On the Heterogeneity of Independent Learning Dynamics in Zero-Sum Stochastic Games

Abstract

We analyze the convergence properties of the two-timescale fictitious play combining the classical fictitious play with the Q-learning for two-player zero-sum stochastic games with player-dependent learning rates. We show its almost sure convergence under the standard assumptions in two-timescale stochastic approximation methods when the discount factor is less than the product of the ratios of player-dependent step sizes. To this end, we formulate a novel Lyapunov function formulation and present a one-sided asynchronous convergence result.

Cite

Text

Sayin and Cetiner. "On the Heterogeneity of Independent Learning Dynamics in Zero-Sum Stochastic Games." Proceedings of The 4th Annual Learning for Dynamics and Control Conference, 2022.

Markdown

[Sayin and Cetiner. "On the Heterogeneity of Independent Learning Dynamics in Zero-Sum Stochastic Games." Proceedings of The 4th Annual Learning for Dynamics and Control Conference, 2022.](https://mlanthology.org/l4dc/2022/sayin2022l4dc-heterogeneity/)

BibTeX

@inproceedings{sayin2022l4dc-heterogeneity,
  title     = {{On the Heterogeneity of Independent Learning Dynamics in Zero-Sum Stochastic Games}},
  author    = {Sayin, Muhammed and Cetiner, Kemal},
  booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference},
  year      = {2022},
  pages     = {994-1005},
  volume    = {168},
  url       = {https://mlanthology.org/l4dc/2022/sayin2022l4dc-heterogeneity/}
}