Learning-augmented smooth integer programs with PAC-learnable oracles

TL;DR

This paper presents a learning-augmented framework for smooth integer programs that uses PAC-learnable oracles to improve approximation quality, extending classical results to near-dense regimes.

Contribution

It introduces a novel framework combining predictive oracles with linear programming for smooth integer programs, and proves the PAC-learnability of these oracles.

Findings

Framework extends tractability to near-dense regimes.

Oracle class has bounded pseudo-dimension.

Oracle can be learned with polynomial samples.

Abstract

This paper investigates learning-augmented algorithms for smooth integer programs, covering canonical problems such as MAX-CUT and MAX-k-SAT. We introduce a framework that incorporates a predictive oracle to construct a linear surrogate of the objective, which is then solved via linear programming followed by a rounding procedure. Crucially, our framework ensures that the solution quality is both consistent and smooth against prediction errors. We demonstrate that this approach effectively extends tractable approximations from the classical dense regime to the near-dense regime. Furthermore, we go beyond the assumption of oracle existence by establishing its PAC-learnability. We prove that the induced algorithm class possesses a bounded pseudo-dimension, thereby ensuring that an oracle with near-optimal expected performance can be learned with polynomial samples.