Rank Collapse Is Recoverable, Growing $|Q|$ Is Not: Out-of-Sample Early Warning for Value Divergence in High-UTD Soft Actor-Critic

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-bang at the action bounds, vanilla SAC already reaches near-optimal return ($-31.6$ vs. a calibrated optimum of $-30.3$) across ten paired seeds. An ungated bypass does saturate the policy (99% of eval steps with $|a|\ge 0.9$) and collapses return to $-195.5$. A gated bypass that fires only on the flat shoulder $|a|\in[0.9,0.999]$ also fails, and does so without leaving a saturated policy. Warm-started MetaDrive fine-tuning shows the same pattern: the bypass does not improve return, and where collision rate falls it is typically traded for out-of-road departures. Auto-tuned entropy coefficient rises against the bypass, which is a push toward the tails. The Jacobian effect is real. Treating it as a bug to be undone is not free, and on the tasks studied here it is not helpful. Saturating a bound is not the same as solving a problem whose optimum lives on that bound.

Reliable temporal-difference targets are central to off-policy actor-critic learning. Direct value improvement refines the next-state target with alternative actions, but the reliability of this refinement depends on how candidate actions are ranked, reviewed, and weighted. Noisy rankings may force premature candidate commitment, reusing selection scores may bias target valuation, and fixed enhancement weights may amplify weak evidence. To address these risks, we develop Conservative Adaptive Ranking and Screening (CARS), which retains an ordered candidate prefix within a preset budget and narrows it only when the observed boundary gap exceeds a disagreement-scaled uncertainty radius. Selector-Evaluator Value Assessment (SEVA) uses selector critics to order candidates and a separately parameterized evaluator critic to review the selected value, then caps the reviewed value at the selector reference. Dynamic Adaptive Risk-aware Enhancement (DARE) then regulates each residual correction using candidate reliability, the gap between selector and evaluator signals, and a finite stage factor. Together, CARS, SEVA, and DARE form CARE-VI, an evidence-regulated target construction framework that preserves the backbone interfaces for critic regression and actor updates. The analysis bounds the CARS boundary error, the SEVA selected-value overestimation, and the one-sided deviation of the DARE residual displacement from its population counterpart, and establishes fixed-policy recovery after the finite-stage perturbation ends. Experiments with SAC, TD3, and TD7 on four MuJoCo tasks show that CARE-VI achieves the highest mean return in all twelve settings. Grouped ablations and scalar diagnostics support the roles of the three components in improving target reliability.

Significant research effort has been directed in recent years towards establishing both asymptotic and non-asymptotic convergence guarantees for two-timescale actor--critic algorithms, where the actor recursion is run on a slower timescale than the critic recursion. This work derives a uniform all-time concentration bound for the actor--critic algorithm with function approximation in the long-run average-reward setting. This bound helps us analyze the behavior of the actor parameter with high probability. We show that, after some finite time, the actor parameter enters a safe region and remains within it thereafter with high probability. Specifically, with probability at least $1-ε_1-ε_2$, the actor error $\Vert θ_k-θ^{*}\Vert$ is $O\left(\frac{n_0^{3/4}}{k}\frac{1}{\sqrt{ε_2}}+\left(\frac{1}{n_0}\right)^{1/4}\log^{1/4}\left(\frac{1}{ε_1}\right)+\left(\frac{1}{n_0}\right)^{1/4}\right)$ for all $k\geq n_0$ and sufficiently large $n_0$. We also present experimental results demonstrating that the aforementioned actor error diminishes with the number of actor-parameter updates.