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arxiv: 2606.07890 · v1 · pith:L2Z3HPS3new · submitted 2026-06-05 · 💻 cs.LG · stat.ML

Partially Performative Prediction

Jaewook Lee , Tijana Zrnic This is my paper

Pith reviewed 2026-06-27 22:12 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords performative predictiondistribution shiftendogenous shiftexogenous shiftrepeated retrainingonline stabilitymachine learning deployment
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The pith

Partially performative prediction models distribution shifts from both model influence and external time variation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper introduces partially performative prediction as a setting where deploying a model changes the data distribution through its own decisions while an external process also alters the distribution independently over time. The work generalizes standard performative prediction, which considers only the model's endogenous effect, by adding the exogenous component. It defines online versions of performative stability and performative optimality that track the combined evolution of the environment. The authors then analyze repeated retraining and characterize conditions under which this heuristic adapts successfully to the mixed shifts. A reader would care because most deployed predictors encounter both self-induced and outside drifts rather than purely one kind.

Core claim

The data distribution evolves both in response to the deployed model and according to an external time-varying process. Online analogues of performative stability and performative optimality are defined to track this evolving partially performative environment. Repeated retraining is analyzed as a practical heuristic, with conditions identified for when it successfully adapts.

What carries the argument

The partially performative prediction framework, which decomposes the data distribution into a model-responsive component and an independent external time-varying process.

If this is right

  • Repeated retraining adapts to the environment when the rates of model-induced and external shifts satisfy the derived conditions.
  • Online performative stability provides a moving target that learning procedures can track over time.
  • Performative optimality extends to a sequence of time-dependent targets rather than a single fixed point.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Deployed systems in recommendation or pricing could estimate external drift rates separately to set retraining schedules.
  • The decomposition might apply to multi-model environments where each model's effect combines with shared external trends.
  • Simulations with controlled external time series could test whether measured adaptation error matches the predicted conditions.

Load-bearing premise

The distribution shift can be cleanly separated into a model-responsive part and an independent external process whose changes do not depend on the model.

What would settle it

An experiment showing that the external process changes in direct response to model deployment in a manner that breaks the independence, causing repeated retraining to fail where the framework predicts success.

Figures

Figures reproduced from arXiv: 2606.07890 by Jaewook Lee, Tijana Zrnic.

Figure 1
Figure 1. Figure 1: Performative stability regret of ARRM (left) and ASGD-lazy with r = 1 (right) in the credit scoring experiment, for varying αt . We consider a randomly varying (top) and a stationary (bottom) exogenous component Pt . their predicted score. To capture “hard” and “easy” exogenous shifts, we consider two cases: in the first, mt is sampled independently from a bounded ball at each round; in the second, mt is s… view at source ↗
Figure 2
Figure 2. Figure 2: Performative stability regret of ARRM, ARGD, ASGD-greedy, and ASGD-lazy with r = 1 in the credit scoring experiment, for varying αt . We consider a randomly varying exogenous component Pt . 0 2 4 6 log T 0.58 0.56 0.54 0.52 0.50 0.48 lo g R e g PS T RRM, Pt stationary 0 2 4 6 log T 0.50 0.25 0.00 0.25 0.50 0.75 lo g R e g PS T RGD, Pt stationary 0 2 4 6 log T 0 1 2 lo g R e g PS T Greedy SGD, Pt stationary… view at source ↗
Figure 3
Figure 3. Figure 3: Performative stability regret of ARRM, ARGD, ASGD-greedy, and ASGD-lazy with r = 1 in the credit scoring experiment, for varying αt . We consider a stationary exogenous component Pt . 38 [PITH_FULL_IMAGE:figures/full_fig_p038_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performative stability regret vs. theoretical upper bounds of ARRM (left) and ARGD (right) in the credit scoring experiment, for varying αt . We consider a randomly varying exogenous component Pt . Results [PITH_FULL_IMAGE:figures/full_fig_p039_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Performative stability regret vs. theoretical upper bounds of ARRM (left) and ARGD (right) in the quadratic￾Gaussian experiment, for varying αt . We consider a randomly varying exogenous component Pt . The quadratic loss is 1-strongly convex in θ and 1-smooth in both θ and z. Since D(θ) and D(θ ′ ) have the same covariance for any θ,θ′ , we have W1  D(θ),D(θ ′ )  = W1  N (Aθ + m,Σ),N (Aθ + m ′ ,Σ)  = ∥… view at source ↗
Figure 6
Figure 6. Figure 6: Representative two-dimensional iterate vs. stability trajectories of ARRM, ARGD, ASGD-greedy, and ASGD-lazy with r = 1 in the 2D quadratic-Gaussian experiment, for αt ∝ t −1.0 . We consider a randomly varying exogenous com￾ponent Pt . The left subfigures show the actual movement of θt and θ PS t in the 2D space for the initial 200 steps, and the right subfigures show the log-log plots of the distance ∥θt −… view at source ↗
read the original abstract

Performative prediction studies feedback loops that arise when predictive models are deployed in consequential domains. In these settings, deploying a model can change the population whose patterns the model aims to predict, inducing a distribution shift that is endogenous to the learning system. This perspective departs from classical treatments of distribution shift, where shifts are typically modeled as exogenous changes in the data-generating process. Yet, in practice, distribution shift is rarely one or the other. Predictive models may influence future data through the decisions they support, while the world itself continues to drift for reasons beyond the learner's control. We study partially performative prediction, a framework that captures both endogenous and exogenous sources of distribution shift. The framework generalizes performative prediction by allowing the data distribution to evolve both in response to the deployed model and according to an external, time-varying process. We extend the central notions of performative stability and performative optimality to this setting by defining their online analogues that track the evolving partially performative environment. We analyze practical learning heuristics, including repeated retraining, and characterize when they successfully adapt to partially performative environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper introduces partially performative prediction as a generalization of performative prediction. It models distribution shift as arising from both an endogenous response to the deployed model and an independent exogenous time-varying external process. The work extends performative stability and optimality to online analogues that track the evolving environment and analyzes practical heuristics such as repeated retraining, characterizing conditions under which they adapt successfully.

Significance. If the decomposition, online stability definitions, and retraining analysis are rigorously developed with clear theorems and examples, the framework would usefully bridge performative prediction and classical exogenous-shift literature, offering a more realistic model for deployed systems. The emphasis on online analogues and heuristic analysis addresses a practical gap, but the abstract provides no derivations, proofs, or results with which to evaluate whether these extensions are non-vacuous or yield new insights.

major comments (1)
  1. [Abstract] Abstract: the central claim that the framework 'generalizes performative prediction' and that repeated retraining 'successfully adapt[s]' cannot be assessed; no definitions of the decomposition, no statements of the online stability or optimality notions, and no theorems or experiments are available to verify internal consistency or non-triviality.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review and summary of the work. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the framework 'generalizes performative prediction' and that repeated retraining 'successfully adapt[s]' cannot be assessed; no definitions of the decomposition, no statements of the online stability or optimality notions, and no theorems or experiments are available to verify internal consistency or non-triviality.

    Authors: Abstracts are concise summaries by design and do not include formal definitions, theorems, or proofs. The full manuscript develops these elements in detail: Section 2 defines the partially performative framework and the decomposition of distribution shift into endogenous (model-induced) and exogenous (time-varying external) components; Section 3 introduces the online analogues of performative stability and optimality with formal statements; Section 4 provides theorems characterizing conditions under which repeated retraining adapts successfully, along with illustrative examples. These sections contain the requested technical content for assessing internal consistency and non-triviality. revision: no

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper defines partially performative prediction as a direct generalization that decomposes distribution shift into an endogenous model-responsive component plus an independent exogenous time-varying process. Central notions of stability and optimality are extended by explicit online analogues constructed from this decomposition, and analysis of repeated retraining follows from the stated framework. No equations, predictions, or load-bearing claims reduce to fitted inputs, self-citations, or prior author results by construction; the work is self-contained as a definitional extension.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract; no free parameters, axioms, or invented entities are identifiable from the provided text.

pith-pipeline@v0.9.1-grok · 5706 in / 851 out tokens · 18801 ms · 2026-06-27T22:12:20.167494+00:00 · methodology

discussion (0)

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