无穷维切换机制随机逼近算法的分析

Infinite dimensional regime-switching stochastic approximation algorithms

本文分析了一类带切换机制的随机逼近算法.此类随机逼近算法可用于对平稳分布的估计,使用固定步长以跟踪占位测度的增量变化.算法中的切换机制可以由可列无穷维Markov链及双时间尺度刻画.本文得到了跟踪误差的最小二乘估计,并在合理的假设条件下证明了算法的连续时间插值形式弱收敛于一类带切换机制的常微分方程系统.此外,本文也对追踪误差的变化速率进行了分析.

We analyze a type of stochastic approximation algorithms with regime switching modulated by a discrete Markov chain having countable state spaces and two-time-timescale construction. In the algorithm, the increments of a sequence of occupation measures are updated using constant step size iterates. We show that least squares estimates of the tracking errors can be developed. Under the assumption that the adaptation rates have the same magnitude as that of times-different parameter, we prove the continuous-time interpolation from the iterates converges weakly to a system of ordinary differential equations with regime switching. In addition, we demonstrate that the suitably scaled sequence of the tracking errors converges to a system of switching diffusions.