We proposetwo finite difference two-timescale simultaneous perturbationstochastic approximation (SPSA)algorithmsfor simulation optimization ofhidden Markov models. Stability and convergence of both thealgorithms is proved.

Numericalexperiments on a queueing model with high-dimensional parameter vectorsdemonstrate orders of magnitude faster convergence using thesealgorithms over related $(N+1)$-Simulation finite difference analoguesand another two-simulation finite difference algorithm that updates incycles.