Sciences) 2018年第9期61卷 168-181页

作者： Yinghui WANG Peng LIN Yiguang HONG University of Chinese Academy of Sciences Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciences

In this paper, distributed regression estimation problem with incomplete data in a time-varying multi-agent network is investigated. Regression estimation is carried out based on local agent information with incomplete in the non-ignorable mechanism. By virtue of gradient-based design and adaptive filter, a distributed algorithm is proposed to deal with a regression estimation problem with incomplete data. With the help of convex analysis and stochastic approximation techniques, the exact convergence is obtained for the proposed algorithm with incomplete data and a jointly-connected multi-agent topology. Moreover, online regret analysis is also given for real-time learning. Then, simulations for the proposed algorithm are also given to demonstrate how it can solve the estimation problem in a distributed way, even when the network configuration is time-varying.

关键词： multi-agent systems time-varying network estimation with incomplete data online learning stochastic approximation

Asymptotic properties of distributed social sampling algorithm

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Science China(Information Sciences) 2020年第1期63卷 152-166页

作者： Qian LIU Xingkang HE Haitao FANG The Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences ACCESS Linnaeus Centre School of Electrical Engineering and Computer ScienceKTH Royal Institute of Technology

Social sampling is a novel randomized message passing protocol inspired by social communication for opinion formation in social networks. In a typical social sampling algorithm, each agent holds a sample from the empirical distribution of social opinions at initial time, and it collaborates with other agents in a distributed manner to estimate the initial empirical distribution by randomly sampling a message from current distribution estimate. In this paper, we focus on analyzing the theoretical properties of the distributed social sampling algorithm over random networks. First, we provide a framework based on stochastic approximation to study the asymptotic properties of the algorithm. Then, under mild conditions, we prove that the estimates of all agents converge to a common random distribution, which is composed of the initial empirical distribution and the accumulation of quantized error. Besides, by tuning algorithm parameters, we prove the strong consistency, namely, the distribution estimates of agents almost surely converge to the initial empirical distribution. Furthermore, the asymptotic normality of estimation error generated by distributed social sample algorithm is addressed. Finally, we provide a numerical simulation to validate the theoretical results of this paper.

关键词： social networks opinion formation social sampling stochastic approximation random networks asymptotic normality

IDENTIFICATION FOR WIENER SYSTEMS WITH INTERNAL NOISE

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Journal of Systems Science & Complexity 2008年第3期21卷 378-393页

作者： Qijiang SONG Hanfu CHEN Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper considers identification of Wiener systems for which the internal variables and output are corrupted by noises. When the internal noise is a sequence of independent and identically distributed （lid） Gaussian random variables, by the Weierstrass transformation （WT） the system under consideration turns to be a Wiener system without internal noise. The nonlinear part of the latter is nothing else than the WT of the nonlinear function of the original system, while the linear subsystem is the same for both systems before and after WT. Under reasonable conditions, the recursive identification algorithms are proposed for the transformed Wiener system, and strong consistency for the estimates is established. By using the inverse WT the nonparametric estimates for the nonlinearity of the original system are derived, and they are strongly consistent if the nonlinearity in the original system is a polynomial, Similar results also hold in the case where the internal noise is non-Gaussian. Simulation results are fully consistent with the theoretical analysis.

关键词： Recursive identification stochastic approximation strong consistency Wiener system Weierstrass transformation