Learning-augmented algorithms have been extensively studied across the computer science community in the recent years, driven by advances in machine learning predictors, which can provide additional information to augment classical algorithms. Such predictions are especially powerful in the context of online problems, where decisions have to be made without knowledge of the future, and which traditionally exhibits impossibility results bounding the performance of any online algorithm. The study of learning-augmented algorithms thus aims to use external advice prudently, to overcome classical impossibility results when the advice is accurate, and still perform comparably to the state-of-the-art online algorithms even when the advice is inaccurate. In this paper, we present learning-augmented algorithmic frameworks for two fundamental optimizations settings, extending and generalizing prior works. For online packing with concave objectives, we present a simple but overarching strategy that switches between the advice and the state-of-the-art online algorithm. For online covering with convex objectives, we greatly extend primal-dual methods for online convex covering programs by Azar et al. (FOCS 2016) and previous learning-augmented framework for online covering linear programs from the literature, to many new applications. We show that our algorithms break impossibility results when the advice is accurate, while maintaining comparable performance with state-of-the-art classical online algorithms even when the advice is erroneous.

翻译：近年来，随着机器学习预测器的进步，学习增强算法在整个计算机科学领域得到了广泛研究。这些预测器能够为经典算法提供额外信息，从而增强其性能。此类预测在在线问题背景下尤其强大，因为在线问题需要在未知未来的情况下做出决策，并且传统上存在限制任何在线算法性能的不可能性结果。因此，学习增强算法的研究旨在审慎利用外部建议：当建议准确时克服经典的不可能性结果；即使建议不准确，仍能保持与最先进在线算法相当的性能。本文针对两种基础优化场景提出了学习增强算法框架，扩展并推广了先前的研究工作。对于具有凹目标的在线打包问题，我们提出了一种简洁但普适的策略，可在建议与最先进在线算法之间进行切换。对于具有凸目标的在线覆盖问题，我们极大地扩展了Azar等人（FOCS 2016）提出的在线凸覆盖规划原始对偶方法，以及文献中现有的在线覆盖线性规划学习增强框架，将其应用于众多新场景。我们证明，当建议准确时，我们的算法能够突破不可能性结果的限制；即使建议存在误差，仍能保持与最先进经典在线算法相当的性能。