Heavy-Ball Q-Learning with Residual Weighting Correction

Donghwan Lee

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arXiv · 2606.27112

Heavy-Ball Q-Learning with Residual Weighting Correction

Donghwan Lee

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Abstract

This paper proposes a corrected heavy-ball Q-learning method for reinforcement learning (RL) and establishes convergence of its deterministic mean dynamics. It also identifies conditions under which the method is theoretically guaranteed to converge faster than standard Q-learning. The same construction is then extended to Q-learning with linear function approximation, where analogous convergence and acceleration statements are derived for the corresponding corrected fixed point. The sampled stochastic versions are treated through conditional-mean recursions and, in the stated linear-function-approximation setting, finite-time bounds. The analysis is based on a switched linear system (SLS) representation of Q-learning algorithms and on the joint spectral radius (JSR) of the associated switching families. This SLS viewpoint is not commonly used in standard analyses of Q-learning, and it provides a complementary framework and new insight into how heavy-ball momentum can accelerate Q-learning.

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Donghwan Lee. 2026-06-25. Heavy-Ball Q-Learning with Residual Weighting Correction. https://arxiv.org/abs/2606.27112

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