Stochastic Optimization on Bayesian Nets

In this paper we are concerned with stochastic optimization problems in the case when the joint probability distribution, associated with random parameters, can be described by means of a Bayesian net. In such a case we suggest that the structured nature of the probability distribution can be exploited for designing efficient gradient estimation algorithm. Such gradient estimates can be used within the general framework of stochastic gradient (quasi-gradient) solution procedures in order to solve complex non-linear stochastic optimization problems. We describe a gradient estimation algorithm and present a case study related to the reliability of semiconductor manufacturing together with numerical experiments.