SOLVING THE MATRIX 3× N GAME FOR COMBINING OPTIMALLY ALGORITHMS OF THE NEURONET LEARNING WITH IDENTIFICATION ERROR MEASURE AFTER THE LEARNING TIME BY A VOLUME OF THE CONSUMED RESOURCES

Abstract

Solving the matrix 3× N game for combining optimally algorithms of the neuronet learning with identification error measure after the learning time by a volume of the consumed resources A neural network is considered with three interdependent indexes: identification error measure, being acquired after the learning time by one of the N available algorithms for the neuronet learning, corresponds to some volume of the consumed resources. For condition of unfeasibility of pointing at the priority and ranking quantitatively these indexes we suggested the conversion into the corresponding 3× N game and its solution in the form of the second player optimal strategy, with whose probabilities the algorithms for the neuronet learning should be combined. Despite the primary inadmissibility of the Bayes-Laplace criterion for optimal algorithm selection this criterion applicability is supported only on the expiry of a certain time period of the neuronet functioning, when the point evaluation of its indexes weights becomes available. In giving an example with four algorithms for the neuronet learning, we calculated its guaranteed indexes after having combined those algorithms optimally, where worsening of such indexes is also demonstrated by the other approach.