We present learning-augmented algorithms for two general classes of online minimization problems: metrical task systems and laminar set cover. Both algorithms achieve improved theoretical guarantees using machine-learned predictions of an optimal solution to the dual linear program. Unlike optimal primal solutions, which can change drastically under tiny instance perturbations, these dual solutions are much more stable, which ensures the existence of good (and learnable) predictions for families of similar instances. While previous work has used dual predictions in offline settings and for online maximization problems, our algorithms are, to the best of our knowledge, the first demonstration that such dual predictions can be effective for online minimization. Our theoretical results are complemented by experiments on the $k$-server problem and the parking permit problem.

翻译：我们针对两类通用的在线最小化问题（度量任务系统与层状集合覆盖）提出了学习增强型算法。这两类算法通过利用对偶线性规划最优解的机器学习预测，实现了改进的理论保证。与最优原始解（其在微小实例扰动下可能发生剧烈变化）不同，这些对偶解具有显著稳定性，从而保证了对于相似实例族存在优质（且可学习）的预测。尽管先前工作已在离线场景及在线最大化问题中应用对偶预测，但据我们所知，本文提出的算法首次证明了这类对偶预测能够有效应用于在线最小化问题。我们通过$k$-服务器问题与停车许可问题的实验对理论结果进行了补充验证。