Approximate dynamic programming solutions of multi-agent graphical games using actor-critic network structures

This paper studies a new class of multi-agent discrete-time dynamical graphical games, where interactions between agents are restricted by a communication graph structure. The paper brings together discrete Hamiltonian mechanics, optimal control theory, cooperative control, game theory, reinforcement learning, and neural network structures to solve the multi-agent dynamical graphical games. Graphical game Bellman equations are derived and shown to be equivalent to certain graphical game Hamilton Jacobi Bellman equations developed herein. Reinforcement Learning techniques are used to solve these dynamical graphical games. Heuristic Dynamic Programming and Dual Heuristic Programming, are extended to solve the graphical games using only neighborhood information. Online adaptive learning structure is implemented using actor-critic networks to solve these graphical games.