Continuous action set learning automata for stochastic optimization

Abstract

The problem of optimization with noisy measurements is common in many areas of engineering. The only available information is the noise corrupted value of the objective function at any chosen point in the parameter space. One well known method for solving this problem is the stochastic approximation procedure. In this paper we consider an adaptive random search procedure, based on the reinforcement learning paradigm. The learning model presented here generalizes the traditional model of a learning automaton [Narendra and Thathachar, Learning Automata : An Introduction, Prentice Hall, Englewood Cliffs, 1989]. This procedure requires a lesser number of function evaluations at each step compared to the stochastic approximation. The convergence properties of the algorithm are theoretically investigated. Simulation results are presented to show the efficacy of the learning method.