Convergence of Two Time-Scale Stochastic Approximation: A Martingale Approach

ArXi:2603.14481v1 Announce Type: cross In this paper, we analyze the two time-scale stochastic approximation (TTSSA) algorithm Our theory is applicable to nonlinear equations, in contrast to many papers in the TTSSA literature which assume that the equations are linear. The convergence of TTSSA is proved in the "almost sure" sense, in contrast to earlier papers on TTSSA that establish convergence in distribution, convergence in the mean, and the like. Moreover, in this paper we establish different rates of convergence for the fast and the slow subsystems, perhaps for the first time.