Author : Quan Yuan
Publisher :
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.:/5 (942 download)
Book Synopsis Stochastic Approximation Algorithms with Applications to Particle Swarm Optimization, Adaptive Optimization, and Consensus by : Quan Yuan
Download or read book Stochastic Approximation Algorithms with Applications to Particle Swarm Optimization, Adaptive Optimization, and Consensus written by Quan Yuan and published by . This book was released on 2015 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: (2) The agents compute and communicate at random times. (3) The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. (4) The functions involved are allowed to vary with respect to time hence nonstationarity can be handled. (5) Multi-scale formulation enriches the applicability of the algorithms. In the setup, the switching process contains a rate parameter $\e> 0$ in the transition probability matrix that characterizes how frequently the topology switches. The algorithm uses a step-size $\mu$ that defines how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under suitable conditions, it is shown that a continuous-time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous-time Markov chain, or to a system of differential equations (an average with respect to certain measure). In addition, a scaled sequence of tracking errors converges to a witching diffusion or a diffusion. Simulation results are presented to demonstrate these findings.