Lyapunov-Certified Direct Switching Theory for Q-Learning

arXiv:2604.19569v1 Announce Type: cross Abstract: Q-learning is one of the most fundamental algorithms in reinforcement learning. We analyze constant-stepsize Q-learning through a direct stochastic switching system representation. The key observation is that the Bellman maximization error can be represented exactly by a stochastic policy. Therefore, the Q-learning error admits a switched linear conditional-mean recursion with martingale-difference noise. The intrinsic drift rate is the joint spe