Continuous action set learning automata for stochastic optimization (Q1898166)

The paper deals with the minimization of a function whose values cannot be determined exactly. However, it is assumed that it is possible (at any chosen point) to observe a random element with the mathematical expectation equal to the corresponding function value. Such situation appears for example in pattern recognition, signal processing, etc. It is well-known, from the mathematical optimization theory, that the stochastic approximation method can be employed to solve the above-mentioned problem. The other possibility is to employ a random search procedure. This investigation deals with an adaptive search procedure that generalizes the traditional model of a learning automaton. The Gaussian distribution is employed. This type of distribution is determined only by two parameters in the one-dimensional case, and by a finite number of parameters in general case. The one-dimensional case and multidimensional case are investigated separately. The convergence properties of the algorithm are investigated theoretically. Simulation results are presented at the end.