Continuous and randomized defensive forecasting: unified view

TL;DR

This paper unifies continuous and randomized defensive forecasting by demonstrating that randomized methods can be derived from continuous ones through a process of smearing Sceptic's moves, providing a cohesive theoretical framework.

Contribution

It shows that randomized defensive forecasting can be obtained from continuous forecasting by smoothing Sceptic's moves, unifying the two approaches.

Findings

Randomized forecasting can be derived from continuous methods.

Smearing Sceptic's moves makes them continuous.

Unified view of defensive forecasting approaches.

Abstract

Defensive forecasting is a method of transforming laws of probability (stated in game-theoretic terms as strategies for Sceptic) into forecasting algorithms. There are two known varieties of defensive forecasting: "continuous", in which Sceptic's moves are assumed to depend on the forecasts in a (semi)continuous manner and which produces deterministic forecasts, and "randomized", in which the dependence of Sceptic's moves on the forecasts is arbitrary and Forecaster's moves are allowed to be randomized. This note shows that the randomized variety can be obtained from the continuous variety by smearing Sceptic's moves to make them continuous.