发表机构
School of Information, Central University of Finance and Economics（中央财经大学信息学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究利用 CASP 方法，通过可验证证书和有界损失 PAC 保证来加速离线 NP 难优化，发展其学习理论，经实验验证该方法在处理噪声预测及分布变化时优于标准方法，能保证正确性且避免最优解损失。
AI 中文摘要
机器学习预测可加速离线 NP 难优化，但直接采用预测可能导致问题无法解决且失去最坏情况保证。CASP 询问可忽略搜索空间的哪些部分，并在多项式时间验证器检查后才接受答案，正确性不依赖预测质量。我们发展了此设计的学习理论，验证器使诱导损失类有界，证书参数可从样本中学习，而未经验证的承诺类无分布无关速率。通过可验证置信度过滤噪声预测优于标准最小组合器，实验验证了理论的定量预测。
英文摘要
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 $Ω(R/\varepsilon^2)$. 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.
