Learning-Augmented Competitive Algorithms for Spatiotemporal Online Allocation with Deadline Constraints

TL;DR

This paper introduces a new online allocation problem with deadlines and spatial considerations, proposing an optimal learning-augmented algorithm that effectively balances prediction use and robustness, with applications in sustainable computing.

Contribution

It formalizes the spatiotemporal online allocation with deadlines problem, providing an optimal competitive algorithm and a learning-augmented approach that leverages predictions for improved performance.

Findings

The proposed extsc{ST-CLIP} algorithm is proven to be optimal in competitive ratio.

extsc{ST-CLIP} outperforms heuristic baselines in simulated workload management.

The algorithm effectively balances prediction accuracy and robustness in dynamic environments.

Abstract

We introduce and study spatiotemporal online allocation with deadline constraints ($\mathsf{SOAD}$), a new online problem motivated by emerging challenges in sustainability and energy. In $\mathsf{SOAD}$, an online player completes a workload by allocating and scheduling it on the points of a metric space $(X, d)$ while subject to a deadline $T$. At each time step, a service cost function is revealed that represents the cost of servicing the workload at each point, and the player must irrevocably decide the current allocation of work to points. Whenever the player moves this allocation, they incur a movement cost defined by the distance metric $d(\cdot, \ \cdot)$ that captures, e.g., an overhead cost. $\mathsf{SOAD}$ formalizes the open problem of combining general metrics and deadline constraints in the online algorithms literature, unifying problems such as metrical task systems and online search. We propose a competitive algorithm for $\mathsf{SOAD}$ along with a matching lower bound establishing its optimality. Our main algorithm, \textsc{ST-CLIP}, is a learning-augmented algorithm that takes advantage of predictions (e.g., forecasts of relevant costs) and achieves an optimal consistency-robustness trade-off. We evaluate our proposed algorithms in a simulated case study of carbon-aware spatiotemporal workload management, an application in sustainable computing that schedules a delay-tolerant batch compute job on a distributed network of data centers. In these experiments, we show that \textsc{ST-CLIP} substantially improves on heuristic baseline methods.