The finite-horizon five-expert prediction problem

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.

Analysis of PDEs (math.AP); Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2609.38035 [math.AP]

(or arXiv:2609.38035v1 [math.AP] for this version)

https://doi.org/10.48550/arXiv.2609.38035 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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