Finite-Time 4-Expert Prediction Problem

Erhan Bayraktar; Ibrahim Ekren; Xin Zhang

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arXiv · 1911.10936

Finite-Time 4-Expert Prediction Problem

Erhan Bayraktar·Ibrahim Ekren·Xin Zhang

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Abstract

We explicitly solve the nonlinear PDE that is the continuous limit of dynamic programming of \emph{expert prediction problem} in finite horizon setting with $N=4$ experts. The \emph{expert prediction problem} is formulated as a zero sum game between a player and an adversary. By showing that the solution is $\mathcal{C}^2$, we are able to show that the strategies conjectured in arXiv:1409.3040G form an asymptotic Nash equilibrium. We also prove the "Finite vs Geometric regret" conjecture proposed in arXiv:1409.3040G for $N=4$, and and show that this conjecture in fact follows from the conjecture that the comb strategies are optimal.

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BibTeX RIS

Erhan Bayraktar, Ibrahim Ekren, Xin Zhang. 2019-11-22. Finite-Time 4-Expert Prediction Problem. https://arxiv.org/abs/1911.10936

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