Numerical analysis of prediction with expert advice

Abstract

This work investigates the online machine learning problem of prediction with expert advice through numerical analysis of a related PDE. The problem is a repeated two-person game involving decision-making at each step informed by n experts with geometric stopping condition; the continuum limit of the consequences of this game over a large number of steps leads to an elliptic PDE. This work presents a numerical scheme that allows us to solve this PDE for general number of experts n, and gives numerical results for n < 9.