Approximation of Optimal Control Surfaces for $2\times 2$ Skew-Symmetric Evolutionary Game Dynamics

Abstract

In this paper we study the problem of approximating the general solution to an optimal control problem whose dynamics arise from a $2\times 2$ skew-symmetric evolutionary game with arbitrary initial condition. Our approach uses a Fourier approximation method and generalizes prior work in the use of orthogonal function approximation for optimal control. At the same time we cast the fitting problem in the context of a non-standard feedforward neural network and derive the back-propagation operator in this context. An example of the efficacy of this approach is provided and generalizations are discussed.

17 pages, 5 figures

References in corpus (2)

• A Brief Survey of Deep Reinforcement Learning
• Mixed finite element approximation of periodic Hamilton--Jacobi--Bellman problems with application to numerical homogenization