A Policy Iteration Algorithm for N-player General-Sum Linear Quadratic Dynamic Games

TL;DR

This paper introduces a new policy iteration algorithm for N-player general-sum linear quadratic dynamic games, demonstrating superior convergence speed and robustness over policy gradient methods through numerical experiments.

Contribution

The paper develops a novel policy iteration algorithm for multi-player linear quadratic games and shows it outperforms existing policy gradient methods in convergence and stability.

Findings

Convergence rate of the proposed algorithm surpasses policy gradient methods.

The algorithm is less sensitive to initial policies and number of players.

Numerical experiments confirm faster and more stable convergence.

Abstract

We present a policy iteration algorithm for the infinite-horizon N-player general-sum deterministic linear quadratic dynamic games and compare it to policy gradient methods. We demonstrate that the proposed policy iteration algorithm is distinct from the Gauss-Newton policy gradient method in the N-player game setting, in contrast to the single-player setting where under suitable choice of step size they are equivalent. We illustrate in numerical experiments that the convergence rate of the proposed policy iteration algorithm significantly surpasses that of the Gauss-Newton policy gradient method and other policy gradient variations. Furthermore, our numerical results indicate that, compared to policy gradient methods, the convergence performance of the proposed policy iteration algorithm is less sensitive to the initial policy and changes in the number of players.