MACHINE LEARNING IN A TWO-LEVEL DECISION-MAKING SYSTEM USING THE MERCER KERNEL FUNCTIONS

Author(s): Sidorov I.G.

Rubric: Information technology

DOI: 10.21777/2500-2112-2022-1-76-82

Release: 2022-1 (38)

Pages: 76-82

Keywords: classification, Mercer kernel, Nash equilibrium, separating function, differential game, potential function

Annotation: This paper proposes a machine learning technique using game theory in the form of a hierarchical differencedifferential game of N+1 persons in a two-level decision-making system. The issues of machine learning based on nonlinear kernels are considered in relation to differential or difference-differential two-level cooperative games. It is proposed to use kernel proximity functions like Mercer kernels as potential learning functions at both levels of the differential hierarchical game. Due to the existence of a fixed point for this type of kernels, the learning algorithm will always converge to the solution of a differential hierarchical two-level game at the Nash equilibrium point. This makes it possible to obtain a sustainable learning algorithm. The paper shows that with the help of some nonlinear transformations of Mercer kernel functions of the radial basis type, it is possible to solve the classification problem for two classes using the method of potential functions. An example of applying the machine learning technique using the kernel approach and non-linear utility (preference functions) is shown. The results obtained can be used in the construction of mathematical models of hierarchical multilevel dynamical systems in order to study their properties.

Bibliography: Sidorov I.G. MACHINE LEARNING IN A TWO-LEVEL DECISION-MAKING SYSTEM USING THE MERCER KERNEL FUNCTIONS // Education Resources and Technologies. – 2022. – № 1 (38). – С. 76-82. doi: 10.21777/2500-2112-2022-1-76-82