arXiv:2610.20255v1 Announce Type: new Abstract: Despite the Markov assumption, safety failures in robot reinforcement learning rarely occur instantaneously; they typically emerge over several steps as the policy enters unfamiliar states under disturbances and domain shift. We address this limitation by learning a receding-horizon safety critic that predicts whether a state will remain non-terminating over the next receding horizon, enabling anticipatory detection of impending locomotion failures. The critic is trained from rollout-derived horizon labels with a composite objective that combines horizon classification, control-barrier-function-inspired temporal consistency, and smoothness regularization, and we aggregate an ensemble of critics with a conservative Conditional Value at Risk estimate to account for uncertainty. Building on the learned critic, we derive a closed-form, differentiable CBF-style safety filter that minimally modifies the policy action to improve predicted safety, and integrate it into PPO with an anticipation loss to reduce policy-filter mismatch during training. In simulated quadruped locomotion, our method improves robustness under action noise, external perturbations, and terrain shifts, reducing catastrophic failures while maintaining competitive returns.