Sign-Separated Finite-Time Error Analysis of Q-Learning
Abstract
This paper develops a sign-separated finite-time error analysis for constant step-size Q-learning. Starting from the switching-system representation, the error is decomposed into its componentwise negative and positive parts. The negative part is dominated by a lower comparison linear time-invariant (LTI) system associated with a fixed optimal policy, whereas the positive part is controlled by a linear switching system. The resulting bounds show that the negative-side LTI certificate is no slower than the positive-side switching certificate and may produce a faster exponential envelope. The analysis identifies a max-induced asymmetry in Q-learning error dynamics. This asymmetry is connected to overestimation: positive action-wise errors can be selected and propagated by the Bellman maximum, whereas negative errors admit an optimal-policy lower comparison. Finite-time bounds are provided for both deterministic and stochastic constant-step-size recursions.
Cite
@article{arxiv.2605.16103,
title = {Sign-Separated Finite-Time Error Analysis of Q-Learning},
author = {Donghwan Lee},
journal= {arXiv preprint arXiv:2605.16103},
year = {2026}
}