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The paper introduces CASP (Certificate-Augmented Solution Pruning), a method that enhances offline NP-hard optimization by allowing machine-learned predictions to be verified before being accepted, thus maintaining worst-case guarantees. By employing a polynomial-time verifier, CASP ensures that only sound predictions are considered, leading to a uniformly bounded loss class that can be learned efficiently. Experiments demonstrate that while unverified pruning can lose up to 26% of the optimal solution under distribution shifts, the verified approach maintains optimality, showcasing the robustness of the method.
Verifiable predictions in optimization can prevent up to 26% loss in performance under distribution shifts, ensuring reliability in machine-learned solutions.
Machine-learned predictions can speed up offline NP-hard optimization, but asking a predictor what to do amounts to asking it to solve the problem, and committing an unchecked prediction forfeits every worst-case guarantee. CASP (Certificate-Augmented Solution Pruning) instead asks which parts of the search space may be ignored, and accepts each answer only after a sound polynomial-time verifier has checked it, so correctness never depends on prediction quality. We develop the learning theory of this design. The verifier makes the induced loss class uniformly bounded, so certificate parameters are learnable from $\tilde O(\varepsilon^{-2}\log K)$ samples ($K$ the maximum instance size), whereas the unverified commitment class admits no distribution-free rate and, under cost spread $R$, none below $\Omega(R/\varepsilon^2)$. Filtering noisy predictions by verifiable confidence dominates the standard min-combiner, with a margin we compute in closed form, and the prediction stays useful even given the LP, because it breaks ties on degenerate optimal faces, where every symmetric LP policy, meaning one whose commitments depend on the instance only through the verifiable confidence values, provably stalls. Experiments on five problems test the theory's quantitative predictions. With trained predictors, unverified pruning loses up to $26%$ of the optimum under distribution shift, while the verified deployment of the same predictions loses nothing.