# The finite-horizon five-expert prediction problem

arXiv: https://arxiv.org/abs/2609.38035 · HTML: https://mlsanity.com/paper/2609.38035/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 14 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 3 of 3)

- [Experimental Evidence for Asymptotic Non-Optimality of Comb Adversary Strategy](https://mlsanity.com/paper/1912.01548/) (2019)
- [An explicit solution of the five-expert prediction PDE and the exact optimality set of COMB](https://mlsanity.com/paper/2609.14892/) (2026)
- [Prediction with Five Experts and Geometric Stopping: A Probabilistic Construction and Analytic Verification](https://mlsanity.com/paper/2609.17986/) (2026)

## Built on by (most cited first, 1 of 1)

- [On prediction from expert advice with more than five experts](https://mlsanity.com/paper/2610.05186/) (2026)

## Abstract (arXiv)

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 x1=x2 and x3=x4. 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.