Asymptotic approximation of the probability of correctly selecting the best systems

Abstract

Consider the problem of selecting the best stochastic system or the best m systems among a finite but large alternative systems. If a limited computational budget is available to be distributed among the different alternatives, then instead of distributing these computations evenly, the optimal computing budget allocation (OCBA) can be used to distribute this budget in a smart way so as to maximize the probability of correct selection (PCS). However, the OCBA does not tell how large is the PCS. In this paper, we present a procedure that resembles the OCBA, but it gives an approximation of PCS. Thus the user can stop the simulation whenever a precision level is reached.