Complexity Classes for Online Problems with and without Predictions
Magnus Berg, Joan Boyar, Lene M. Favrholdt, Kim S. Larsen

TL;DR
This paper develops a new complexity theory framework for online problems with predictions, introducing hierarchies of classes based on error measures, and analyzing their properties and relationships to classical online problems.
Contribution
It introduces a formal hierarchy of complexity classes for online problems with predictions, including notions of reductions, hardness, and completeness, expanding theoretical understanding.
Findings
Hierarchy of complexity classes for online problems with predictions
Reductions and completeness notions within the new framework
Lower bounds for paging with discard predictions apply broadly
Abstract
With the developments in machine learning, there has been a surge in interest and results focused on algorithms utilizing predictions, not least in online algorithms where most new results incorporate the prediction aspect for concrete online problems. While the structural computational hardness of problems with regards to time and space is quite well developed, not much is known about online problems where time and space resources are typically not in focus. Some information-theoretical insights were gained when researchers considered online algorithms with oracle advice, but predictions of uncertain quality is a very different matter. We initiate the development of a complexity theory for online problems with predictions, focusing on binary predictions for minimization problems. Based on the most generic hard online problem type, string guessing, we define a family of hierarchies of…
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Taxonomy
TopicsOptimization and Search Problems · Complexity and Algorithms in Graphs · Machine Learning and Algorithms
