Stochastic optimization over continuous and discrete variables with applications to concept learning under noise

We consider optimization problems where the objective function is defined over some continuous and some discrete variables, and only noise corrupted values of the objective function are observable. Such optimization problems occur naturally in PAC learning with noisy samples. We propose a stochastic learning algorithm based on the model of a hybrid team of learning automata involved in a stochastic game with incomplete information to solve this optimization problem and establish its convergence properties. We then illustrate an application of this automata model in learning a class of conjunctive logic expressions over both nominal and linear attributes under noise.