Dual recoverability gate for policy switching

(1) Integration point: place the gate immediately before action execution in an RL policy, diffusion-action sampler, or MoE router. The primary policy produces the proposed action, while a conservative fallback produces an alternative. Feed both critics the same normalized state features, including velocity, recent actions, proprioception, contact indicators, and task context if relevant. (2) Pseudocode: sample states from several upstream policies; from each state execute the primary policy for a short horizon; set \(y=1\) iff the rollout reaches \(\mathcal G\) without entering \(\mathcal F\); update \(\phi\) with the displayed binary cross-entropy. Separately roll out a fallback policy or learned dynamics model and construct a conservative reach-avoid target for \(\psi\). At inference compute \(p=\hat P_\phi(s)\) and \(v=\hat V_\psi(s)\); execute the primary action iff \(p\geq\eta_p\) and \(v\leq\eta_r\), otherwise execute fallback. (3) The Boolean gate and threshold logic come directly from the paper; probabilities, recoverability targets, and thresholds are estimated. Calibrate \(p\) on held-out trajectories and select thresholds to meet a target failure rate while maximizing primary-policy coverage. (4) First experiment: use PPO on MuJoCo Hopper or Walker2d as the primary controller and a damping or robust-policy controller as fallback. Evaluate under mass perturbations, action delays, observation noise, and initial-state shifts. Compare no gate, one critic, and the dual gate. Success is lower catastrophic-failure rate at equal reward, higher reward at a fixed failure rate, or higher safe primary-policy coverage with similar critic overhead.