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Online Algorithms with Uncertainty-Quantified Predictions

Bo Sun, Jerry Huang, Nicolas Christianson, Mohammad Hajiesmaili, Adam Wierman, Raouf Boutaba

TL;DR

The paper tackles leveraging uncertainty-quantified predictions in online algorithms by introducing distributionally-robust competitive analysis (DRCR) and probabilistic interval predictions (PIP). It develops an optimization-based design that maps UQ to algorithm choice, achieving optimal DRCR for canonical problems like ski rental and online search, and complements this with an online-learning framework that attains sublinear policy regret across multiple instances under mild Lipschitz conditions. The results provide both per-instance optimal algorithms and data-driven learning methods, showing that explicit use of UQ can outperform traditional worst-case or blindly-prediction approaches. The work advances reliable, prediction-aware online decision-making and lays a foundation for extending UQ-driven design to a broader class of online problems with practical impact in systems that rely on ML-informed decisions.

Abstract

The burgeoning field of algorithms with predictions studies the problem of using possibly imperfect machine learning predictions to improve online algorithm performance. While nearly all existing algorithms in this framework make no assumptions on prediction quality, a number of methods providing uncertainty quantification (UQ) on machine learning models have been developed in recent years, which could enable additional information about prediction quality at decision time. In this work, we investigate the problem of optimally utilizing uncertainty-quantified predictions in the design of online algorithms. In particular, we study two classic online problems, ski rental and online search, where the decision-maker is provided predictions augmented with UQ describing the likelihood of the ground truth falling within a particular range of values. We demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the UQ predictions. Moreover, we consider how to utilize more general forms of UQ, proposing an online learning framework that learns to exploit UQ to make decisions in multi-instance settings.

Online Algorithms with Uncertainty-Quantified Predictions

TL;DR

The paper tackles leveraging uncertainty-quantified predictions in online algorithms by introducing distributionally-robust competitive analysis (DRCR) and probabilistic interval predictions (PIP). It develops an optimization-based design that maps UQ to algorithm choice, achieving optimal DRCR for canonical problems like ski rental and online search, and complements this with an online-learning framework that attains sublinear policy regret across multiple instances under mild Lipschitz conditions. The results provide both per-instance optimal algorithms and data-driven learning methods, showing that explicit use of UQ can outperform traditional worst-case or blindly-prediction approaches. The work advances reliable, prediction-aware online decision-making and lays a foundation for extending UQ-driven design to a broader class of online problems with practical impact in systems that rely on ML-informed decisions.

Abstract

The burgeoning field of algorithms with predictions studies the problem of using possibly imperfect machine learning predictions to improve online algorithm performance. While nearly all existing algorithms in this framework make no assumptions on prediction quality, a number of methods providing uncertainty quantification (UQ) on machine learning models have been developed in recent years, which could enable additional information about prediction quality at decision time. In this work, we investigate the problem of optimally utilizing uncertainty-quantified predictions in the design of online algorithms. In particular, we study two classic online problems, ski rental and online search, where the decision-maker is provided predictions augmented with UQ describing the likelihood of the ground truth falling within a particular range of values. We demonstrate that non-trivial modifications to algorithm design are needed to fully leverage the UQ predictions. Moreover, we consider how to utilize more general forms of UQ, proposing an online learning framework that learns to exploit UQ to make decisions in multi-instance settings.
Paper Structure (59 sections, 10 theorems, 36 equations, 1 figure, 6 algorithms)

This paper contains 59 sections, 10 theorems, 36 equations, 1 figure, 6 algorithms.

Table of Contents

  1. Introduction
  2. Optimal online algorithms under distributionally-robust analysis
  3. Optimization-based algorithmic approach
  4. Online learning for exploiting UQs across multiple instances
  5. Related Literature
  6. Algorithms with untrusted predictions
  7. Online learning
  8. Online Algorithms with UQ Predictions
  9. Distributionally-Robust Competitive Analysis
  10. Probabilistic interval predictions
  11. An Optimization-Based Algorithmic Approach
  12. Ski Rental Problem with UQ Prediction
  13. Problem statement
  14. Warm-up: A Deterministic Algorithm
  15. A simple meta-algorithm
  16. ...and 44 more sections

Key Result

Proposition 1

No parameterized algorithms $A(\boldsymbol{w}), \boldsymbol{w}\in\Omega$ can achieve a DRCR smaller than $(1-\delta)\eta^* + \delta \gamma^*$.

Figures (1)

  • Figure 1: Comparisons of cumulative empirical ratios (minus $1$) of the following algorithms: WOA: worst-case optimal randomized algorithm that is $e/e-1$-competitive. FTP: follow-the-prediction algorithm that fully trusts the prediction; OL-Dynamic: online learning with respect to policy regret by leveraging UQ predictions. OL-Static: online learning with respect to static regret without considering UQ predictions. RSR-PIP: randomized algorithm with PIP (Algorithm \ref{['alg:os2']}) that achieves the optimal DRCR.

Theorems & Definitions (11)

  • Definition 1
  • Proposition 1
  • Theorem 1
  • Theorem 2
  • Lemma 1
  • Theorem 3
  • Lemma 2
  • Theorem 4
  • Theorem 5
  • Corollary 1
  • ...and 1 more