Finite-Time 4-Expert Prediction Problem

Abstract

We explicitly solve the nonlinear PDE that is the continuous limit of dynamic programming of expert prediction problem in finite horizon setting with N=4 experts. The expert prediction problem is formulated as a zero sum game between a player and an adversary. By showing that the solution is 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.

Tasks

Reproductions