Prediction with Advice of Unknown Number of Experts

TL;DR

This paper introduces a new regret bound in prediction with expert advice that depends solely on the effective number of experts, utilizing defensive forecasting and multivalued supermartingales for improved theoretical guarantees.

Contribution

It presents a novel regret bound that excludes the nominal number of experts, advancing the theoretical understanding of prediction algorithms with expert advice.

Findings

New regret bound independent of nominal expert count

Application of defensive forecasting to multivalued supermartingales

Improved theoretical guarantees in expert advice prediction

Abstract

In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the NormalHedge bound, which mainly depends on the effective number of experts and also weakly depends on the nominal one, we obtain a bound that does not contain the nominal number of experts at all. We use the defensive forecasting method and introduce an application of defensive forecasting to multivalued supermartingales.