Parsimonious Learning-Augmented Online Metric Matching

We present learning-augmented algorithms for two general classes of online minimization problems: metrical task systems and laminar set cover. Both algorithms achieve improved theoretical guarantees using machine-learned predictions of an optimal solution to the dual linear program. Unlike optimal primal solutions, which can change drastically under tiny instance perturbations, these dual solutions are much more stable, which ensures the existence of good (and learnable) predictions for families of similar instances. While previous work has used dual predictions in offline settings and for online maximization problems, our algorithms are, to the best of our knowledge, the first demonstration that such dual predictions can be effective for online minimization. Our theoretical results are complemented by experiments on the $k$-server problem and the parking permit problem.

Learning-augmented paging has been extensively studied in recent years. A key advantage over naive ML-based approaches is \emph{bounded robustness}, which guarantees worst-case performance even when predictions are inaccurate, making these algorithms valuable for real-world systems. Prior work achieves robustness bounds of $2H_k + O(1)$ in the randomized setting, leaving a gap to the optimal competitive ratio $H_k$. In this paper, we study how to close this gap. We begin by reviewing online optimality and proving a new property of the latest $H_k$-competitive algorithm, which facilitates our analysis in the learning-augmented setting. Then, we review existing learning-augmented paging algorithms and introduce a unifying primitive, the \emph{relative prediction budget}, which captures the essence of establishing robustness and reveals that prior algorithms either overuse or underutilize predictions. Guided by the above analysis, we develop a new framework that achieves the best-possible robustness up to an additive constant for learning-augmented paging: $H_k + O(1)$. Experiments further demonstrate strong practical performance.

Learning-augmented algorithms have emerged as a powerful paradigm to surpass traditional worst-case lower bounds by integrating potentially noisy predictions. While this framework has seen success in online scheduling, existing work primarily optimizes job latency while relying on frequent, ``blind'' preemptions. This ignores the fundamental trade-off between algorithmic performance and preemption complexity. We provide the first systematic study of learning-augmented scheduling that curbs preemption while optimizing latency. We establish that the gap between theoretical latency bounds and preemption overhead can be bridged with solid analytical foundations. Our results include $O(1)$-competitive algorithms for single and unrelated parallel machines with only $O(1)$ preemptions per job under accurate predictions, with overhead scaling logarithmically with the prediction error. By providing the first bounded-preemption guarantees for unrelated and malleable machines, we extend the theoretical reach of the learning-augmented framework to more constrained and realistic settings. Finally, our algorithms are validated through experiments.