DISTRIBUTED STOCHASTIC METHODS AND APPLICATION

Chapter 1Introduction1 1.1Distributed optimization4 1.1.1Distributed deterministic optimization4 1.1.2Distributed stochastic optimization10 1.2Distributed machine learning13 1.2.1Distributed regression problem14 1.2.2Distributed classification problem16 1.2.3Distributed clustering problems17 1.3Structure and work of this book17 Chapter 2Preliminaries19 2.1Convex analysis19 2.1.1Euclidean norm inequalities19 2.1.2Lipschitz continuous gradient22 2.2Probability theory23 Chapter 3Distributed Stochastic Sub-gradient Descent Algorithm24 3.1Distributed stochastic sub-gradient descent algorithm for convex optimization24 3.1.1Background24 3.1.2Problem,algorithm and assumptions25 3.1.3Basic relations27 3.1.4Convergence in mean28 3.1.5Almost sure and mean square convergence29 3.2Distributed stochastic sub-gradient descent algorithm for regression estimation with incomplete data30 3.2.1Background31 3.2.2Problem formulation33 3.2.3Distributed adaptive gradient-based algorithm36 3.2.4Main results of DAGA38 3.2.5Simulations47 3.2.6Conclusion50 3.3Distributed classification learning based on nonlinear vector support machines for switching networks51 3.3.1Background51 3.3.2Preliminary and SVM formulation53 3.3.3Distributed nonlinear SVM learning54 3.3.4Distributed stochastic sub-gradient based SVM algorithm58 3.3.5Simulations63 3.3.6Conclusion67 Chapter 4Distributed Mirror-descent Algorithm68 4.1Distributed stochastic mirror descent algorithm over time-varying network68 4.1.1Background68 4.1.2Preliminaries and assumptions70 4.1.3Distributed stochastic mirror descent algorithm72 4.1.4Main result73 4.1.5Simulation78 4.1.6Conclusions79 4.2A Stochastic mirror-descent algorithm for solving AXB=C over an multi-agent system80 4.2.1Background80 4.2.2Preliminaries81 4.2.3Problem formulation and algorithm design83 4.2.4Main result86 4.2.5Simulation95 4.2.6Conclusions96 4.3Distributed stochastic mirror descent algorithm for resource allocation problem97 4.3.1Background97 4.3.2Preliminaries99 4.3.3Problem formulation and algorithm design100 4.3.4Main result103 4.3.5Simulation109 4.3.6Conclusions113 4.4Distributed communication-sliding algorithm for nonsmooth resource allocation problem113 4.4.1Background113 4.4.2Preliminaries115 4.4.3Problem formulation and algorithm design119 4.4.4Main result122 4.4.5Simulation130 4.4.6Conclusion132 Chapter 5Distributed Subgradient-free Algorithm133 5.1Distributed subgradient-free stochastic optimization algorithm for nonsmooth convex functions over time-varying nentworks133 5.1.1Background133 5.1.2Preliminaries136 5.1.3Distributed algorithm and hypotheses139 5.1.4Main results143 5.1.5Simulations154 5.1.6Conclusions158 5.2A zeroth-order algorithm to distributed optimization with stochastic stripe observations158 5.2.1Background159 5.2.2Mathematical preliminaries161 5.2.3Formulation and algorithm162 5.2.4Main results166 5.2.5Simulation171 5.2.6Conclusion173 5.3Distributed online optimization with gradient-free design174 5.3.1Background175 5.3.2Notations and preliminaries176 5.3.3Formulation and algorithm178 5.3.4Main results181 5.3.5Simulation184 Chapter 6Distributed Stochastic Accelerated Descent Algorithm186 6.1Convergence analysis of accelerated distributed gradient methods with random sleeping scheme186 6.1.1Background186 6.1.2Preliminaries and problem formulation188 6.1.3Main results189 6.1.4Conclusions200 6.2Distributed accelerated descent algorithm for energy resource coordination in multi-agent integrated energy systems200 6.2.1Background201 6.2.2MA-IES structure and DERC modeling203 6.2.3Distributed algorithm for the DERC 208 6.2.4Case studies214 6.2.5Simulation 223 Chapter 7Distributed Algorithm in Machine Learning225 7.1Consensus-based EM algorithm for gaussian mixtures in time-varying networks225 7.1.1Background225 7.1.2Preliminaries and problem formulation227 7.1.3Standard EM algorithm229 7.1.4Consensus-based jointly-connected EM algorithm231 7.1.5Simulation234 7.1.6Conclusion237 7.2Distributed boosting algorithm over multi-agent networks239 7.2.1Background239 7.2.2Preliminary and previous work241 7.2.3Distributed algorithm244 7.2.4Simulation246 7.2.5Conclusions249 References250