Learning-augmented smooth integer programs with PAC-learnable oracles
Hao-Yuan He, Jiang-Tian Xue, Ming Li, Zhi-Hua Zhou
原文摘要
We study an end-to-end learning-augmented framework for smooth integer programs, a broad class of Boolean polynomial optimization problems including MAX-CUT and MAX-k-SAT. An oracle learned from sampled instances predicts a full Boolean assignment for each unseen instance. For fixed-degree objectives, our polynomial-time pipeline, LEAP, linearizes the objective around the predicted assignment, solves an error-budgeted linear program, and rounds the fractional solution. We establish two guarantees. First, for any prediction, the approximation loss of LEAP degrades gracefully with prediction error: it is controlled by an error footprint that quantifies how much mispredicted coordinates can perturb the objective's local coefficients. Second, we bound the pseudo-dimension of the LEAP-induced cost class, yielding a PAC-style guarantee for learning an oracle from a predictor class via empirical risk minimization on instances from an unknown distribution. Together, these results give an end-to-end bound that separates the expected footprint loss of the best oracle in the class from the statistical error of learning. In experiments on MAX-CUT and MAX-SAT, LEAP substantially repairs imperfect predictions, empirical risk minimization selects effective oracle candidates, and the pipeline scales to application benchmarks with up to two million clauses.
cs.DS · cs.AI · cs.LG