On Theorem 2.3 in "Prediction, Learning, and Games" by Cesa-Bianchi and Lugosi

TL;DR

This paper provides a modified proof of a loss bound for the exponentially weighted average forecaster with time-varying potential, showing the regret is bounded by sqrt{n ln(N)} across steps.

Contribution

It offers a new proof technique for the regret bound of the exponentially weighted average forecaster with time-varying potential.

Findings

Regret bound is upper-bounded by sqrt{n ln(N)}.

The proof applies uniformly across all steps n.

The result enhances understanding of the forecaster's performance.

Abstract

The note presents a modified proof of a loss bound for the exponentially weighted average forecaster with time-varying potential. The regret term of the algorithm is upper-bounded by sqrt{n ln(N)} (uniformly in n), where N is the number of experts and n is the number of steps.