In this paper we study simulation based optimization algorithms for solving
discrete time optimal stopping problems. This type of algorithms became popular
among practioneers working in the area of quantitative finance. Using large
deviation theory for the increments of empirical processes, we derive optimal
convergence rates and show that they can not be improved in general. The rates
derived provide a guide to the choice of the number of simulated paths needed
in optimization step, which is crucial for the good performance of any
simulation based optimization algorithm. Finally, we present a numerical
example of solving optimal stopping problem arising in option pricing that
illustrates our theoretical findings