Improving Online Algorithms via ML Predictions (2407.17712v1)

Abstract: In this work we study the problem of using machine-learned predictions to improve the performance of online algorithms. We consider two classical problems, ski rental and non-clairvoyant job scheduling, and obtain new online algorithms that use predictions to make their decisions. These algorithms are oblivious to the performance of the predictor, improve with better predictions, but do not degrade much if the predictions are poor.

• The paper introduces ML-enhanced algorithms that improve competitive ratios by balancing consistency with robustness.
• For the ski rental problem, both deterministic and randomized strategies are designed with competitive ratios tuned by a trade-off parameter.
• In non-clairvoyant job scheduling, the Preferential Round-Robin algorithm leverages predictions to achieve notable performance gains.

An Insightful Overview of "Improving Online Algorithms via ML Predictions"

In the paper "Improving Online Algorithms via ML Predictions," the authors explore the employment of machine-learned predictions to enhance the performance of online algorithms. They concentrate on two exemplary problems, the ski rental problem and non-clairvoyant job scheduling, where predictions provide a significant advantage. The key contribution of this work is the design of algorithms that, when leveraging predictions, demonstrate improved competitive ratios in cases of accurate predictions while remaining robust against erroneous predictions.

Methodological Innovations and Key Results

The paper investigates a paradigm where online algorithms incorporate ML-based predictions without assuming any intervals about predictor performance. It introduces consistency and robustness as dual objectives for algorithm evaluation:

• Consistency ensures that algorithms perform close to optimal when predictions are accurate.
• Robustness guarantees acceptable performance akin to classical online algorithms when predictions are faulty.

Ski Rental Problem

For the ski rental domain, the paper proposes both deterministic and randomized algorithms. In particular:

• A deterministic approach achieves a competitive ratio of $1 + \frac{1}{\lambda}$ for robustness and $1 + \lambda$ for consistency, where $\lambda$ is a chosen trade-off parameter.
• A more sophisticated randomized strategy proposes robustness of $\frac{1 + 1/b}{1 - e^{-(\lambda - 1/b)}}$ and consistency bounded by $\frac{1}{1 - e^{-\lambda}}$, enhancing the balance of robustness and consistency over deterministic methods.

Non-clairvoyant Job Scheduling

For non-clairvoyant job scheduling, the Preferential Round-Robin algorithm is introduced, leveraging sorting by predictions and a preferential treatment for shorter predicted tasks. It has a competitive ratio of $$\min\left\{\frac{1 + \lambda n}{2}, \frac{2}{1-\lambda}\right\}$$, with notable improvements when prediction errors are low.

Implications of Research and Future Directions

This paper contributes significantly to the ongoing discourse on integrating machine learning predictions into classical online algorithm design, offering empirical evidence of performance enhancements under varied prediction accuracies. The bridging of ML outputs with robust algorithmic techniques could lead to computational benefits in fields where uncertainties play a pivotal role, such as cloud resource management, task scheduling in operating systems, and dynamic pricing.

Future exploration could be directed towards extending these theoretical models to more complex scenarios like multi-dimensional decision spaces, online models beyond the single-decision making framework, or cross-domain problems such as the k-server problem. Additionally, understanding the impact of prediction error distributions, beyond the examined settings, might reveal further optimization opportunities. As ML algorithms increasingly shape predictive landscapes, robust integration with online decision-making remains a fertile research trajectory.