论文标题
机器学习和控制理论
Machine Learning and Control Theory
论文作者
论文摘要
我们在本文中调查了机器学习与控制理论之间的联系。控制理论为机器学习提供了有用的概念和工具。相反的机器学习可用于解决大型控制问题。在本文的第一部分中，我们开发了加强学习与马尔可夫决策过程之间的联系，这是离散的时间控制问题。在第二部分中，我们回顾了监督学习的概念以及与静态优化的关系。扩展监督学习的深度学习可以看作是控制问题。在第三部分中，我们介绍了随机梯度下降与平均场理论之间的联系。相反，在第四部分和第五部分中，我们回顾了机器学习方法来解决随机控制问题，并专注于确定性案例，以更容易地解释数值算法。
We survey in this article the connections between Machine Learning and Control Theory. Control Theory provide useful concepts and tools for Machine Learning. Conversely Machine Learning can be used to solve large control problems. In the first part of the paper, we develop the connections between reinforcement learning and Markov Decision Processes, which are discrete time control problems. In the second part, we review the concept of supervised learning and the relation with static optimization. Deep learning which extends supervised learning, can be viewed as a control problem. In the third part, we present the links between stochastic gradient descent and mean-field theory. Conversely, in the fourth and fifth parts, we review machine learning approaches to stochastic control problems, and focus on the deterministic case, to explain, more easily, the numerical algorithms.
