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Improving Online Algorithms via ML Predictions

Ravi Kumar, Manish Purohit, Zoya Svitkina

TL;DR

The paper addresses improving online algorithms using machine-learned predictions while guaranteeing robustness to prediction errors. It develops predictor-aware algorithms for two core problems: ski rental and non-clairvoyant scheduling, offering deterministic and randomized robust-consistent designs with tunable trade-offs via $\lambda$. For ski rental, it yields $(1+1/\lambda)$-robust and $(1+\lambda)$-consistent (deterministic) and improved randomized bounds; for scheduling, it achieves a randomized $(2/(1-\lambda))$-robust and $(1/\lambda)$-consistent result through a Preferential Round-Robin construction that combines SPJF and RR. Experiments corroborate practical gains, showing improved performance over traditional online algorithms even with imperfect predictions. The work lays a foundation for extending predictive guarantees to broader online optimization problems and exploiting predictor error structure to refine bounds.

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.

Improving Online Algorithms via ML Predictions

TL;DR

The paper addresses improving online algorithms using machine-learned predictions while guaranteeing robustness to prediction errors. It develops predictor-aware algorithms for two core problems: ski rental and non-clairvoyant scheduling, offering deterministic and randomized robust-consistent designs with tunable trade-offs via . For ski rental, it yields -robust and -consistent (deterministic) and improved randomized bounds; for scheduling, it achieves a randomized -robust and -consistent result through a Preferential Round-Robin construction that combines SPJF and RR. Experiments corroborate practical gains, showing improved performance over traditional online algorithms even with imperfect predictions. The work lays a foundation for extending predictive guarantees to broader online optimization problems and exploiting predictor error structure to refine bounds.

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.
Paper Structure (13 sections, 9 theorems, 19 equations, 5 figures, 1 table, 3 algorithms)

This paper contains 13 sections, 9 theorems, 19 equations, 5 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Ski rental with prediction
  3. Warmup: A simple consistent, non-robust algorithm
  4. A deterministic robust and consistent algorithm
  5. A randomized robust and consistent algorithm
  6. Extensions
  7. Non-clairvoyant job scheduling with prediction
  8. A preferential round-robin algorithm
  9. Experimental results
  10. Ski rental
  11. Non-clairvoyant scheduling
  12. Conclusions
  13. Deferred Proofs

Key Result

Lemma 2.1

Let $\mathsf{ALG}$ denote the cost of the solution obtained by Algorithm alg:ski-simple and let $\mathsf{OPT}$ denote the optimal solution cost on the same instance. Then $\mathsf{ALG} \leq \mathsf{OPT} + \eta$.

Figures (5)

  • Figure 1: Ski rental: Robustness vs. consistency.
  • Figure 2: Average competitive ratio over varying prediction errors.
  • Figure : A simple 1-consistent algorithm
  • Figure : A deterministic robust and consistent algorithm.
  • Figure : A randomized robust and consistent algorithm

Theorems & Definitions (18)

  • Lemma 2.1
  • proof
  • Theorem 2.2
  • proof
  • Theorem 2.3
  • proof
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • ...and 8 more