Defensive Generation

Gabriele Farina, Juan Carlos Perdomo
Proceedings of Thirty Ninth Conference on Learning Theory, PMLR 336:2399-2427, 2026.

Abstract

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 $1/\sqrt T$ rate for generation error.

Cite this Paper

BibTeX
@InProceedings{pmlr-v336-farina26a, title = {Defensive Generation}, author = {Farina, Gabriele and Perdomo, Juan Carlos}, booktitle = {Proceedings of Thirty Ninth Conference on Learning Theory}, pages = {2399--2427}, year = {2026}, editor = {Hanneke, Steve and Lattimore, Tor}, volume = {336}, series = {Proceedings of Machine Learning Research}, month = {29 Jun--03 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v336/main/assets/farina26a/farina26a.pdf}, url = {https://proceedings.mlr.press/v336/farina26a.html}, abstract = {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 $1/\sqrt T$ rate for generation error.} }
Endnote
%0 Conference Paper %T Defensive Generation %A Gabriele Farina %A Juan Carlos Perdomo %B Proceedings of Thirty Ninth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2026 %E Steve Hanneke %E Tor Lattimore %F pmlr-v336-farina26a %I PMLR %P 2399--2427 %U https://proceedings.mlr.press/v336/farina26a.html %V 336 %X 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 $1/\sqrt T$ rate for generation error.
APA
Farina, G. & Perdomo, J.C.. (2026). Defensive Generation. Proceedings of Thirty Ninth Conference on Learning Theory, in Proceedings of Machine Learning Research 336:2399-2427 Available from https://proceedings.mlr.press/v336/farina26a.html.

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