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 language | English (US) |
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Journal | Journal of Machine Learning Research |
Volume | 24 |
State | Published - 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