On the Convergence of Semi-Gradient TD: A Mean Field Perspective

Abstract:Semi-gradient temporal-difference learning is a core algorithmic component of reinforcement learning, but bootstrapping with function approximation generally induces a non-conservative vector field and can lead to instability. We analyze this effect for two-layer neural networks in the mean-field regime and identify a simple stability mechanism in which entropy-induced relaxation dominates the sensitivity of the moving bootstrap target. Under this condition, we prove exponential convergence to a unique fixed point and quantify its bias relative to the unregularized Bellman solution. We also show that the same mechanism extends to entropy-regularized off-policy control through soft Q-learning.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.20014 [cs.LG]

(or arXiv:2610.20014v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.20014 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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