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LIT-1336: Performative Prediction

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StatusActive — read 2026-10-21 (NOTE-1044) in full, from arXiv:2002.06673v4; worth reading for the split between performative stability (optimal for the distribution one's own deployment induces, the fixed point of retraining) and performative optimality, for the exact conditions under which retraining converges to a unique stable point (smooth, strongly convex loss and ε < γ/β, each shown necessary; THEORY-861), and for the bound 2L_zε/γ between stable points and optima (THEORY-839). Read it knowing that its conditions hold in its own simulation only at the smallest ε, that the distribution map depends on the current model alone, and that it says nothing about how to reach the optimum.
Version2
Tagslearning-theory, anthology-candidate
Cited as “paper” byNOTE-1044 — Perdomo, Zrnic, Mendler-Dünner and Hardt — Performative prediction
Cited as “source” byTHEORY-839 — A model optimal for the distribution its own deployment induces, a performatively stable point, need not minimize the risk it actually incurs, and the gap is bounded: for a loss that is L_z-Lipschitz in the data and γ-strongly convex in the parameters, and a distribution map that is ε-Lipschitz in Wasserstein-1 distance, every stable point lies within 2L_zε/γ of every performative optimum; in a biased-coin example the stable point is µ/(1 − ε) and the optimum µ/(1 − 2ε), equal only when the prediction has no effect, THEORY-861 — When a deployed model changes the distribution it is scored on, retraining on the distribution the last model induced contracts at rate εβ/γ, for a β-jointly smooth, γ-strongly convex loss and a distribution map that is ε-Lipschitz in Wasserstein-1 distance, and so converges to a unique performatively stable point when ε < γ/β; each condition is needed, since dropping strong convexity, joint smoothness or the bound on ε each admits a case where retraining never converges

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Perdomo, J. C., Zrnic, T., Mendler-Dünner, C. & Hardt, M. (2020). Performative Prediction. Proceedings of the 37th International Conference on Machine Learning, PMLR 119: 7599–7609. Preprint: arXiv:2002.06673 (16 February 2020).

Read 2026-10-21 in full, in NOTE-1044. The summary was checked against the reading.

Why this is here

A25 called it “essential prior art for any claim about representations participating in the reproduction of the social structures they describe”, and drew the warning that “a description that is well calibrated against outcomes generated under its own use need not be an adequate description of the system under a different policy or observational regime.” A26 §2 built on it. Bears on CLAIM-402, CLAIM-407 and TERM-064, and on CLAIM-350.

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