Safe Reinforcement Learning with Receding-Horizon Safety Critic and Differentiable Action Shields

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.

Reinforcement learning (RL) policies enable dynamic legged locomotion but lack mechanisms to avoid violations of safety constraints that are absent during training. Large-scale offline safe learning is impractical for covering all edge cases. Existing safety frameworks either rely on reduced-order models that cannot reason about whole-body behaviors or require conservative recovery controllers that degrade task performance. We propose a predictive safety filter that post-hoc filters the nominal contact locations fed to the RL policy. When a collision is predicted, a sampling-based optimizer asynchronously searches for safer contact sequences using a full-physics model, while a learned value function bootstraps long-horizon returns. Our three algorithmic components (geometric projection of sampled contacts, momentum-augmented updates, and replica-exchange) make the optimization tractable in a discontinuous contact landscape. We validate the filter on a quadruped robot in dense, cluttered environments, both in simulation and in the real world, showing substantial reductions in safety violations with minimal deviation from the nominal input.

Safe reinforcement learning (RL) for robotic systems requires policies that improve task performance while satisfying state and input constraints during both training and deployment. Control barrier functions (CBFs) provide a principled mechanism for enforcing forward invariance through minimally invasive safety filters, but their use in model-free RL is limited by the need for accurate dynamics and hand-designed barrier certificates. We propose Robust Koopman-CBF SAC, a safety-filtered actor--critic framework that learns a finite-dimensional Koopman predictor from data, constructs affine CBF constraints in the lifted space, and enforces them through a quadratic-program safety layer. To account for finite-dimensional Koopman approximation error, the CBF condition is tightened using a projected residual margin estimated from held-out rollout data. The critic is trained on the executed safe action, while the actor is regularized toward the Koopman-CBF feasible set, reducing dependence on the filter over training. Across safe-control benchmarks, the method achieves zero constraint violations on CartPole stabilization and tracking while matching or exceeding unconstrained SAC returns. On high-dimensional Safety Gymnasium locomotion tasks, the method reduces violations in some settings but also exposes important limitations of first-order velocity barriers and linear EDMD models, motivating high-order and multi-step Koopman-CBF extensions. These results suggest that robust Koopman-CBF filters are a promising bridge between model-free RL and certifiable safety, while clarifying the structural conditions under which such filters remain effective.