Ultra-Local Neural Safety Shield

1. Exact integration point: place the shield after the neural policy output and before the environment or actuator. The policy produces $u_k^{NN}$; the shield modifies it only when the robust barrier is violated. Measure the scalar safety output $y_k$ and estimate its derivative with a filtered finite difference, for example $\widehat{\dot y}_k=(y_k-y_{k-1})/T_s$ followed by an exponential low-pass filter. Maintain $\theta_k=[\widehat F_k,\widehat\beta_k]$. 2. Pseudocode: compute $r_k=\widehat{\dot y}_k-[1,u_{k-1}]\theta_k$; update $\theta\leftarrow\theta+\eta_\theta[1,u_{k-1}]^\top r_k$; calculate recent residuals $r_{k-j}$ and a Welford running mean and variance; set $\widehat\Delta_m=q\sqrt{v_r}+b_r$, where q is 2 or 3 and $b_r$ is a recent absolute-residual or drift allowance; solve the one-dimensional quadratic program above, clipping to actuator limits. Reject or freeze the estimate when $|\widehat\beta|<\beta_{\min}$, since the barrier then has no reliable control authority. 3. Computed from the paper: the ultra-local regression, recursive gradient update, uncertainty-envelope propagation, and robust barrier inequality. Estimated empirically: derivative noise, residual variance, drift allowance, q, $k_c$, and feasibility frequency. 4. First cheap experiment: use a two-dimensional point-mass navigation task or an adaptive-cruise-control simulator, with a small MLP policy and distance y as safety output. Compare PPO or SAC with no shield, a nominal CBF using $\widehat F,\widehat\beta$ but no uncertainty, and this robust shield. Sweep action-step size and disturbance magnitude. The predicted signature is that violations remain near zero while the nominal shield fails once residual magnitude exceeds its unmodeled margin; the robust shield should begin rejecting actions when $y<y_{\min}+\widehat\Delta_m/k_c$, and measured violations should concentrate in samples where $|\delta_k|>\widehat\Delta_{m,k}$. Test whether violation rate rises sharply when $|\delta_k|/\widehat\Delta_{m,k}>1$, and whether increasing $k_c$ reduces the virtual-boundary shift approximately as $1/k_c$.