The classical work of (Arora et al., 1999) provides a scheme that gives, for any $\epsilon>0$, a polynomial time $1-\epsilon$ approximation algorithm for dense instances of a family of $\mathcal{NP}$-hard problems, such as Max-CUT and Max-$k$-SAT. In this paper we extend and speed up this scheme using a logarithmic number of one-bit predictions. We propose a learning augmented framework which aims at finding fast algorithms which guarantees approximation consistency, smoothness and robustness with respect to the prediction error. We provide such algorithms, which moreover use predictions parsimoniously, for dense instances of various optimization problems.

翻译：（Arora等人，1999）的经典工作提出了一种方案，该方案对于任意$\epsilon>0$，能够为一系列$\mathcal{NP}$难问题（例如Max-CUT和Max-$k$-SAT）的稠密实例提供多项式时间的$1-\epsilon$近似算法。在本文中，我们利用对数个单比特预测来扩展并加速这一方案。我们提出了一个学习增强框架，旨在寻找能够保证近似一致性、平滑性以及对预测误差具有鲁棒性的快速算法。我们为此类稠密实例的多种优化问题提供了相应的算法，并且这些算法能够以稀疏的方式使用预测信息。