Two-timescale algorithms for simulation optimization of hidden Markov models

We propose two finite difference two-timescale Simultaneous Perturbation Stochastic Approximation (SPSA) algorithms for simulation optimization of hidden Markov models. Stability and convergence of both the algorithms is proved. Numerical experiments on a queueing model with high-dimensional parameter vectors demonstrate orders of magnitude faster convergence using these algorithms over related (N + 1)-Simulation finite difference analogues and another Two-Simulation finite difference algorithm that updates in cycles.