In Defense of Defensive Forecasting

Abstract

This tutorial provides a survey of algorithms for Defensive Forecasting, where predictions are derived not by prognostication but by correcting past mistakes. Pioneered by Vovk, Defensive Forecasting frames the goal of prediction as a sequential game, and derives predictions to minimize metrics no matter what outcomes occur. We present an elementary introduction to this general theory and derive simple, near-optimal algorithms for online learning, calibration, prediction with expert advice, and online conformal prediction.