# In Defense of Defensive Forecasting

arXiv: https://arxiv.org/abs/2506.11848 · HTML: https://mlsanity.com/paper/2506.11848/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Loss Minimization through the Lens of Outcome Indistinguishability](https://mlsanity.com/paper/2210.08649/) (2022)
- [A Unifying Theory of Distance from Calibration](https://mlsanity.com/paper/2211.16886/) (2022)
- [Online Multivalid Learning: Means, Moments, and Prediction Intervals](https://mlsanity.com/paper/2101.01739/) (2021)
- [High-Dimensional Prediction for Sequential Decision Making](https://mlsanity.com/paper/2310.17651/) (2023)
- [Oracle Efficient Online Multicalibration and Omniprediction](https://mlsanity.com/paper/2307.08999/) (2023)
- [Near-Optimal Algorithms for Omniprediction](https://mlsanity.com/paper/2501.17205/) (2025)
- [On Equivalence of Martingale Tail Bounds and Deterministic Regret Inequalities](https://mlsanity.com/paper/1510.03925/) (2015)
- [Online Minimax Multiobjective Optimization: Multicalibeating and Other Applications](https://mlsanity.com/paper/2108.03837/) (2021)
- [Forecast Hedging and Calibration](https://mlsanity.com/paper/2210.07169/) (2022)
- [Approachability, Regret and Calibration; implications and equivalences](https://mlsanity.com/paper/1301.2663/) (2013)
- [On the Distance from Calibration in Sequential Prediction](https://mlsanity.com/paper/2402.07458/) (2024)
- [Breaking the T2/3 Barrier for Sequential Calibration](https://mlsanity.com/paper/2406.13668/) (2024)
- [From Fairness to Infinity: Outcome-Indistinguishable (Omni)Prediction in Evolving Graphs](https://mlsanity.com/paper/2411.17582/) (2024)
- [Revisiting the Predictability of Performative, Social Events](https://mlsanity.com/paper/2503.11713/) (2025)

## Built on by (most cited first, 5 of 5)

- [An Efficient Black-Box Reduction from Online Learning to Multicalibration, and a New Route to Phi-Regret Minimization](https://mlsanity.com/paper/2604.19592/) (2026)
- [Defensive Generation](https://mlsanity.com/paper/2602.21390/) (2026)
- [Defensive Boosting for Online Probabilistic Forecasting](https://mlsanity.com/paper/2608.13554/) (2026)
- [A Unifying Perspective on Probabilities as Model Predictions](https://mlsanity.com/paper/2609.09855/) (2026)
- [Stabilizing Performative Feedback Loops with Minimal Model Deployments](https://mlsanity.com/paper/2609.14065/) (2026)

## Abstract (arXiv)

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.