Learning Principle of Least Action with Reinforcement Learning

TL;DR

This paper introduces a reinforcement learning approach to physics, where agents learn physical trajectories by optimizing the action integral, demonstrating the method on light refraction and connecting it to classical principles.

Contribution

The paper proposes a novel reinforcement learning framework that incorporates the principle of least action to learn physical paths, verified through light refraction experiments.

Findings

Agent recovers minimal-time paths consistent with Fermat's principle

Reinforcement learning aligns with classical physics laws

Method connects path integral formalism with RL

Abstract

Nature provides a way to understand physics with reinforcement learning since nature favors the economical way for an object to propagate. In the case of classical mechanics, nature favors the object to move along the path according to the integral of the Lagrangian, called the action $\mathcal{S}$. We consider setting the reward/penalty as a function of $\mathcal{S}$, so the agent could learn the physical trajectory of particles in various kinds of environments with reinforcement learning. In this work, we verified the idea by using a Q-Learning based algorithm on learning how light propagates in materials with different refraction indices, and show that the agent could recover the minimal-time path equivalent to the solution obtained by Snell's law or Fermat's Principle. We also discuss the similarity of our reinforcement learning approach to the path integral formalism.