Sign-Separated Finite-Time Error Analysis of Q-Learning

arXiv:2605.16103v1 Announce Type: new 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.

Source: arXiv cs.AI | 2026-05-18