Secretary and online matching problems with machine learned advice

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2023-05-01 DOI:10.1016/j.disopt.2023.100778

Antonios Antoniadis , Themis Gouleakis , Pieter Kleer , Pavel Kolev

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引用次数: 89

Abstract

The classic analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. In contrast, machine learning approaches shine in exploiting patterns in past inputs in order to predict the future. However, such predictions, although usually accurate, can be arbitrarily poor. Inspired by a recent line of work, we augment three well-known online settings with machine learned predictions about the future, and develop algorithms that take these predictions into account. In particular, we study the following online selection problems: (i) the classic secretary problem, (ii) online bipartite matching and (iii) the graphic matroid secretary problem. Our algorithms still come with a worst-case performance guarantee in the case that predictions are subpar while obtaining an improved competitive ratio (over the best-known classic online algorithm for each problem) when the predictions are sufficiently accurate. For each algorithm, we establish a trade-off between the competitive ratios obtained in the two respective cases.

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秘书和在线匹配问题与机器学习建议

在线算法的经典分析，由于其最坏情况的性质，当手头的输入实例远不是最坏情况时，可能会非常悲观。相比之下，机器学习方法在利用过去输入中的模式来预测未来方面大放异彩。然而，这样的预测虽然通常是准确的，但也可能很差。受最近一项工作的启发，我们用机器学习的对未来的预测来增强三个著名的在线设置，并开发将这些预测考虑在内的算法。特别地，我们研究了以下在线选择问题：（i）经典秘书问题，（ii）在线二部分匹配和（iii）图形拟阵秘书问题。在预测不合格的情况下，我们的算法仍然具有最坏情况下的性能保证，同时在预测足够准确的情况下获得改进的竞争比（相对于每个问题的最著名的经典在线算法）。对于每种算法，我们在两种情况下获得的竞争比率之间建立一个权衡。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.