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Non-clairvoyant Scheduling with Partial Predictions

Ziyad Benomar, Vianney Perchet

TL;DR

This work investigates non-clairvoyant scheduling when predictions are available for only a subset of jobs. It introduces a formal $(n,B)$-competitive framework, derives lower bounds, and presents two perfect-prediction algorithms: CRRR, which leverages only the known order of the $B$ jobs, and Switch, which uses the actual predicted sizes to achieve tighter performance. It then extends to imperfect predictions with a learning-augmented approach that jointly tunes robustness, consistency, and smoothness via hyperparameters, demonstrating a novel consistency-smoothness tradeoff unique to the partial-predictions setting. Empirically, Switch and the proposed learning-augmented scheme show favorable performance and reveal how prediction quality and the number of predictions influence the tradeoffs, with clear guidance for practical deployment in constrained-data environments.

Abstract

The non-clairvoyant scheduling problem has gained new interest within learning-augmented algorithms, where the decision-maker is equipped with predictions without any quality guarantees. In practical settings, access to predictions may be reduced to specific instances, due to cost or data limitations. Our investigation focuses on scenarios where predictions for only $B$ job sizes out of $n$ are available to the algorithm. We first establish near-optimal lower bounds and algorithms in the case of perfect predictions. Subsequently, we present a learning-augmented algorithm satisfying the robustness, consistency, and smoothness criteria, and revealing a novel tradeoff between consistency and smoothness inherent in the scenario with a restricted number of predictions.

Non-clairvoyant Scheduling with Partial Predictions

TL;DR

This work investigates non-clairvoyant scheduling when predictions are available for only a subset of jobs. It introduces a formal -competitive framework, derives lower bounds, and presents two perfect-prediction algorithms: CRRR, which leverages only the known order of the jobs, and Switch, which uses the actual predicted sizes to achieve tighter performance. It then extends to imperfect predictions with a learning-augmented approach that jointly tunes robustness, consistency, and smoothness via hyperparameters, demonstrating a novel consistency-smoothness tradeoff unique to the partial-predictions setting. Empirically, Switch and the proposed learning-augmented scheme show favorable performance and reveal how prediction quality and the number of predictions influence the tradeoffs, with clear guidance for practical deployment in constrained-data environments.

Abstract

The non-clairvoyant scheduling problem has gained new interest within learning-augmented algorithms, where the decision-maker is equipped with predictions without any quality guarantees. In practical settings, access to predictions may be reduced to specific instances, due to cost or data limitations. Our investigation focuses on scenarios where predictions for only job sizes out of are available to the algorithm. We first establish near-optimal lower bounds and algorithms in the case of perfect predictions. Subsequently, we present a learning-augmented algorithm satisfying the robustness, consistency, and smoothness criteria, and revealing a novel tradeoff between consistency and smoothness inherent in the scenario with a restricted number of predictions.
Paper Structure (39 sections, 15 theorems, 149 equations, 4 figures, 3 algorithms)

This paper contains 39 sections, 15 theorems, 149 equations, 4 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related work
  4. Problem and notations
  5. Lower Bounds
  6. Known Partial Order
  7. Action predictions
  8. Predictions of the Job Sizes
  9. Perfect Predictions
  10. Imperfect Predictions
  11. Preferential algorithm
  12. Experiments
  13. Perfect information
  14. Preferential algorithm
  15. Consistency-smoothness
  16. ...and 24 more sections

Key Result

Theorem 2.1

Let $\varphi : [0,\infty) \to [0,\infty)$ be a continuously differentiable and increasing function satisfying $\varphi(0) > 0$, $\varphi'/\varphi$ is non-increasing and $\int_0^\infty \frac{dt}{\varphi(t)^2} < \infty$, and let $\alpha_\varphi$ a non-negative constant satisfying If $B = wn + o(n)$ for some $w \in [0,1]$, then it holds for any randomized algorithm $\textsf{A}$ that Moreover, if $\

Figures (4)

  • Figure 1: Lower bounds and competitive ratios for $B$ known job sizes.
  • Figure 2: Lower bounds and ratios of $\textsf{Switch}$, $\textsf{CRRR}$
  • Figure 3: Preferential Algorithm (PA) with different parameters
  • Figure 4: Tradeoff between consistency and smoothness

Theorems & Definitions (33)

  • Theorem 2.1
  • Corollary 2.2
  • Corollary 2.3
  • Remark 2.4
  • Theorem 3.1
  • Theorem 4.1
  • Proposition 4.2
  • Lemma 4.3
  • Lemma 4.4
  • Theorem 4.5
  • ...and 23 more