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.
@article{arxiv.2506.11848,
title = {In Defense of Defensive Forecasting},
author = {Juan Carlos Perdomo and Benjamin Recht},
journal= {arXiv preprint arXiv:2506.11848},
year = {2025}
}