Recently, Antoniadis et al. (ICLR 2025) proposed a framework for incorporating predictions to approximate NP-hard selection problems.
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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.
arXiv:2606. 05380v1 Announce Type: cross Abstract: We present learning-augmented algorithms for two general classes of online minimization problems: metrical task systems and laminar set cover.
The paper tackles the single‑machine scheduling problem of minimizing total completion time in a non‑clairvoyant setting, where job processing times are unknown until completion. It introduces a robustness framework that uses a classification model’s confusion matrix to describe uncertainty as permutations within predicted classes, avoiding the computational challenges of traditional robust metrics. The authors present an optimal non‑adaptive strategy for three robust criteria and show that adaptive and randomized algorithms can outperform it when the confusion matrix has certain structural properties.
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.
arXiv:2605. 09382v2 Announce Type: replace Abstract: The Linear Assignment Problem is a fundamental combinatorial optimization task where classical exact solvers ensure optimality but suffer from an $\mathcal{O}(N^{3})$ bottleneck, while recent neural approximations struggle with scalability and exactness.
arXiv:2607. 05759v1 Announce Type: cross Abstract: Submodular maximization is an important building block for developing algorithms in many areas such as machine learning and data mining.