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Signal-Aware Workload Shifting Algorithms with Uncertainty-Quantified Predictors

Ezra Johnson, Adam Lechowicz, Mohammad Hajiesmaili

TL;DR

This work tackles online workload shifting where decisions must be made under uncertain external signals. It introduces UQ-Advice, a learning-augmented algorithm that leverages uncertainty-quantified forecasts via a decision uncertainty score (DUS) to adaptively mix forecast-driven and robust decisions, achieving theoretical guarantees of consistency, robustness, and UQ-robustness. The approach unifies robust optimization with multi-stage uncertainty through a principled mixing parameter and demonstrates strong empirical gains on trace data for carbon intensity and electricity prices. The results show practical benefits, reducing costs and emissions while reducing the need for manual trust tuning in deployment.

Abstract

A wide range of sustainability and grid-integration strategies depend on workload shifting, which aligns the timing of energy consumption with external signals such as grid curtailment events, carbon intensity, or time-of-use electricity prices. The main challenge lies in the online nature of the problem: operators must make real-time decisions (e.g., whether to consume energy now) without knowledge of the future. While forecasts of signal values are typically available, prior work on learning-augmented online algorithms has relied almost exclusively on simple point forecasts. In parallel, the forecasting research has made significant progress in uncertainty quantification (UQ), which provides richer and more fine-grained predictive information. In this paper, we study how online workload shifting can leverage UQ predictors to improve decision-making. We introduce $\texttt{UQ-Advice}$, a learning-augmented algorithm that systematically integrates UQ forecasts through a $\textit{decision uncertainty score}$ that measures how forecast uncertainty affects optimal future decisions. By introducing $\textit{UQ-robustness}$, a new metric that characterizes how performance degrades with forecast uncertainty, we establish theoretical performance guarantees for $\texttt{UQ-Advice}$. Finally, using trace-driven experiments on carbon intensity and electricity price data, we demonstrate that $\texttt{UQ-Advice}$ consistently outperforms robust baselines and existing learning-augmented methods that ignore uncertainty.

Signal-Aware Workload Shifting Algorithms with Uncertainty-Quantified Predictors

TL;DR

This work tackles online workload shifting where decisions must be made under uncertain external signals. It introduces UQ-Advice, a learning-augmented algorithm that leverages uncertainty-quantified forecasts via a decision uncertainty score (DUS) to adaptively mix forecast-driven and robust decisions, achieving theoretical guarantees of consistency, robustness, and UQ-robustness. The approach unifies robust optimization with multi-stage uncertainty through a principled mixing parameter and demonstrates strong empirical gains on trace data for carbon intensity and electricity prices. The results show practical benefits, reducing costs and emissions while reducing the need for manual trust tuning in deployment.

Abstract

A wide range of sustainability and grid-integration strategies depend on workload shifting, which aligns the timing of energy consumption with external signals such as grid curtailment events, carbon intensity, or time-of-use electricity prices. The main challenge lies in the online nature of the problem: operators must make real-time decisions (e.g., whether to consume energy now) without knowledge of the future. While forecasts of signal values are typically available, prior work on learning-augmented online algorithms has relied almost exclusively on simple point forecasts. In parallel, the forecasting research has made significant progress in uncertainty quantification (UQ), which provides richer and more fine-grained predictive information. In this paper, we study how online workload shifting can leverage UQ predictors to improve decision-making. We introduce , a learning-augmented algorithm that systematically integrates UQ forecasts through a that measures how forecast uncertainty affects optimal future decisions. By introducing , a new metric that characterizes how performance degrades with forecast uncertainty, we establish theoretical performance guarantees for . Finally, using trace-driven experiments on carbon intensity and electricity price data, we demonstrate that consistently outperforms robust baselines and existing learning-augmented methods that ignore uncertainty.

Paper Structure

This paper contains 19 sections, 8 theorems, 76 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem and Preliminaries
  3. Problem Formulation
  4. Performance Metrics
  5. Assumptions
  6. Leveraging Uncertainty Estimates
  7. Algorithm Design
  8. Background
  9. The UQ-Advice algorithm
  10. Evaluation
  11. Experimental Setup
  12. Experimental Results
  13. Conclusion
  14. Deferred Proofs from \ref{['sec:leverage']}
  15. Deferred Proofs from \ref{['sec:alg']}
  16. ...and 4 more sections

Key Result

Theorem 3.1

Let $y^\star$ denote the true global optimal value of $\texttt{DUS}\xspace(\mathcal{U}, \hat{\mathbf{p}})$ (in eq:dus). A global non-convex optimizer can find a solution $\hat{y}$ that satisfies the following inequality: for any fixed $\varepsilon > 0$ in finite time, using $O\left( \left( \frac{\sqrt{T} \cdot \text{diam}(\mathcal{U})}{2 \lambda \cdot \varepsilon} \right)^T \right)$ iterations Ma

Figures (3)

  • Figure 1: Two instances of SASP with identical point forecasts but different uncertainty sets to illustrate our decision uncertainty score (DUS). The left instance has a small uncertainty set and a small DUS, while the right instance has a large uncertainty set and a large DUS. In both instances, we plot the optimal decisions for the point forecasts (orange) and the optimal decisions for the worst-case scenario in the uncertainty set (blue). The DUS score captures how much the optimal decisions can vary due to uncertainty in the forecasts.
  • Figure 2: Cumulative distribution functions (CDFs) of the empirical competitive ratio for each tested algorithm in two experimental settings: (a) details those experiments where the objective is to minimize carbon footprint (i.e., carbon intensity signal traces), while (b) details experiments where the objective is to minimize the cost of electricity.
  • Figure 3: Experiments with varying parameters. With the exception of (d), all experiments average over all four signal traces. (a): Changing the "width" of UQ sets and resulting synthetic forecast quality using $\xi$ parameter introduced in \ref{['sec:exp-setup']}. (b): Changing the deadline (i.e., time horizon) $T$ -- as $T$ grows, all algorithms have more flexibility to shift the workload in time. (c): Changing the switching cost parameter $\beta$ (see \ref{['eq:obj']}) -- as $\beta$ grows, changes in online decisions are penalized more. (d): Evaluating the effects of different signal traces (i.e., data sets). Note that the NYISO trace is used for electricity cost minimization experiments, while all other traces are used for carbon footprint minimization experiments (see \ref{['sec:exp-setup']}).

Theorems & Definitions (20)

  • definition 1: The UQ forecast model
  • definition 2: Competitive Ratio
  • definition 3: Consistency and Robustness
  • definition 4: UQ-Robustness
  • Theorem 3.1
  • Theorem 4.1
  • Theorem 4.2: Consistency of UQ-Advice
  • Theorem 4.3: Robustness of UQ-Advice
  • Theorem 4.4: UQ-Robustness of UQ-Advice
  • proof : Proof of \ref{['thm:global-optimum-dus']}
  • ...and 10 more