SAFTER: Safety-Aware Filtering Through Explicit Recoverability for Robust Reinforcement Learning under Distribution Shift

Learning safe policies that generalize to unseen environments is difficult under bounded actuation, where an unsafe decision may become unrecoverable. Conventional control barrier function (CBF) filters enforce only instantaneous safety and ignore future recoverability. We propose SAFTER (Safety-Aware Filtering Through Explicit Recoverability), which embeds a differentiable, closed-form backup-CBF filter into Soft Actor-Critic training. SAFTER unifies current safety, finite-horizon backup safety, terminal recoverability, and input admissibility into a single differentiable certificate. Its CBF condition yields an exact minimum-intervention projection without iterative online optimization. In quadruped navigation, SAFTER reaches 90% training success with 30.6% fewer transitions than Vanilla SAC and 34.1-35.1% fewer than current-state CBF-filtered SAC baselines. Across unseen simulated environments, SAFTER improves success by up to 42.4 and 61.4 percentage points over the state-of-the-art methods CBF-RL and SEA-Nav, respectively, and achieves 73.3% and 76.7% success on two real-world navigation maps. Ablations identify accurate differentiation through the safety filter as a key contributor to robustness, in which replacing the projection Jacobian with the identity approximation reduces success rate in a High-Shift environment from 61.4% to 6.2%. These results show that recoverability-aware filtering serves as both a runtime safety mechanism and a learning mechanism for sample-efficient, robust policies.