Double Coverage with Machine-Learned Advice

TL;DR

This paper introduces a learning-augmented version of the Double Coverage algorithm for the k-server problem on a line, which adaptively balances trust in machine-learned advice with robustness, improving performance especially with accurate predictions.

Contribution

It presents a novel memoryless, learning-augmented algorithm for the k-server problem that achieves an optimal tradeoff between consistency and robustness, outperforming previous advice-based algorithms.

Findings

Achieves an error-dependent competitive ratio interpolating between optimal consistency and robustness.

Outperforms previous advice-based algorithms, especially with high-quality predictions.

Demonstrates practical effectiveness through experiments on real-world data.

Abstract

We study the fundamental online k-server problem in a learning-augmented setting. While in the traditional online model, an algorithm has no information about the request sequence, we assume that there is given some advice (e.g. machine-learned predictions) on an algorithm's decision. There is, however, no guarantee on the quality of the prediction and it might be far from being correct. Our main result is a learning-augmented variation of the well-known Double Coverage algorithm for k-server on the line (Chrobak et al., SIDMA 1991) in which we integrate predictions as well as our trust into their quality. We give an error-dependent competitive ratio, which is a function of a user-defined confidence parameter, and which interpolates smoothly between an optimal consistency, the performance in case that all predictions are correct, and the best-possible robustness regardless of the prediction quality. When given good predictions, we improve upon known lower bounds for online algorithms without advice. We further show that our algorithm achieves for any k an almost optimal consistency-robustness tradeoff, within a class of deterministic algorithms respecting local and memoryless properties. Our algorithm outperforms a previously proposed (more general) learning-augmented algorithm. It is remarkable that the previous algorithm crucially exploits memory, whereas our algorithm is memoryless. Finally, we demonstrate in experiments the practicability and the superior performance of our algorithm on real-world data.