Reinforcement Learning for a Discrete-Time Linear-Quadratic Control Problem with an Application

The concept of reinforcement learning (RL) can be traced back to Minsky (1954), who studied the theory of neural-analog reinforcement systems and its application to the brain model problem. Since then, RL, as a subfield of machine learning, has achieved significant theoretical and technical advancements across various fields, including engineering, biostatistics, economics, business, and financial investment. More recently, RL has shown increasing applicability to real-world problems such as biological data analysis, autonomous driving, robotics control, computer vision, and gaming. Yu et al. (2000) provided an overview of successful RL applications, highlighting its use in adaptive treatment regimes for chronic diseases and critical care, automated clinical diagnosis, and other healthcare domains like clinical resource allocation and optimal process control. They also discussed the challenges, open issues, and future directions for RL research in healthcare. Wang and Zhou (2019) noted that the application of RL in quantitative finance has attracted more attention in recent years.