A PDE approach for regret bounds under partial monitoring

Erhan Bayraktar; Ibrahim Ekren; Xin Zhang

A PDE approach for regret bounds under partial monitoring

Probability 2022-09-07 v1 Machine Learning Optimization and Control

Authors: Erhan Bayraktar , Ibrahim Ekren , Xin Zhang

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.

Keywords

partial monitoring regret bounds wasserstein space pde approach online learning verification argument

Cite

@article{arxiv.2209.01256,
  title  = {A PDE approach for regret bounds under partial monitoring},
  author = {Erhan Bayraktar and Ibrahim Ekren and Xin Zhang},
  journal= {arXiv preprint arXiv:2209.01256},
  year   = {2022}
}

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Keywords: machine learning, expert advice framework, bandit problem, asymptotic expansion, Wasserstein derivative

A PDE approach for regret bounds under partial monitoring

Abstract

Keywords

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