New Research Presents Lyapunov-Certified Direct Switching Theory for Q-Learning

A recent theoretical framework offers an analysis of Q-learning, a key algorithm in reinforcement learning, through a representation of direct stochastic switching systems. The study reveals that the Bellman maximization error can be precisely depicted by a stochastic policy, leading to the Q-learning error being formulated as a switched linear conditional-mean recursion accompanied by martingale-difference noise. The intrinsic drift rate is recognized as the joint spectral radius of the direct switching family, which may be less than the conventional row-sum rate. This representation facilitates the derivation of a finite-time final-iterate bound using a JSR-induced Lyapunov function, along with a computable quadratic-certificate version. Published on arXiv under Computer Science > Machine Learning, the paper, identified as arXiv:2604.19569, enhances the theoretical framework of reinforcement learning by providing new analytical tools and performance bounds. Additionally, the arXivLabs framework is acknowledged for supporting collaborative experimental projects focused on openness and user data privacy.