Convergence Rate of Stochastic Approximation Algorithms in the Degenerate Case

作     者：Han-Fu Chen Laboratory of Systems and Control, Institute of Systems Science, The Chinese Academy of Sciences, Beijing 100080, P. R. China 

会议名称：《1995年中国控制会议》

会议日期：1995年

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

基　　金：Work supported by the National Natural Science Foundation of China 

关 键 词：Stochastic approximation convergence rate. 

摘      要：正Let f（·） be an unknown function whose root x0 is sought by stochastic approximation. This paper demonstrates the convergence rate of stochastic approximation algorithms for the degenerate case f’（x0 ） = 0. In comparison with the previous work, here no growth rate restriction is imposed on f（·）, no statistical property is required for the measurement noise, the general step size is considered and the result is obtained for the multidimensional case, which is not a straightforward extension of the one-dimensional result.