Machine Learning and Control Theory
It provides a foundational overview for researchers in both fields, but is incremental as it synthesizes existing knowledge without introducing new methods.
This paper surveys the connections between Machine Learning and Control Theory, exploring how control theory provides tools for machine learning and how machine learning can solve large control problems, including reinforcement learning, supervised learning, deep learning, and stochastic gradient descent.
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.