Sastry,Stochastic optimization over continuous and discrete variables with applications to concept learning under noise,IEEE Trans. Syst. Man Cybern.—Part A: Systems and Humans 29

Abstract—We consider optimization problems where the objec-tive function is defined over some continuous and some discrete variables, and only noise corrupted values of the objective func-tion 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. Index Terms—Concept learning, learning automata, ODE anal-ysis of learning algorithms, optimization, PAC learning, risk minimization. I