Interacting Particle Systems for Fast Linear Quadratic RL

TL;DR

This paper introduces a particle interaction-based algorithm for linear quadratic reinforcement learning, significantly accelerating convergence and providing theoretical guarantees on sample complexity and error scaling.

Contribution

It presents a novel particle interaction algorithm for RL with proven faster convergence and theoretical error bounds in the linear quadratic setting.

Findings

Mean square error scales as 1/N with N particles

Algorithm demonstrates faster convergence in numerical experiments

Provides new theoretical bounds for sample complexity

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. 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.