A PDE approach for regret bounds under partial monitoring

Erhan Bayraktar; Ibrahim Ekren; Xin Zhang

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arXiv · 2209.01256

A PDE approach for regret bounds under partial monitoring

Erhan Bayraktar·Ibrahim Ekren·Xin Zhang

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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.

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Erhan Bayraktar, Ibrahim Ekren, Xin Zhang. 2022-09-02. A PDE approach for regret bounds under partial monitoring. https://arxiv.org/abs/2209.01256

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