# The Role of Target Update Frequencies in Q-Learning

arXiv: https://arxiv.org/abs/2602.03911 · HTML: https://mlsanity.com/paper/2602.03911/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 13 of 13)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Minimax Regret Bounds for Reinforcement Learning](https://mlsanity.com/paper/1703.05449/) (2017)
- [A Theoretical Analysis of Deep Q-Learning](https://mlsanity.com/paper/1901.00137/) (2019)
- [Understanding Multi-Step Deep Reinforcement Learning: A Systematic Study of the DQN Target](https://mlsanity.com/paper/1901.07510/) (2019)
- [Resetting the Optimizer in Deep RL: An Empirical Study](https://mlsanity.com/paper/2306.17833/) (2023)
- [Convergence rates for the Adam optimizer](https://mlsanity.com/paper/2407.21078/) (2024)
- [Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates](https://mlsanity.com/paper/1803.08600/) (2018)
- [Periodic Q-Learning](https://mlsanity.com/paper/2002.09795/) (2020)
- [ODE approximation for the Adam algorithm: General and overparametrized setting](https://mlsanity.com/paper/2511.04622/) (2025)
- [Multilevel Optimization for Inverse Problems](https://mlsanity.com/paper/2204.13732/) (2022)
- [Controlling the Flow: Stability and Convergence for Stochastic Gradient Descent with Decaying Regularization](https://mlsanity.com/paper/2505.11434/) (2025)

## Abstract (arXiv)

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.