# Thompson sampling for linear quadratic mean-field teams

arXiv: https://arxiv.org/abs/2011.04686 · HTML: https://mlsanity.com/paper/2011.04686/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Scalable regret for learning to control network-coupled subsystems with unknown dynamics](https://mlsanity.com/paper/2108.07970/) (2021)
- [A relaxed technical assumption for posterior sampling-based reinforcement learning for control of unknown linear systems](https://mlsanity.com/paper/2108.08502/) (2021)
- [Learning distributed channel access policies for networked estimation: data-driven optimization in the mean-field regime](https://mlsanity.com/paper/2112.05837/) (2021)

## Abstract (arXiv)

We consider optimal control of an unknown multi-agent linear quadratic (LQ) system where the dynamics and the cost are coupled across the agents through the mean-field (i.e., empirical mean) of the states and controls. Directly using single-agent LQ learning algorithms in such models results in regret which increases polynomially with the number of agents. We propose a new Thompson sampling based learning algorithm which exploits the structure of the system model and show that the expected Bayesian regret of our proposed algorithm for a system with agents of |M| different types at time horizon T is tildeO big( |M|1.5 √T big) irrespective of the total number of agents, where the tildeO notation hides logarithmic factors in T. We present detailed numerical experiments to illustrate the salient features of the proposed algorithm.