The Role of Target Update Frequencies in Q-Learning

• URL: http://arxiv.org/abs/2602.03911v1
• Date: Tue, 03 Feb 2026 15:19:20 GMT
• Title: The Role of Target Update Frequencies in Q-Learning
• Authors: Simon Weissmann, Tilman Aach, Benedikt Wille, Sebastian Kassing, Leif Döring,
• Abstract summary: The target network update frequency (TUF) is a central stabilization mechanism in (deep) Q-learning.<n>We formulate periodic target updates as a nested optimization scheme in which each outer iteration applies an inexact Bellman optimality operator.<n>We show that the optimal target update frequency increases geometrically over the course of the learning process.
• Score: 4.76285598583384
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The target network update frequency (TUF) is a central stabilization mechanism in (deep) Q-learning. However, their selection remains poorly understood and is often treated merely as another tunable hyperparameter rather than as a principled design decision. This work provides a theoretical analysis of target fixing in tabular Q-learning through the lens of approximate dynamic programming. We formulate periodic target updates as a nested optimization scheme in which each outer iteration applies an inexact Bellman optimality operator, approximated by a generic inner loop optimizer. Rigorous theory yields a finite-time convergence analysis for the asynchronous sampling setting, specializing to stochastic gradient descent in the inner loop. Our results deliver an explicit characterization of the bias-variance trade-off induced by the target update period, showing how to optimally set this critical hyperparameter. We prove that constant target update schedules are suboptimal, incurring a logarithmic overhead in sample complexity that is entirely avoidable with adaptive schedules. Our analysis shows that the optimal target update frequency increases geometrically over the course of the learning process.

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