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

TL;DR

This work introduces SOAD, a general online optimization problem that merges movement costs on arbitrary metrics with deadline constraints. It develops PCM, a competitive online algorithm leveraging metric embeddings and pseudo-cost minimization, and ST-CLIP, a learning-augmented method that achieves the optimal robustness-consistency trade-off under untrusted predictions. The authors prove competitive guarantees: PCM is $O(\log n)\eta$-competitive with a tight lower bound, and ST-CLIP attains $(1+\varepsilon)$-consistency and $O(\log n)\gamma^{(\varepsilon)}$-robustness, with $\gamma^{(\varepsilon)}$ characterized by a transcendental equation. They extend results to time-varying metrics (SOAD-T) and validate the framework through a carbon-aware data-center workload management case study, showing practical improvements over heuristics. The work thus bridges MTS/SOCO and online search with long-term constraints in a unified, practically relevant setting, enabling data-driven, deadline-respecting decisions in complex metric spaces.

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.

Figures (21)

• Figure 1: An illustration of the probabilistic tree embedding (\ref{['dfn:tree']}) for the motivating application. Points in the metric are represented as pairs of circles on the left. On the right, the first three levels of the tree approximate the metric space $(X,d)$Fakcharoenphol:07, and the last level captures the $\mathtt{ON}$ / $\mathtt{OFF}$ structure of $\mathsf{SOAD}$.
• Figure 2: CDFs of competitive ratios for each algorithm, across all average carbon intensity experiments.
• Figure 3: Average empirical competitive ratios for varying job data size $G$, with $T \thicksim \text{Unif}_{\mathbb{Z}}(12, 48)$.
• Figure 4: Average empirical competitive ratios for varying energy factor $\kappa$, with $G = 4, T \thicksim \text{Unif}_{\mathbb{Z}}(12, 48).$
• Figure 5: Average empirical competitive ratios for varying volatility factor $\Upsilon$. $G = 4, T \thicksim \text{Unif}_{\mathbb{Z}}(12, 48).$

Theorems & Definitions (18)

• Definition 2.3: Probabilistic tree embedding $\mathcal{T} = (V,E)$ for $\mathsf{SOAD}$
• Definition 2.4: Vector space $(K, \Vert \cdot \Vert_{\ell_1(\mathbf{w})})$
• Theorem 2.5
• Definition 3.1: Pseudo-cost function $\psi$ for $\mathsf{SOAD}$
• theorem 1
• Theorem 3.2
• Theorem 3.3
• Lemma 3.4
• Lemma 3.5
• Definition 4.1: Black-box advice model for $\mathsf{SOAD}$