Convex Programs and Lyapunov Functions for Reinforcement Learning: A Unified Perspective on the Analysis of Value-Based Methods
This work provides a novel theoretical perspective for analyzing RL algorithms, potentially benefiting researchers in reinforcement learning and control theory by bridging these fields.
The authors tackled the analysis of value-based reinforcement learning methods by developing a unified control-theoretic framework that connects them to dynamic systems, enabling the use of convex programs to derive convergence results and construct Lyapunov functions.
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.