Learning-Augmented Online Covering Problems

TL;DR

This paper introduces a versatile framework that enhances online covering algorithms by integrating predictions, allowing for improved competitive ratios with accurate forecasts and graceful degradation as prediction errors increase.

Contribution

The authors present a general black-box framework that incorporates predictions into online covering algorithms, surpassing traditional worst-case bounds when predictions are accurate.

Findings

Framework applies to various online covering problems.

Achieves better competitive ratios with accurate predictions.

Degrades gracefully as prediction errors increase.

Abstract

We give a very general and simple framework to incorporate predictions on requests for online covering problems in a rigorous and black-box manner. Our framework turns any online algorithm with competitive ratio $\rho(k, \cdot)$ depending on $k$, the number of arriving requests, into an algorithm with competitive ratio of $\rho(\eta, \cdot)$, where $\eta$ is the prediction error. With accurate enough prediction, the resulting competitive ratio breaks through the corresponding worst-case online lower bounds, and smoothly degrades as the prediction error grows. This framework directly applies to a wide range of well-studied online covering problems such as facility location, Steiner problems, set cover, parking permit, etc., and yields improved and novel bounds.