The emerging field of learning-augmented online algorithms uses ML techniques
to predict future input parameters and thereby improve the performance of
online algorithms. Since these parameters are, in general, real-valued
functions, a natural approach is to use regression techniques to make these
predictions. We introduce this approach in this paper, and explore it in the
context of a general online search framework that captures classic problems
like (generalized) ski rental, bin packing, minimum makespan scheduling, etc.
We show nearly tight bounds on the sample complexity of this regression
problem, and extend our results to the agnostic setting. From a technical
standpoint, we show that the key is to incorporate online optimization
benchmarks in the design of the loss function for the regression problem,
thereby diverging from the use of off-the-shelf regression tools with standard
bounds on statistical error.

本文介绍了在学习增强的在线算法中使用回归技术来预测未来输入参数的方法，并在广义滑雪租赁、装箱问题、最小完成时间调度等一般在线搜索方案的背景下探讨了这种方法。通过在设计回归问题的损失函数中结合在线优化基准，我们显示了这种回归问题样本复杂度的近似上下界，并将我们的结果扩展到了不可知设置。