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, using defensive forecasting and multivalued supermartingales, improving upon previous bounds.

Contribution

It presents a novel regret bound that depends only on the effective number of experts, eliminating reliance on the nominal number, via an innovative application of defensive forecasting.

Findings

New regret bounds independent of nominal expert count

Application of defensive forecasting to multivalued supermartingales

Improved theoretical guarantees in prediction with expert advice

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 Normal- Hedge bound, which mainly depends on the effective number of experts but 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.