On the convergence rate of ordinal optimization for a class of stochastic discrete resource allocation problems

The authors previously (1998) considered stochastic discrete resource allocation problems were which are hard due to the combinatorial explosion of the feasible allocation search space, as well as the absence of closed-form expressions for the cost function of interest. An ordinal optimization algorithm for solving a class of such problems was then shown to converge in probability to the global optimum. In this paper, we show that this result can be strengthened to almost sure convergence, under some additional mild conditions, and we determine the associated rate of convergence. In the case of regenerative systems, we further show that the algorithm converges exponentially fast.