Machine Learning and Control Theory

TL;DR

This survey explores the deep connections between Machine Learning and Control Theory, highlighting how concepts and tools from each field can enhance the other across various problem types and methodologies.

Contribution

It provides a comprehensive review of the interplay between Machine Learning and Control Theory, including reinforcement learning, supervised learning, deep learning, and stochastic control, emphasizing their mutual benefits.

Findings

Reinforcement learning relates closely to Markov Decision Processes.

Deep learning can be viewed as a control problem.

Machine learning approaches are effective for stochastic control problems.

Abstract

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.