# Defensive Generation

arXiv: https://arxiv.org/abs/2602.21390 · HTML: https://mlsanity.com/paper/2602.21390/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Outcome Indistinguishability](https://mlsanity.com/paper/2011.13426/) (2020)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [Moment Multicalibration for Uncertainty Estimation](https://mlsanity.com/paper/2008.08037/) (2020)
- [Loss Minimization through the Lens of Outcome Indistinguishability](https://mlsanity.com/paper/2210.08649/) (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)
- [Near-Optimal Algorithms for Omniprediction](https://mlsanity.com/paper/2501.17205/) (2025)
- [Efficient Convex Optimization with Membership Oracles](https://mlsanity.com/paper/1706.07357/) (2017)
- [Forecast Hedging and Calibration](https://mlsanity.com/paper/2210.07169/) (2022)
- [Sample Efficient Omniprediction and Downstream Swap Regret for Non-Linear Losses](https://mlsanity.com/paper/2502.12564/) (2025)
- [From Fairness to Infinity: Outcome-Indistinguishable (Omni)Prediction in Evolving Graphs](https://mlsanity.com/paper/2411.17582/) (2024)
- [High dimensional online calibration in polynomial time](https://mlsanity.com/paper/2504.09096/) (2025)
- [High-Dimensional Calibration from Swap Regret](https://mlsanity.com/paper/2505.21460/) (2025)
- [Expected Variational Inequalities](https://mlsanity.com/paper/2502.18605/) (2025)
- [In Defense of Defensive Forecasting](https://mlsanity.com/paper/2506.11848/) (2025)

## Built on by (most cited first, 1 of 1)

- [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)

## Abstract (arXiv)

We study the problem of efficiently producing, in an online fashion, generative models of scalar, multiclass, and vector-valued outcomes that cannot be falsified on the basis of the observed data and a pre-specified collection of computational tests. Our contributions are twofold. First, we expand on connections between online high-dimensional multicalibration with respect to an RKHS and recent advances in expected variational inequality problems, enabling efficient algorithms for the former. We then apply this algorithmic machinery to the problem of outcome indistinguishability. Our procedure, Defensive Generation, is the first to efficiently produce online outcome indistinguishable generative models of non-Bernoulli outcomes that are unfalsifiable with respect to infinite classes of tests, including those that examine higher-order moments of the generated distributions. Furthermore, our method runs in near-linear time in the number of samples and achieves the optimal, vanishing T^{-1/2} rate for generation error.