CASP Improves NP-Hard Optimization with Verifiable AI Predictions

This research introduces CASP, a novel approach to enhance offline NP-hard optimization problems using machine learning. Unlike traditional methods where AI directly proposes solutions, CASP leverages AI to identify parts of the search space that can be safely ignored. Crucially, every AI-suggested pruning action is subjected to a sound, polynomial-time verifier, ensuring that the overall correctness of the optimization process never depends on the AI's prediction quality. The paper develops a learning theory for this design, demonstrating that the verifier makes the induced loss class uniformly bounded, allowing certificate parameters to be learned efficiently. This verifiable filtering of noisy predictions significantly outperforms standard unverified approaches, especially under distribution shifts, where unverified pruning can lead to substantial losses in optimality. CASP's ability to break ties on degenerate optimal faces, where symmetric policies often fail, further highlights its utility.