Online Learning of Facility Locations

TL;DR

This paper introduces a new online learning algorithm for the Facility Location problem, providing theoretical guarantees and a quasi-linear time solution suitable for real-world applications.

Contribution

The paper develops a novel quasi-linear time algorithm for online Facility Location with strong theoretical performance guarantees.

Findings

Algorithm achieves near-optimal competitive ratio.

Significantly reduces computational complexity compared to Hedge.

Provides rigorous theoretical analysis of online facility location.

Abstract

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.