Optimal training for adversarial games (Q2043435)

In this paper, adversarial games that have an associated differential system induced by a Hamiltonian function are solved using a continuous version of the simultaneous gradient descent method. As Nash equilibrium is not always reached by that method, optimal training times are discussed as well. After giving three distinct prototype examples, the authors dive into Hamiltonian systems and Hamiltonian solutions flow. After this, the main portion of the paper, a discussion of Quadratic Hamiltonian Functions, begins. Here the Hamiltonian flow is solved for by using a resulting nonhomogeneous linear system created by the functions of the Hamilton flow. Two cases come up as a result. The elliptic case where the determinant of the system's matrix coefficient is greater than zero, and the hyperbolic case where it is less than zero. In both of the cases, the corresponding equilibrium points and optimal training times are found. Along with this, discrete systems and quadratic approximation are also discussed. Many areas for future research are listed as well.