Prediction with Advice of Unknown Number of Experts
This work provides an incremental improvement in online learning theory by refining regret bounds for scenarios with unknown expert counts.
The paper tackles the problem of improving regret bounds in prediction with expert advice by eliminating dependence on the nominal number of experts, achieving a bound that relies solely on the effective number of experts.
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.