# Online Learning of Facility Locations

arXiv: https://arxiv.org/abs/2007.02801 · HTML: https://mlsanity.com/paper/2007.02801/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Sum-max Submodular Bandits](https://mlsanity.com/paper/2311.05975/) (2023)
- [Learning-Augmented Algorithms for k-median via Online Learning](https://mlsanity.com/paper/2603.18157/) (2026)

## Abstract (arXiv)

In this paper, we provide a rigorous theoretical investigation of an online learning version of the Facility Location problem which is motivated by emerging problems in real-world applications. In our formulation, we are given a set of sites and an online sequence of user requests. At each trial, the learner selects a subset of sites and then incurs a cost for each selected site and an additional cost which is the price of the user's connection to the nearest site in the selected subset. The problem may be solved by an application of the well-known Hedge algorithm. This would, however, require time and space exponential in the number of the given sites, which motivates our design of a novel quasi-linear time algorithm for this problem, with good theoretical guarantees on its performance.