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In this paper we study simulation based optimization algorithms for solvingdiscrete time optimal stopping problems. This type of algorithms became popularamong practioneers working in the area of quantitative finance. Using largedeviation theory for the increments of empirical processes, we derive optimalconvergence rates and show that they can not be improved in general. The ratesderived provide a guide to the choice of the number of simulated paths neededin optimization step, which is crucial for the good performance of anysimulation based optimization algorithm. Finally, we present a numericalexample of solving optimal stopping problem arising in option pricing thatillustrates our theoretical findings.

On the rates of convergence of simulation based optimization algorithms for optimal stopping problems