Global Convergence of Policy Gradient for Sequential Zero-Sum Linear Quadratic Dynamic Games
Systems and Control
2019-11-13 v1 Systems and Control
Optimization and Control
Abstract
We propose projection-free sequential algorithms for linear-quadratic dynamics games. These policy gradient based algorithms are akin to Stackelberg leadership model and can be extended to model-free settings. We show that if the leader performs natural gradient descent/ascent, then the proposed algorithm has a global sublinear convergence to the Nash equilibrium. Moreover, if the leader adopts a quasi-Newton policy, the algorithm enjoys a global quadratic convergence. Along the way, we examine and clarify the intricacies of adopting sequential policy updates for LQ games, namely, issues pertaining to stabilization, indefinite cost structure, and circumventing projection steps.
Cite
@article{arxiv.1911.04672,
title = {Global Convergence of Policy Gradient for Sequential Zero-Sum Linear Quadratic Dynamic Games},
author = {Jingjing Bu and Lillian J. Ratliff and Mehran Mesbahi},
journal= {arXiv preprint arXiv:1911.04672},
year = {2019}
}