Convergence rates of discrete-time stochastic approximation consensus algorithms: Graph-related limit bounds

2018 ◽  
Vol 112 ◽  
pp. 9-17 ◽  
Author(s):  
Huaibin Tang ◽  
Tao Li
Keyword(s):  
Stochastic Approximation ◽  
Discrete Time ◽  
Convergence Rates ◽  
Consensus Algorithms

scholarly journals A homogeneity property of discrete‐time systems: Stability and convergence rates

2019 ◽  
Vol 29 (8) ◽  
pp. 2406-2421 ◽  
Author(s):  
Tonametl Sanchez ◽  
Denis Efimov ◽  
Andrey Polyakov ◽  
Jaime A. Moreno ◽  
Wilfrid Perruquetti
Keyword(s):  
Discrete Time ◽  
Convergence Rates ◽  
Stability And Convergence ◽  
Discrete Time Systems ◽  
Homogeneity Property ◽  
Time Systems

scholarly journals Weak Convergence Rates of Population Versus Single-Chain Stochastic Approximation MCMC Algorithms

2014 ◽  
Vol 46 (04) ◽  
pp. 1059-1083 ◽  
Author(s):  
Qifan Song ◽  
Mingqi Wu ◽  
Faming Liang
Keyword(s):  
Monte Carlo ◽  
Weak Convergence ◽  
Stochastic Approximation ◽  
Convergence Rates ◽  
Gain Factor ◽  
Single Chain ◽  
Practical Applications ◽  
Mcmc Algorithms ◽  
Factor Sequence ◽  
Number Of Iterations

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1 / t), where t indexes the number of iterations. This is of interest for practical applications.

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