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Unthrottling the Tanh Jacobian in SAC: A Negative Result on Bang-Bang Control and MetaDrive

arXiv · AI, language, vision and robotics · article · Sep 8, 2026 · UTC

Soft Actor-Critic (SAC) represents a continuous policy as an unbounded Gaussian that is squashed by tanh. The Jacobian of that map is $\partial a/\partial u = 1-a^2$, which vanishes as $|a|\to 1$. A natural concern is that this throttle starves the actor of critic signal exactly where extreme actions (full brake, full throttle) are optimal. We test a minimal intervention that restores the missing signal: one extra term in the actor loss whose gradient on the pre-tanh mean is the detached action-gradient of $Q$, with no gain parameter. On a minimum-time double integrator whose optimum is bang-b

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