  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 of the present
paper is to show that convergence rates can be accelerated dramatically through
careful design of interactions between particles. Theory focuses 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.
