Following the research agenda initiated by Munoz & Vassilvitskii [1] and Lykouris & Vassilvitskii [2] on learning-augmented online algorithms for classical online optimization problems, in this work, we consider the Online Facility Location problem under this framework. In Online Facility Location (OFL), demands arrive one-by-one in a metric space and must be (irrevocably) assigned to an open facility upon arrival, without any knowledge about future demands. We present an online algorithm for OFL that exploits potentially imperfect predictions on the locations of the optimal facilities. We prove that the competitive ratio decreases smoothly from sublogarithmic in the number of demands to constant, as the error, i.e., the total distance of the predicted locations to the optimal facility locations, decreases towards zero. We complement our analysis with a matching lower bound establishing that the dependence of the algorithm's competitive ratio on the error is optimal, up to constant factors. Finally, we evaluate our algorithm on real world data and compare our learning augmented approach with the current best online algorithm for the problem.

翻译：遵循Munoz & Vassilvitskii [1]与Lykouris & Vassilvitskii [2]提出的关于经典在线优化问题的学习增强型在线算法研究议程，本文在此框架下考虑在线设施选址问题。在线设施选址问题中，需求在度量空间中逐一到达，且必须在到达时（不可撤销地）分配给某个已开放的设施，而未来需求信息完全未知。我们提出一种利用最优设施位置可能不完美预测的在线设施选址算法。我们证明，当预测误差（即预测位置与最优设施位置之间的总距离）趋近于零时，算法竞争比从关于需求数量的次对数函数平滑下降至常数。我们通过匹配下界分析证明，算法竞争比关于误差的依赖性在常数因子意义下达到最优。最后，我们使用真实数据评估算法性能，并将本文提出的学习增强方法与当前该问题最优在线算法进行对比。