Unified algorithms for online learning and competitive analysis

Niv Buchbinder, Shahar Chen, Joseph Seffi Naor, Ohad Shamir

Research output: Contribution to journalArticlepeer-review


Online learning and competitive analysis are two widely studied frameworks for online decision-making settings. Despite the frequent similarity of the problems they study, there are significant differences in their assumptions, goals, and techniques, hindering a unified analysis and richer interplay between the two. In this paper, we provide several contributions in this direction. We provide a single unified algorithm, which, by parameter tuning, interpolates between optimal regret for learning from experts (in online learning) and optimal competitive ratio for the metrical task systems problem (MTS) (in competitive analysis), improving upon previous results. The algorithm also allows us to obtain new regret bounds against "drifting" experts, which might be of independent interest. Moreover, our approach allows us to go beyond experts/MTS, obtaining similar unifying results for structured action sets and "combinatorial experts," whenever the setting has a certain matroid structure.

Original languageEnglish
Pages (from-to)612-625
Number of pages14
JournalMathematics of Operations Research
Issue number2
StatePublished - May 2016


  • Competitive analysis
  • Experts
  • Matroids
  • Metrical task systems
  • Online learning


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