Metrical Task Systems with Online Machine Learned Advice

TL;DR

This paper explores how machine learned advice can improve online algorithms for the Metrical Task Systems problem, achieving better competitive ratios when the predictor's error is bounded.

Contribution

It introduces a new online algorithm leveraging machine learning advice for uniform Metrical Task Systems, reducing the competitive ratio based on predictor accuracy.

Findings

Achieves a competitive ratio of Θ(min(√η₀, log n)) with learned advice.

Provides a Θ(log η₀) lower bound on randomized algorithms.

Demonstrates the benefit of machine learning advice in online dynamic systems.

Abstract

Machine learning algorithms are designed to make accurate predictions of the future based on existing data, while online algorithms seek to bound some performance measure (typically the competitive ratio) without knowledge of the future. Lykouris and Vassilvitskii demonstrated that augmenting online algorithms with a machine learned predictor can provably decrease the competitive ratio under as long as the predictor is suitably accurate. In this work we apply this idea to the Online Metrical Task System problem, which was put forth by Borodin, Linial, and Saks as a general model for dynamic systems processing tasks in an online fashion. We focus on the specific class of uniform task systems on $n$ tasks, for which the best deterministic algorithm is $O(n)$ competitive and the best randomized algorithm is $O(\log n)$ competitive. By giving an online algorithms access to a machine learned oracle with absolute predictive error bounded above by $\eta_0$, we construct a $\Theta(\min(\sqrt{\eta_0}, \log n))$ competitive algorithm for the uniform case of the metrical task systems problem. We also give a $\Theta(\log \eta_0)$ lower bound on the competitive ratio of any randomized algorithm.