论文标题
通过增强学习的学习原理最少动作
Learning Principle of Least Action with Reinforcement Learning
论文作者
论文摘要
大自然提供了一种通过增强学习来理解物理学的方法，因为自然有利于对象传播的经济方式。在经典力学的情况下，自然有利于根据拉格朗日的积分沿路径移动的对象，称为动作$ \ Mathcal {s} $。我们考虑将奖励/惩罚设置为$ \ Mathcal {s} $的函数，因此代理可以通过增强学习在各种环境中学习粒子的物理轨迹。在这项工作中，我们通过使用基于Q学习的算法来验证了这一想法，该算法在学习具有不同折射率指数的材料中如何传播光线，并证明代理可以恢复与Snell定律或费米特原理获得的解决方案相等的最小时间路径。我们还讨论了我们强化学习方法与整体形式主义的相似性。
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.
