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Algorithms for Caching and MTS with reduced number of predictions

Karim Abdel Sadek, Marek Elias

TL;DR

This work studies learning-augmented caching and Metrical Task Systems (MTS) under action-prediction models, seeking to minimize predictor usage while preserving strong guarantees. The authors design parsimonious algorithms that achieve $1$-consistency for caching with bounded predictor access and develop a general MTS approach where consistency and smoothness scale linearly with the number of predictions available; with unlimited predictions, these results match prior optimal guarantees. The analysis introduces follower-robust compositions, works functions, and the FtSP framework to handle well-separated queries, producing robust, smooth, and competitive outcomes even under prediction errors. Empirical results on real and synthetic predictors show the proposed methods can rival or outperform prior ML-augmented approaches while reducing the predictor budget, highlighting practical viability for heavy-weight predictors in constrained environments. Overall, the paper advances parsimonious-use prediction strategies for online caching and MTS, offering both tight theoretical bounds and supportive experiments.

Abstract

ML-augmented algorithms utilize predictions to achieve performance beyond their worst-case bounds. Producing these predictions might be a costly operation -- this motivated Im et al. '22 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. '20, focusing on the parameters of consistency (performance with perfect predictions) and smoothness (dependence of their performance on the prediction error). Our algorithm for caching is 1-consistent, robust, and its smoothness deteriorates with the decreasing number of available predictions. We propose an algorithm for general MTS whose consistency and smoothness both scale linearly with the decreasing number of predictions. Without the restriction on the number of available predictions, both algorithms match the earlier guarantees achieved by Antoniadis et al. '20.

Algorithms for Caching and MTS with reduced number of predictions

TL;DR

This work studies learning-augmented caching and Metrical Task Systems (MTS) under action-prediction models, seeking to minimize predictor usage while preserving strong guarantees. The authors design parsimonious algorithms that achieve -consistency for caching with bounded predictor access and develop a general MTS approach where consistency and smoothness scale linearly with the number of predictions available; with unlimited predictions, these results match prior optimal guarantees. The analysis introduces follower-robust compositions, works functions, and the FtSP framework to handle well-separated queries, producing robust, smooth, and competitive outcomes even under prediction errors. Empirical results on real and synthetic predictors show the proposed methods can rival or outperform prior ML-augmented approaches while reducing the predictor budget, highlighting practical viability for heavy-weight predictors in constrained environments. Overall, the paper advances parsimonious-use prediction strategies for online caching and MTS, offering both tight theoretical bounds and supportive experiments.

Abstract

ML-augmented algorithms utilize predictions to achieve performance beyond their worst-case bounds. Producing these predictions might be a costly operation -- this motivated Im et al. '22 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. '20, focusing on the parameters of consistency (performance with perfect predictions) and smoothness (dependence of their performance on the prediction error). Our algorithm for caching is 1-consistent, robust, and its smoothness deteriorates with the decreasing number of available predictions. We propose an algorithm for general MTS whose consistency and smoothness both scale linearly with the decreasing number of predictions. Without the restriction on the number of available predictions, both algorithms match the earlier guarantees achieved by Antoniadis et al. '20.
Paper Structure (26 sections, 24 theorems, 53 equations, 10 figures, 2 tables)

This paper contains 26 sections, 24 theorems, 53 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Our results
  3. Related work
  4. Preliminaries
  5. Action predictions for MTS
  6. Caching: Belady's algorithm, Marking, and Lazy algorithms
  7. MTS and advice complexity
  8. Bounded number of predictions
  9. Analysis of Follower
  10. Analysis of $\mathop{\mathrm{Robust}}\nolimits_f$
  11. Well-separated queries to the predictor
  12. MTS
  13. Work functions.
  14. Algorithm of EmekFKR09.
  15. Algorithm FtSP
  16. ...and 11 more sections

Key Result

Theorem 1.1

Let $f$ be an increasing convex function such that $f(0)=0$ and $f(i)\leq 2^i-1$ for each $i\geq 0$. There is an algorithm for caching requiring $O(f(\log k))\mathop{\mathrm{OPT}}\nolimits$ predictions which achieves consistency $1$, robustness $O(\log k)$, and smoothness $O(f^{-1}(\eta/OPT))$, wher

Figures (10)

  • Figure 1: BrightKite dataset with Synthetic predictor, standard deviation at most 0.003 and 300 resp.
  • Figure 2: BrightKite dataset with Synthetic predictor: competitive ratio
  • Figure 3: BrightKite dataset with Synthetic predictor: number of used predictors
  • Figure 4: Competitive ratios on CitiBike dataset with $k=100$, standard deviation at most 0.001
  • Figure 5: Competitive ratios with predictors POPU and PLECO
  • ...and 5 more figures

Theorems & Definitions (41)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Theorem 1.5
  • Proposition 2.5: EmekFKR09
  • Lemma 3.3
  • Lemma 3.4
  • proof
  • proof : Proof of Theorem \ref{['thm:FnR']}
  • ...and 31 more