2022/02/14 by Xingang Guo, Bin Hu, Guo, Xingang +1
Economics, Econometrics and Finance · #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Health Systems, Economic Evaluations, Quality of Life #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2202.06922
openalex publication_date 2022/02/14 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
Value-based methods play a fundamental role in Markov decision processes (MDPs) and reinforcement learning (RL). In this paper, we present a unified control-theoretic framework for analyzing valued-based methods such as value computation (VC), value iteration (VI), and temporal difference (TD) learning (with linear function approximation). Built upon an intrinsic connection between value-based methods and dynamic systems, we can directly use existing convex testing conditions in control theory to derive various convergence results for the aforementioned value-based methods. These testing conditions are convex programs in form of either linear programming (LP) or semidefinite programming (SDP), and can be solved to construct Lyapunov functions in a straightforward manner. Our analysis reveals some intriguing connections between feedback control systems and RL algorithms. It is our hope that such connections can inspire more work at the intersection of system/control theory and RL.