An analysis of Mirror-Descent Soft Actor-Critic

Abstract:Soft Actor-Critic (SAC) is widely used for entropy-regularised reinforcement learning with continuous action spaces, and practical implementations perform only a few actor steps towards an evolving target. In this work, we prove convergence guarantees when the target policy arises from policy mirror descent and compare it with the classical Gibbs target. We derive sufficient conditions for the strong convexity and smoothness of the actor objective, characterised by the curvature of the $Q$-function estimate through the Legendre differential operator, and establish an $\mathcal{O}\!\left(N^{-\frac{1}{5}}\right)$ best-iterate finite-time convergence rate up to actor and critic approximation errors. Moreover, the mirror-descent step size $\lambda$ directly controls the target drift and hence actor tracking error, whereas the analogous Gibbs bound contains a non-vanishing tracking term.

Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2609.35466 [cs.LG]

(or arXiv:2609.35466v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.35466 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.