Strategically Deceptive Model Deployment in Performative Prediction

Javier Sanguino Bautiste; Jose A. Lozano; Novi Quadrianto; Thomas Kehrenberg

arxiv: 2506.09044 · v2 · submitted 2025-06-10 · 💻 cs.LG

Strategically Deceptive Model Deployment in Performative Prediction

Javier Sanguino Bautiste , Thomas Kehrenberg , Jose A. Lozano , Novi Quadrianto This is my paper

Pith reviewed 2026-05-19 10:04 UTC · model grok-4.3

classification 💻 cs.LG

keywords performative predictionmodel deploymentdecoupled modelsstrategic deceptiondeception costuser behavior shiftinstitutional risk

0 comments

The pith

Decoupled Performative Prediction allows institutions to achieve lower risk by disclosing a different model to users than the one used for decisions.

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

The paper introduces Decoupled Performative Prediction to model cases where institutions use one model internally for decisions but disclose another to users who then change their behavior. This setup creates new solutions in the optimization landscape that provably lower the institution's risk compared to classical performative prediction where the models are the same. The authors provide an algorithm that converges to these better solutions and introduce a deception cost to quantify the mismatch experienced by users. They show that even when institutions include this cost in their objectives due to reputational concerns, it does not adequately safeguard users against deception.

Core claim

By decoupling the model that governs institutional decisions from the model disclosed to users, the optimization admits distinct solutions that achieve lower institutional risk than those available when the models must coincide as in standard performative prediction.

What carries the argument

The Decoupled Performative Prediction framework that separates the decision model from the disclosure model and analyzes the resulting optimization landscape for improved institutional outcomes.

If this is right

Distinct equilibria exist with lower risk for the institution.
An algorithm converges to these solutions with provable guarantees under standard assumptions.
Incorporating a deception cost into optimization still permits deceptive deployment.
Model disclosure becomes a core technical decision rather than just an ethical one.
Regulations may be needed to hold institutions accountable for mismatches.

Where Pith is reading between the lines

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

Users might benefit from mechanisms to detect model mismatches in real deployments.
This framework could extend to other feedback loop settings in machine learning where information asymmetry exists.
Institutions might strategically choose disclosure levels based on expected user response and detection probability.
Testing in simulated environments could reveal the practical gains from such decoupling.

Load-bearing premise

The institution unilaterally controls model disclosure and users respond solely to the disclosed model without effective ways to detect or correct for any mismatch.

What would settle it

An empirical study measuring whether institutions in practice deploy mismatched models and observe reduced risk compared to matched-model baselines in performative settings.

Figures

Figures reproduced from arXiv: 2506.09044 by Javier Sanguino Bautiste, Jose A. Lozano, Novi Quadrianto, Thomas Kehrenberg.

**Figure 2.** Figure 2: Two plots of the decoupled risk, DR(θM, θD), for different settings. The black line corresponds to the performative risk P R(θ). These definitions of stable and optimal points will become handy when practically analysing realistic PP, as seen in Section 5.2. 4 Understanding Performative Prediction via the Decoupled Risk Landscape In this section, we apply the visualization technique to the performative pre… view at source ↗

**Figure 3.** Figure 3: (A) Shows the plane of Fig. 2a for θD = θM = θ. The optimal point is the minimum of that intersection. (B) Section of the Fig. 2a – which represents the mixture example decouple loss landscape – for θD = θ1 and θD = θ2 respectively. Only θ1 is a stable point because the section of the plane for θD = θ1 is an horizontal line, i.e. ∇θM DR(θM, θ1) = 0, ∀θM. Repeated Gradient Descent (RGD) [1]. Uses the gradie… view at source ↗

**Figure 4.** Figure 4: Each column shows the evolution of the risk and the trajectory of the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Give Me Some Credit dataset with strategic classification, example used in [1]. More details can be found in the appendix. All PerfGD use the reparametrization trick. Normal Gradient Descent (GD) has been used widely in the literature, however, other optimization methods retrieve better results Surveying the risk landscape in realistic setups. Example 2.3 shows a smooth risk landscape for a simple scenario… view at source ↗

**Figure 6.** Figure 6: (A) Total revenue (higher is better) for 100 products, i.e., d = 100, on the pricing dataset. Optimizing for the decoupled optimum retrieves more revenue than reaching the standard optimal point of PP. (B) Norms of the gradient vectors for 4 algorithms on the pricing dataset: RGD converges to the stable point so only ∇θM DR(θD, θM) goes to zero (Proposition 3.2); both PerfGD converge to the optimal point b… view at source ↗

**Figure 7.** Figure 7: (A) shows the accuracy on the Give Me Some Credit dataset [19] (money lending) with a strategic classification distribution map with a 2-layer NN (100 hidden neurons) for multiple algorithms. (B) shows the loss and (C) shows the gradient norms. PerfGD outperforms RGD, the gradient plot shows that it is able to escape the stable point. In the EPP (with DPerfGD), the gradients do not go to zero – as would be… view at source ↗

**Figure 8.** Figure 8: PP’s formulation extends the classical risk by incorporating the [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗

**Figure 9.** Figure 9: The plots of the decoupled risk, DR(θM, θD), for the additional examples. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗

**Figure 10.** Figure 10: Plane of Fig. 9a for θD = θM = θ. The optimal point is the minimum of that intersection [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗

**Figure 11.** Figure 11: Section of the Fig. 9a – which represents the mixture example [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗

**Figure 12.** Figure 12: Each column shows the evolution of the loss and the trajectory of the [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗

read the original abstract

Machine Learning systems are increasingly deployed in decision-making settings that shape user behavior and, in turn, the data on which future decisions are based. Performative Prediction (PP) formalizes this feedback loop by modeling how deployed models induce distributional shifts. It studies how to learn robust and well-performing models under such dynamics. However, existing PP frameworks typically assume that the model governing these decisions is the same model observed by users (therefore, to which they respond). In practice, deployer institutions may instead disclose curated models, while internally relying on distinct opaque models. We introduce Decoupled Performative Prediction (DPP), a framework that explicitly models mismatches between the model governing institutional decisions and the model that shapes user behavior. By analyzing the resulting optimization landscape, we show that DPP admits new different solutions that provably achieve lower risk for the institution than those under classical PP. We further propose an algorithm with provable convergence guarantees under standard assumptions, demonstrating how easy institutions can benefit from strategically deceptive deployment when they control model disclosure and users lack countervailing power. To capture the implications of such behavior, we introduce the deception cost, a quantitative measure of the degree of deception experienced by users. We study settings in which institutions incorporate this cost into the optimization process, motivated by reputational concerns or potential user abandonment, and show that such self-imposed constraints are insufficient to protect users. Overall, our results demonstrate that model disclosure is not merely an ethical consideration but a core technical design decision, underscoring the need for regulations that hold institutions accountable for deceptive deployment practices.

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.

Desk Editor's Note private letter to a colleague

The paper introduces Decoupled Performative Prediction to capture mismatches between an institution's internal decision model and the one shown to users, claiming this yields strictly lower risk than classical performative prediction under unilateral disclosure control.

read the letter

The main takeaway is that they formalize a gap between the model used for actual decisions and the one disclosed to users, then show this setup can produce better outcomes for the deployer than standard performative prediction. They add a deception cost term to quantify the mismatch from the user's side and analyze how institutions might optimize around it or self-impose penalties for reputational reasons. The algorithm they give comes with convergence guarantees under the usual assumptions, which is a concrete step beyond just describing the landscape. That part is useful for anyone already working in performative prediction who wants to extend the model to deployment choices. The framework is new in the literature they cite, and the lower-risk claim is stated directly rather than left vague. The central assumption is that users react only to the disclosed model and have no effective way to detect or respond to the internal one. If that holds, the separation between the two maps gives the claimed advantage; if any feedback couples the internal model back into the distribution shift, the benefit disappears and you are back in the classical case. The paper treats unilateral control as the practical default, so the results are conditional on that setup. They also show that adding the deception cost to the objective does not fully shield users, which aligns with the idea that self-regulation falls short. This work is for researchers in performative prediction or those looking at technical levers in high-stakes deployment. A reader who already knows the classical PP results will see the extension clearly and can judge whether the new equilibria are worth exploring. It deserves peer review because the modeling choice is explicit and the regulatory angle follows from the math rather than being tacked on.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Decoupled Performative Prediction (DPP), extending classical Performative Prediction (PP) by allowing an institution to optimize an internal decision model θ while disclosing a distinct model φ to users. It claims that this decoupling yields equilibria with strictly lower institutional risk than standard PP, proposes an algorithm with convergence guarantees under standard assumptions, defines a deception cost to quantify user impact, and shows that incorporating this cost as a self-imposed constraint fails to protect users, calling for external regulations on disclosure practices.

Significance. If the separation between the performative map for φ and the risk objective for θ is rigorously established without implicit coupling, the work identifies a technically exploitable asymmetry in performative settings that could systematically favor deceptive deployment. The introduction of deception cost as a quantitative regularizer and the convergence analysis provide concrete tools for studying such asymmetries, with direct relevance to both algorithmic design and regulatory discussions in deployed ML systems.

major comments (2)

[Abstract and framework definition] Abstract and framework definition: The central claim that DPP admits solutions achieving strictly lower institutional risk requires that the performative distribution (and thus the risk for θ) depends only on the disclosed model φ. The optimization landscape analysis must explicitly derive the decoupled risk function and demonstrate that it is not equivalent to the classical PP objective; without this separation shown formally (including any assumption that users respond exclusively to φ), the lower-risk result does not follow.
[Deployment discussion and final claims] Deployment discussion and final claims: The assumption that institutions unilaterally control disclosure while users possess no effective detection or countervailing power is treated as given. This modeling choice is load-bearing for the advantage over PP; the manuscript should state it explicitly as an axiom and analyze robustness (e.g., partial information flow from θ back into the shift), as any such coupling collapses the claimed distinction.

minor comments (2)

[Abstract] The abstract contains the awkward phrasing 'new different solutions'; rephrase to 'distinct solutions' for clarity.
Notation for the disclosed model φ and internal model θ should be introduced with a clear table or diagram early in the paper to distinguish them from standard PP notation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below, providing clarifications on the framework and assumptions while committing to revisions that strengthen the formal presentation without altering the core contributions.

read point-by-point responses

Referee: [Abstract and framework definition] Abstract and framework definition: The central claim that DPP admits solutions achieving strictly lower institutional risk requires that the performative distribution (and thus the risk for θ) depends only on the disclosed model φ. The optimization landscape analysis must explicitly derive the decoupled risk function and demonstrate that it is not equivalent to the classical PP objective; without this separation shown formally (including any assumption that users respond exclusively to φ), the lower-risk result does not follow.

Authors: We agree that an explicit formal separation strengthens the presentation. The manuscript defines the performative map such that the induced distribution P_φ depends solely on the disclosed model φ, while the institutional objective is the risk of the internal decision model θ evaluated under P_φ. This yields the decoupled risk R(θ, φ) = E_{x ∼ P_φ}[ℓ(θ, x)], which is distinct from the classical PP objective where the single model must serve both roles simultaneously. We will revise Section 2 to include a dedicated derivation of R(θ, φ) and a short proposition establishing that inf_θ,φ R(θ, φ) ≤ inf_θ R(θ, θ), with strict inequality possible when the optimal φ for a given θ differs from θ itself. The assumption that users respond exclusively to φ is already implicit in the problem setup but will be stated explicitly as part of the framework definition. revision: yes
Referee: [Deployment discussion and final claims] Deployment discussion and final claims: The assumption that institutions unilaterally control disclosure while users possess no effective detection or countervailing power is treated as given. This modeling choice is load-bearing for the advantage over PP; the manuscript should state it explicitly as an axiom and analyze robustness (e.g., partial information flow from θ back into the shift), as any such coupling collapses the claimed distinction.

Authors: We accept that this modeling choice requires explicit statement. We will add it as Assumption 1 in the revised manuscript: users observe and respond only to the disclosed model φ, with no direct information about or feedback from the internal model θ. For robustness, we will include a brief discussion in Section 5 noting that partial leakage of information about θ would effectively create a composite signal to which users respond; in such cases the advantage of decoupling shrinks but does not necessarily vanish unless the leakage is complete. Full equilibrium analysis under endogenous detection lies outside the current scope, but the added discussion will clarify the boundary conditions under which the DPP advantage persists. revision: partial

Circularity Check

0 steps flagged

No significant circularity; DPP lower-risk claim follows from explicit decoupling assumption

full rationale

The paper defines Decoupled Performative Prediction by separating the disclosed model φ (inducing the performative shift) from the internal decision model θ (used for institutional decisions). The optimization landscape analysis and lower-risk solutions are derived directly from this separation under the stated assumption that users respond only to φ. This is a modeling choice with independent content, not a reduction by construction to prior fitted parameters, self-citations, or ansatzes. No load-bearing self-citation chains or renaming of known results appear in the derivation. The framework remains self-contained against external performative prediction benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review limited to abstract; ledger populated only with items explicitly referenced. No free parameters or invented entities are named. Relies on standard optimization convergence assumptions.

axioms (1)

standard math Standard assumptions for convergence in optimization algorithms
Invoked to support the proposed algorithm's provable convergence guarantees.

pith-pipeline@v0.9.0 · 5821 in / 1233 out tokens · 58903 ms · 2026-05-19T10:04:58.201864+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages · 2 internal anchors

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Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur. Sharpness-aware minimization for efficiently improving generalization.arXiv preprint arXiv:2010.01412, 2020. 16 A From traditional Machine Learning to extended Performative Prediction As further illustration, we include Fig. 8. P er f ormativ e Pr ediction Ext ended P er f ormativ e Pr edi...

work page internal anchor Pith review Pith/arXiv arXiv 2010

[1] [1]

Performative prediction

Juan Perdomo, Tijana Zrnic, Celestine Mendler-Dünner, and Moritz Hardt. Performative prediction. InInternational Conference on Machine Learning, pages 7599–7609. PMLR, 2020

work page 2020

[2] [2]

Visualizing the loss landscape of neural nets.Advances in neural information processing systems, 31, 2018

Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, and Tom Goldstein. Visualizing the loss landscape of neural nets.Advances in neural information processing systems, 31, 2018

work page 2018

[3] [3]

Qualitatively charac- terizing neural network optimization problems

Ian J Goodfellow, Oriol Vinyals, and Andrew M Saxe. Qualitatively charac- terizing neural network optimization problems. InICLR, 2015

work page 2015

[4] [4]

An empirical analysis of the optimization of deep network loss surfaces

Daniel Jiwoong Im, Michael Tao, and Kristin Branson. An empirical analysis of the optimization of deep network loss surfaces, 2017. URL https://arxiv.org/abs/1612.04010

work page internal anchor Pith review Pith/arXiv arXiv 2017

[5] [5]

Performative prediction with neural networks

Mehrnaz Mofakhami, Ioannis Mitliagkas, and Gauthier Gidel. Performative prediction with neural networks. InInternational Conference on Artificial Intelligence and Statistics, pages 11079–11093. PMLR, 2023

work page 2023

[6] [6]

Performative prediction in a stateful world

Gavin Brown, Shlomi Hod, and Iden Kalemaj. Performative prediction in a stateful world. InInternational conference on artificial intelligence and statistics, pages 6045–6061. PMLR, 2022. 14

work page 2022

[7] [7]

Regret minimization with performative feedback

Meena Jagadeesan, Tijana Zrnic, and Celestine Mendler-Dünner. Regret minimization with performative feedback. InInternational Conference on Machine Learning, pages 9760–9785. PMLR, 2022

work page 2022

[8] [8]

Perfor- mative reinforcement learning

Debmalya Mandal, Stelios Triantafyllou, and Goran Radanovic. Perfor- mative reinforcement learning. InInternational Conference on Machine Learning, pages 23642–23680. PMLR, 2023

work page 2023

[9] [9]

Stochastic optimization schemes for performative prediction with nonconvex loss

Qiang Li and Hoi To Wai. Stochastic optimization schemes for performative prediction with nonconvex loss. InThe Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https://openreview. net/forum?id=ejIzdt50ek

work page 2024

[10] [10]

The limitations of model retraining in the face of performativity

Anmol Kabra and Kumar Kshitij Patel. The limitations of model retraining in the face of performativity. InHumans, Algorithmic Decision-Making and Society: Modeling Interactions and Impact, ICML 2024 Workshop, 2024

work page 2024

[11] [11]

How to learn when data reacts to your model: performative gradient descent

Zachary Izzo, Lexing Ying, and James Zou. How to learn when data reacts to your model: performative gradient descent. InInternational Conference on Machine Learning, pages 4641–4650. PMLR, 2021

work page 2021

[12] [12]

Simple statistical gradient-following algorithms for connectionist reinforcement learning.Machine learning, 8:229–256, 1992

Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning.Machine learning, 8:229–256, 1992

work page 1992

[13] [13]

Outside the echo chamber: Optimizing the performative risk

John P Miller, Juan C Perdomo, and Tijana Zrnic. Outside the echo chamber: Optimizing the performative risk. InInternational Conference on Machine Learning, pages 7710–7720. PMLR, 2021

work page 2021

[14] [14]

Opti- mal classification under performative distribution shift

Edwige Cyffers, Muni Sreenivas Pydi, Jamal Atif, and Olivier Cappé. Opti- mal classification under performative distribution shift. InThe Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https://openreview.net/forum?id=3J5hvO5UaW

work page 2024

[15] [15]

Kingma and Max Welling

Diederik P. Kingma and Max Welling. Auto-encoding variational bayes. In Yoshua Bengio and Yann LeCun, editors,International Conference on Learning Representations, ICLR, 2014

work page 2014

[16] [16]

Plug-in performative optimization

Licong Lin and Tijana Zrnic. Plug-in performative optimization. InForty- first International Conference on Machine Learning, 2024. URL https: //openreview.net/forum?id=jh7FDDwDBf

work page 2024

[17] [17]

Distributionally robust performative pre- diction

Songkai Xue and Yuekai Sun. Distributionally robust performative pre- diction. In The Thirty-eighth Annual Conference on Neural Informa- tion Processing Systems, 2024. URL https://openreview.net/forum? id=E8wDxddIqU

work page 2024

[18] [18]

Strategic classification in the dark

Ganesh Ghalme, Vineet Nair, Itay Eilat, Inbal Talgam-Cohen, and Nir Rosenfeld. Strategic classification in the dark. InInternational Conference on Machine Learning, pages 3672–3681. PMLR, 2021. 15

work page 2021

[19] [19]

Give me some credit.https://kaggle

Credit Fusion and Will Cukierski. Give me some credit.https://kaggle. com/competitions/GiveMeSomeCredit, 2011. Kaggle

work page 2011

[20] [20]

Perfor- mative power

Moritz Hardt, Meena Jagadeesan, and Celestine Mendler-Dünner. Perfor- mative power. Advances in Neural Information Processing Systems, 35: 22969–22981, 2022

work page 2022

[21] [21]

Strategic classification

Moritz Hardt, Nimrod Megiddo, Christos Papadimitriou, and Mary Woot- ters. Strategic classification. InProceedings of the 2016 ACM conference on innovations in theoretical computer science, pages 111–122, 2016

work page 2016

[22] [22]

Sharpness-Aware Minimization for Efficiently Improving Generalization

Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur. Sharpness-aware minimization for efficiently improving generalization.arXiv preprint arXiv:2010.01412, 2020. 16 A From traditional Machine Learning to extended Performative Prediction As further illustration, we include Fig. 8. P er f ormativ e Pr ediction Ext ended P er f ormativ e Pr edi...

work page internal anchor Pith review Pith/arXiv arXiv 2010