The finite-horizon five-expert prediction problem

Jeff Calder; Nadejda Drenska

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arXiv · 2609.38035

The finite-horizon five-expert prediction problem

Jeff Calder·Nadejda Drenska

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Abstract

We give an explicit solution to the five expert prediction with expert advice partial differential equation (PDE) in the finite-time horizon setting. The solution formula establishes that the adversary's rank strategy $(1,0,1,0,0)$ is globally optimal, and the COMB strategy $(1,0,1,0,1)$ is optimal exactly on the set where $x_1=x_2$ and $x_3=x_4$. The formula is derived from the solution of the geometric-stopping problem given in our companion paper through the transform principle of Bayraktar, Ekren and Zhang, which links the two problems by a Laplace transform. Inverting the transform term by term expresses the solution through a series of Gaussian and complementary error function kernels. The optimality of $(1,0,1,0,0)$ is reduced to the signs of $41$ one-variable Gaussian series, which are certified with computer assistance by Poisson summation, first-mode domination and interval arithmetic on $1616$ rational cells. The proofs of our main theorems, certificates included, are also formalized in the Lean proof assistant.

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BibTeX RIS

Jeff Calder, Nadejda Drenska. 2026-09-29. The finite-horizon five-expert prediction problem. https://arxiv.org/abs/2609.38035

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