Learning-Augmented Approximation for Unrelated-Machines Makespan Scheduling
Recently, Antoniadis et al. (ICLR 2025) proposed a framework for incorporating predictions to approximate NP-hard selection problems.
arXiv:2606. 18807v1 Announce Type: cross Abstract: The field of learning-augmented algorithms has demonstrated that machine-learned predictions can bypass worst-case lower bounds across a wide range of problems.
Recently, Antoniadis et al. (ICLR 2025) proposed a framework for incorporating predictions to approximate NP-hard selection problems.
Learning-augmented algorithms combine fallible predictions with formal performance guarantees. This survey reviews prediction interfaces, error measures, consistency–robustness trade-offs, and five construction mechanisms across online optimization, caching, learned data structures, graph problems, and mechanism design. It distinguishes theorem-level upper bounds from matched asymptotic dependence, separates formal guarantees from empirical evidence, and outlines open problems in cost-aware prediction, endogenous error, semantic predictors, and benchmarking.
The paper investigates how algorithms for hard combinatorial optimization problems converge to trivial solutions, focusing on finite-size behavior rather than asymptotic limits. By analyzing large-graph asymptotics and running numerical experiments on problems like maximum independent set and maximum K‑SAT, the authors show that convergence to theoretically predicted bounds is surprisingly slow. In the intermediate regime of high constraint density, local algorithms actually outperform their asymptotic predictions, highlighting a gap between finite-regime performance and asymptotic theory.
arXiv:2606. 19587v1 Announce Type: cross Abstract: We propose a scalable method for training prediction (machine learning) models in the predict-then-optimize paradigm, where model outputs serve as coefficients for a subsequent linear optimization task.
arXiv:2606. 01342v1 Announce Type: cross Abstract: Learning-augmented paging has been extensively studied in recent years.
arXiv:2602. 03972v3 Announce Type: replace-cross Abstract: The best-arm identification (BAI) problem is one of the most fundamental problems in interactive machine learning, which has two flavors: the fixed-budget setting (FB) and the fixed-confidence setting (FC).
arXiv:2608. 12231v2 Announce Type: replace Abstract: We study adversarial combinatorial bandits with $m$-set actions, where at each round the learner selects $m$ out of $d$ items and observes only the aggregate loss of the selected items.
arXiv:2608. 12231v1 Announce Type: new Abstract: We study adversarial combinatorial bandits with $m$-set actions, where at each round the learner selects $m$ out of $d$ items and observes only the aggregate loss of the selected items.
arXiv:2602. 21312v4 Announce Type: replace-cross Abstract: This work considers a number of optimization problems and reductive relations between them.
The paper investigates how optimization algorithms for hard combinatorial problems converge to trivial solutions. By combining rigorous large‑graph asymptotics with numerical experiments on maximum independent set and maximum K‑SAT, the authors show that convergence to the theoretically predicted bounds is extremely slow, especially in the intermediate regime of high constraint density. This reveals a significant gap between finite‑size performance and asymptotic expectations, indicating that practical algorithm design remains essential even when theory predicts inevitable failure.
arXiv:2607. 03385v1 Announce Type: cross Abstract: Policy learning has received substantial attention with the goal of learning policies from observational data for decision-making.
We introduce Multinomial Subset Routing (MSR), a new online routing framework over $K$ experts in which the learner keeps a multinomial routing policy instead of a deterministic subset of experts. At each round, the learner samples $M$ experts i.