Large-Deviation Safety Buffer

Integrate this at the decision layer of an online RL or model-monitoring system, rather than inside the neural network's forward pass. Define a binary violation at each future step, such as reward below a safety floor, constraint breach, abstention failure, or prediction error above a tolerance. Maintain a fixed historical window of n binary outcomes, compute the violation count S and q=S/n, choose a target joint failure probability delta, and set c=log(1/delta)/n. Numerically evaluate the profile on a grid y_j in (epsilon, gamma(q)-epsilon] and include a small-y region; compute p_y=1/(1+exp(y_j)), d_j=q*log(q/p_y)+(1-q)*log((1-q)/(1-p_y)), r_j=max(c-d_j,0)/y_j, and f=max_j r_j. Use stable log-domain operations and clip q to [epsilon, 1/2-epsilon]. Set the cumulative future buffer to C=n*f and trigger intervention, policy fallback, early stopping, or abstention when the future random-walk maximum exceeds C. Pseudocode: observe violations; update S and q; compute c; loop over y values; calculate p_y, d_j, and r_j; set C=n*max(r_j); monitor cumulative signed risk and intervene at C. The paper supplies the profile and Lundberg mechanism; q is estimated directly from data and the y grid is a numerical approximation. First test on a small CartPole constraint task or a synthetic Bernoulli random walk with an RL policy. Compare against the plug-in buffer C_plugin=log(1/delta)/gamma(q), a Hoeffding upper-confidence buffer, and a fixed conservative threshold. Use independent historical and future trials with n in {32,64,128,256}. Success means empirical probability of any future breach is at or below the target delta while producing fewer unnecessary interventions than confidence-bound baselines.