On prediction from expert advice with more than five experts

Abstract

We prove that no single rank ordered adversary strategy is globally optimal for the prediction with expert advice problem with six or more experts, in both the geometric stopping and finite time horizon settings. The proof is based on establishing a leading order correction when one expert moves far ahead of the others. This allows us to connect optimal strategies between $n$ and $j<n$ experts and utilize recent results on the exact optimality set for the five expert problem.

arXiv comment42 pages. Lean formalization: https://doi.org/10.5281/zenodo.23136818