Solving Two-Player General-Sum Games Between Swarms

TL;DR

This paper extends physics-informed neural network methods to solve two-player swarm-level general-sum games, demonstrating improved policies over some reinforcement learning approaches and comparable results with traditional numerical solvers.

Contribution

It introduces a novel approach for applying PINNs to swarm-level games using the Kolmogorov forward equation, addressing high-dimensional challenges.

Findings

PINN-based policies outperform Nash DDQN in payoff.

PINN results are comparable to numerical solvers.

Extension from agent-level to swarm-level games achieved.

Abstract

Hamilton-Jacobi-Isaacs (HJI) PDEs are the governing equations for the two-player general-sum games. Unlike Reinforcement Learning (RL) methods, which are data-intensive methods for learning value function, learning HJ PDEs provide a guaranteed convergence to the Nash Equilibrium value of the game when it exists. However, a caveat is that solving HJ PDEs becomes intractable when the state dimension increases. To circumvent the curse of dimensionality (CoD), physics-informed machine learning methods with supervision can be used and have been shown to be effective in generating equilibrial policies in two-player general-sum games. In this work, we extend the existing work on agent-level two-player games to a two-player swarm-level game, where two sub-swarms play a general-sum game. We consider the \textit{Kolmogorov forward equation} as the dynamic model for the evolution of the densities of the swarms. Results show that policies generated from the physics-informed neural network (PINN) result in a higher payoff than a Nash Double Deep Q-Network (Nash DDQN) agent and have comparable performance with numerical solvers.