Algorithms for Caching and Metrical Task Systems with Reduced Number of Predictions

Core Concepts

We design parsimonious algorithms for caching and metrical task systems that use a reduced number of predictions while achieving strong consistency, robustness, and smoothness guarantees.

Abstract

The paper proposes algorithms for caching and metrical task systems (MTS) that use a reduced number of predictions while maintaining strong performance guarantees.
For caching:

The algorithm, called F&R, consists of two parts: Follower and Robust.
Follower is 1-consistent (optimal with perfect predictions) but lacks robustness and smoothness.
Robust is used when Follower detects an incorrect prediction, providing the desired robustness and smoothness.
The algorithm uses O(f(log k)) OPT predictions, where f is an increasing convex function, and achieves consistency 1, robustness O(log k), and smoothness O(f^-1(η/OPT)).
For general MTS:

The algorithm queries the predictor only once every a time steps, making at most T/a queries in total.
It achieves consistency O(a) and smoothness O(a)(1 + 2η/OFF), where OFF is the cost of an arbitrary offline algorithm and η is the prediction error.
The algorithm can be combined with any online algorithm for MTS to achieve robustness comparable to that algorithm.
The paper also provides lower bounds, showing that the number of predictions used by the algorithms is close to optimal and that the smoothness cannot be improved beyond a certain threshold when the predictions are queried only periodically.

Stats

The number of page faults incurred by the offline optimal solution (OPT) is used to bound the number of predictions required by the caching algorithm.
The cost of an arbitrary offline algorithm (OFF) is used to bound the performance of the MTS algorithm.
The total prediction error (η) is used to quantify the smoothness of both algorithms.

Quotes

"Producing these predictions might be a costly operation – this motivated Im et al. (2022) to introduce the study of algorithms which use predictions parsimoniously."
"We design parsimonious algorithms for caching and MTS with action predictions, proposed by Antoniadis et al. (2023), focusing on the parameters of consistency (performance with perfect predictions) and smoothness (dependence of their performance on the prediction error)."

Key Insights Distilled From

Algorithms for Caching and MTS with reduced number of predictions

by Karim Abdel ... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2404.06280.pdf

Deeper Inquiries

How can the proposed algorithms be extended to handle other online problems beyond caching and metrical task systems

The proposed algorithms can be extended to handle other online problems beyond caching and metrical task systems by adapting the concepts of action predictions and parsimonious use of predictions. For different online problems, the key lies in defining the prediction setup specific to that problem and designing algorithms that can effectively utilize these predictions. By identifying the critical information needed from predictions and structuring the algorithm to make decisions based on this information, the same principles can be applied to various online problems. Additionally, the smoothness and robustness properties can be tailored to suit the specific requirements of the new problem, ensuring optimal performance even with a reduced number of predictions.

What are the practical implications of the reduced number of predictions required by the algorithms, especially in scenarios with heavy-weight predictors

The reduced number of predictions required by the algorithms has significant practical implications, especially in scenarios with heavy-weight predictors. In such cases, where generating predictions is computationally intensive or resource-consuming, the ability to achieve competitive performance with a smaller number of predictions is highly beneficial. This can lead to improved efficiency, reduced computational costs, and faster decision-making processes. Additionally, the algorithms' ability to maintain consistency, robustness, and smoothness even with fewer predictions ensures reliable performance in real-world applications where prediction accuracy may vary.

Can the techniques used in this work be applied to design parsimonious algorithms for other learning-augmented settings, such as those with probabilistic or noisy predictions

The techniques used in this work can be applied to design parsimonious algorithms for other learning-augmented settings, such as those with probabilistic or noisy predictions, by adapting the algorithms to handle the uncertainty in the predictions. By incorporating probabilistic or noisy predictions into the prediction setup, the algorithms can be modified to make decisions based on the likelihood or confidence levels associated with the predictions. This adaptation would involve adjusting the consistency, robustness, and smoothness parameters to account for the probabilistic nature of the predictions, ensuring that the algorithms can still perform effectively even in scenarios with less precise predictions.