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)的经典工作提供了一种方案，使得对于任意$\epsilon>0$，针对一类$\mathcal{NP}$-困难问题（如Max-CUT和Max-$k$-SAT）的稠密实例，存在多项式时间的$1-\epsilon$近似算法。本文利用对数数量的一比特预测对该方案进行了扩展与加速。我们提出了一种学习增强框架，旨在设计快速算法，保证其关于预测误差的近似一致性、平滑性和鲁棒性。我们针对多种优化问题的稠密实例提供了此类算法，且这些算法对预测的使用极为精简。