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.

本文研究了在经典力学背景下，将 S 作为奖励函数，使用强化学习方法学习粒子在各种介质中传播的物理轨迹，通过在不同的折射率材料中传播的光线的情况来验证这个想法，并展示了智能体能够恢复等价于 Snell 定律或 Fermat 定律的最短时间路径。我们还讨论了强化学习与路径积分形式主义的相似性。