In Defense of Defensive Forecasting

TL;DR

This paper surveys Defensive Forecasting algorithms that generate predictions by correcting past errors, framing prediction as a sequential game to achieve robust, near-optimal results across various online learning tasks.

Contribution

It provides an elementary introduction and derives simple, near-optimal algorithms for multiple online prediction problems based on Defensive Forecasting.

Findings

Derived simple, near-optimal algorithms for online learning tasks.

Unified framework for calibration, expert advice, and conformal prediction.

Demonstrated robustness of predictions regardless of outcomes.

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.