A new perspective on feasibility determination

We consider the problem of feasibility determination in a stochastic setting. In particular, we wish to determine whether a system belongs to a given set ¿ based on a performance measure estimated through Monte Carlo simulation. Our contribution is two-fold: (i) we characterize fractional allocations that are asymptotically optimal; and (ii) we provide an easily implementable algorithm, rooted in stochastic approximation theory, that results in sampling allocations that provably achieve in the limit the same performance as the optimal allocations. The finite-time behavior of the algorithm is also illustrated on two small examples.