A PDE approach for regret bounds under partial monitoring

Erhan Bayraktar, Ibrahim Ekren, Xin Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study a learning problem in which a forecaster only observes partial information. By properly rescaling the problem, we heuristically derive a limiting PDE on Wasserstein space which characterizes the asymptotic behavior of the regret of the forecaster. Using a verification type argument, we show that the problem of obtaining regret bounds and efficient algorithms can be tackled by finding appropriate smooth sub/supersolutions of this parabolic PDE.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
Volume24
StatePublished - 2023

Keywords

  • asymptotic expansion
  • bandit problem
  • expert advice framework
  • machine learning
  • Wasserstein derivative

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Statistics and Probability
  • Artificial Intelligence

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