Interacting Particle Systems for Fast Linear Quadratic RL

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Abstract

This paper is concerned with the design of algorithms based on systems of interacting particles to represent, approximate, and learn the optimal control law for reinforcement learning (RL). The primary contribution is that convergence rates are greatly accelerated by the interactions between particles. The focus is on the linear quadratic stochastic optimal control problem for which a complete and novel theory is presented. Apart from the new algorithm, sample complexity bounds are obtained, and it is shown that the mean square error scales as $1/N$ where $N$ is the number of particles. The theoretical results and algorithms are illustrated with numerical experiments and comparisons with other recent approaches, where the faster convergence of the proposed algorithm is numerically demonstrated.

Citation

@InProceedings{pmlr-v283-joshi25a,
  title =    {Interacting Particle Systems for Fast Linear Quadratic RL},
  author =       {Joshi, Anant A. and Chang, Heng-Sheng and Taghvaei, Amirhossein and Mehta, Prashant G. and Meyn, Sean P.},
  booktitle =    {Proceedings of the 7th Annual Learning for Dynamics & Control Conference},
  pages =    {99--111},
  year =     {2025},
  editor =     {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro},
  volume =     {283},
  series =     {Proceedings of Machine Learning Research},
  month =    {04--06 Jun},
  publisher =    {PMLR},
  pdf =      {https://raw.githubusercontent.com/mlresearch/v283/main/assets/joshi25a/joshi25a.pdf},
  url =      {https://proceedings.mlr.press/v283/joshi25a.html},
  abstract =     {This paper is concerned with the design of algorithms based on systems of interacting particles to represent, approximate, and learn the optimal control law for reinforcement learning (RL). The primary contribution is that convergence rates are greatly accelerated by the interactions between particles. The focus is on the linear quadratic stochastic optimal control problem for which a complete and novel theory is presented. Apart from the new algorithm, sample complexity bounds are obtained, and it is shown that the mean square error scales as $1/N$ where $N$ is the number of particles. The theoretical results and algorithms are illustrated with numerical experiments and comparisons with other recent approaches, where the faster convergence of the proposed algorithm is numerically demonstrated.}
}