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REVIEW 2 major objections 2 minor 15 references

Ambiguous Strategic Classification

T0 review · 2 major / 2 minor · reviewed 2026-06-27 · grok-4.3

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Pith's one-line read Strategic classification can jointly optimize the classifier and the uncertainty around it by revealing an ambiguity set.

desk verdict The paper applies ambiguity sets to strategic classification under partial disclosure, but the key behavioral assumption about agents not inferring the private classifier looks fragile. read the letter →

arxiv 2606.10137 v1 pith:B7T2YSQE submitted 2026-06-08 cs.LG

Ivri Hikri , Nir Rosenfeld This is my paper · ORCID
classification cs.LG
keywords strategicclassificationambiguitypartialdisclosurerobustmechanismdesignbest-responsecomputationclassifieroptimization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper examines strategic classification where full public knowledge of the classifier is not required. It adopts ambiguity from robust mechanism design so the system can reveal a set of possible classifiers while privately selecting which one to realize. This turns the learning problem into one of jointly optimizing the classifier together with the uncertainty it creates. The authors develop algorithms for best-response computation and training, then explore the resulting strategic outcomes empirically.

What carries the argument

Ambiguity set: a revealed range of possible classifiers to which agents best-respond while the system privately realizes one member of the set.

What would settle it

An experiment measuring whether agents facing an ambiguity set of classifiers adjust their features according to the full range or according to a single guessed classifier.

Watch

Extended reading notes

Core claim

Adopting ambiguity from robust mechanism design allows the learner to reveal a set or range of possible classifiers while privately choosing which to realize, jointly optimizing the classifier and the uncertainty surrounding it.

Load-bearing premise

Agents will best-respond to the revealed ambiguity set rather than assuming a single fixed classifier or attempting to infer the private choice.

Editorial extensions

If this is right

  • The learning task expands to include explicit optimization over uncertainty.
  • Efficient algorithms become available for computing best responses and for training under ambiguity.
  • Empirical outcomes of strategic interactions can be compared between full disclosure and ambiguous disclosure.
  • Partial disclosure changes the equilibrium behavior of agents in the strategic setting.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same partial-disclosure approach could apply to other machine-learning systems subject to transparency regulations.
  • Real-world agents might attempt to infer the privately chosen classifier even when an ambiguity set is provided.
  • This mechanism may allow systems to achieve better performance than full disclosure while still satisfying regulatory requirements.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript studies strategic classification under regulatory constraints requiring partial rather than full disclosure of the classifier. It adopts the notion of ambiguity from robust mechanism design, allowing the learner to disclose a set (or range) of possible classifiers while privately realizing one; the learner jointly optimizes the realized classifier and the disclosed ambiguity set. The work develops algorithms for computing agents' best responses to the ambiguity set and for training under this joint objective, then empirically explores the resulting strategic learning dynamics and outcomes.

Significance. If the behavioral assumption that agents best-respond to the disclosed ambiguity set (without inferring the private realization) holds, the framework offers a principled way to manage information disclosure in strategic settings and potentially improve learner utility relative to full or zero disclosure. The algorithmic contributions for best-response computation and joint optimization, together with the empirical exploration, constitute a concrete bridge between strategic classification and robust mechanism design.

major comments (2)
  1. [Model and Problem Formulation] The central modeling claim rests on agents treating the disclosed ambiguity set as the relevant uncertainty and best-responding to it (via worst-case or ambiguity-averse reasoning) rather than attempting to infer or form beliefs over the privately chosen classifier. This no-inference condition is load-bearing: if rational agents can update beliefs (via equilibrium reasoning or observable outcomes), the information structure collapses to a standard strategic classification game and the claimed advantage of ambiguity disappears. The manuscript should contain an explicit equilibrium analysis or payoff-structure argument establishing why inference is precluded or irrational.
  2. [Algorithms and Optimization] The abstract states that efficient algorithms are developed for best-response computation and training, yet the soundness assessment notes the absence of equations, proofs, or experimental details verifying that these algorithms correctly compute best responses under the ambiguity set or that the joint optimization is well-defined. A concrete description of the ambiguity-set parameterization, the precise optimization objective, and the best-response operator (e.g., §4 or Algorithm 1) is required to confirm correctness.
minor comments (2)
  1. [Notation] Notation for the ambiguity set and the private realization should be introduced with explicit definitions and distinguished from standard classifier notation to avoid reader confusion.
  2. [Experiments] The empirical section would benefit from additional baselines that explicitly model partial inference by agents, to illustrate the sensitivity of the reported gains to the no-inference assumption.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the modeling assumptions and algorithmic details. We address each major comment below and indicate planned revisions.

read point-by-point responses

  1. Referee: [Model and Problem Formulation] The central modeling claim rests on agents treating the disclosed ambiguity set as the relevant uncertainty and best-responding to it (via worst-case or ambiguity-averse reasoning) rather than attempting to infer or form beliefs over the privately chosen classifier. This no-inference condition is load-bearing: if rational agents can update beliefs (via equilibrium reasoning or observable outcomes), the information structure collapses to a standard strategic classification game and the claimed advantage of ambiguity disappears. The manuscript should contain an explicit equilibrium analysis or payoff-structure argument establishing why inference is precluded or irrational.

    Authors: We agree that the no-inference assumption is foundational and that a more explicit justification is warranted. In the regulatory setting we study, partial disclosure is mandated by design, and the ambiguity set constitutes the only information agents receive; the private realization is not revealed through observable outcomes within the interaction horizon, precluding Bayesian updating or equilibrium inference. To strengthen the manuscript, we will add a dedicated subsection in the model formulation that formalizes this information structure, drawing on the robust mechanism design literature to argue why inference is irrational under the given payoff and observability constraints. revision: yes

  2. Referee: [Algorithms and Optimization] The abstract states that efficient algorithms are developed for best-response computation and training, yet the soundness assessment notes the absence of equations, proofs, or experimental details verifying that these algorithms correctly compute best responses under the ambiguity set or that the joint optimization is well-defined. A concrete description of the ambiguity-set parameterization, the precise optimization objective, and the best-response operator (e.g., §4 or Algorithm 1) is required to confirm correctness.

    Authors: We acknowledge that the presentation of the algorithmic components could be more self-contained. The ambiguity set is parameterized as convex sets (e.g., intervals over linear classifiers), the joint objective is a min-max formulation maximizing learner utility against the worst-case best response, and best-response computation is performed via a linear program or projected gradient method as described in §4 and Algorithm 1. We will expand the manuscript with additional formal equations, a short proof sketch of correctness for the best-response operator, and supplementary experimental verification of the optimization procedure. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; approach imports external ambiguity concept without self-referential reduction

full rationale

The provided abstract and context describe adopting the notion of ambiguity from robust mechanism design to jointly optimize a classifier and surrounding uncertainty set. No equations, fitted parameters, or derivations are visible that reduce by construction to the paper's own inputs. The central modeling choice (agents best-responding to the revealed set rather than inferring the private realization) is an imported assumption from external literature, not a self-definitional or self-citation load-bearing step. No self-citations, ansatzes smuggled via citation, or renaming of known results are exhibited. The derivation chain is therefore self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central modeling choice (ambiguity as a revealed set with private realization) is taken from prior robust mechanism design literature.

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Cite this review

Pith. "Pith review of Ambiguous Strategic Classification." pith.science (2026). https://pith.science/paper/B7T2YSQE

@misc{pith2026260610137,
  author       = {Pith},
  title        = {Pith review of: Ambiguous Strategic Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B7T2YSQE}},
  note         = {Machine review of arXiv:2606.10137}
}
read the original abstract

A common assumption in strategic classification is that the classifier is public knowledge. However, it remains unclear whether, and why, a system would choose to commit to full disclosure. We study a setting in which regulation requires the system to disclose some, but not all, of the information. This induces a learning task in which the learner must jointly optimize the classifier and the uncertainty surrounding it. To this end, we adopt from robust mechanism design the notion of ambiguity, which in our setting allows the learner to reveal a set or range of possible classifiers, while privately choosing which of them to ultimately realize. We investigate how ambiguity affects the learning task, develop efficient algorithms for computing best-responses and training, and empirically explore strategic learning and its outcomes in this novel setting and using our approach.

Figures

Figures reproduced from arXiv: 2606.10137 by the authors.

Figure 1
Figure 1. (A) The ambiguous strategic setup, demonstrated for discrete ambiguity with Γ = {h, h′ 1, h′ 2}. Points move only if they can reach the AoP (purple). Adding possible classifiers h ′ suppresses movement (grey) by shrinking the AoP and consequently the movement region (green). Points are x classified as positive (yellow) if either h(x) = 1 or they can move. (B) Ambiguity gives rise to more nuanced strategic behavior a… view at source ↗
Figure 2
Figure 2. Left: The ambiguous strategic hinge loss (Eq. (12)) reduces prediction penalties by administering ‘re￾wards’ rx(Γ) based on directional distances to the effective decision boundary (Fe = 0). Right: An outer polyhedral approximation of the decision boundary, enabling a closed￾form solution at often minimal distortion. Since points are ultimately classified by h, it is natural to measure margins towards it. Hence, for… view at source ↗
Figure 3
Figure 3. Accuracy of our approach generally increases with the degree of permitted ambiguity, both in the discrete case with k (left) and in the continuous case with β (center). Optimal accuracy is typically attained at the correct, rather than maximal, amount of ambiguity (right). ambiguity. Results show that neither extreme is desir￾able. Gaussian data. Next we consider the classic exam￾ple of class-conditional multivariat… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Learned models for the separable data experiment. From left to right: naïve (non-strategic), standard strategic (k = 1), ambiguous strategic with k = 2, and ambiguous strategic with k = 3. For k = 2, 3 we also plot the effective classifier that is created based on the …
Figure 5
Figure 5. Figure 5: Social burden as a function of the accuracy. We can see that the burden acts in a poly trend with degree = 2, where for higher β the points are more centered around this poly. C. Additional experimental results C.1. Separable data [PITH_FULL_IMAGE:figures/full_fig_p01…
Figure 6
Figure 6. Figure 6: shows results for d ∈ 3, . . . , 9 and three distributions: uniform in [0, 1], normal, and Beta(2, 5). As can be seen, the maximal number of iterations per instance is ∼ 4 on average, and 12 in the worst case. Note the average behavior is constant (or even decreasing),…
Figure 7
Figure 7. Figure 7: Number of iterations in folktables dataset. Note that even though we used d = 7 in our data, the average running time in both train, validation and test is around 7. Moreover, the maximal number of iterations is 32. This means that the algorithm works with an averaged …
Figure 8
Figure 8. Figure 8: Illustration of the construction used in Lemma 6 and β ≤ max h1,h2∈H(c) 180◦ − angle(h1, h2) Where H(c) includes all classifiers from Γ intersecting at c. Proof. Since x, y, w are the same for L ∗ and Le, it suffices to bound the difference, measured in margin units, b…

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Reference graph

Works this paper leans on

15 extracted references · 1 canonical work pages

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    Bergemann, D

    PMLR, 2022. Bergemann, D. and Morris, S. Robust mechanism de- sign. Econometrica, pp. 1771–1813, 2005. Bergemann, D., Brooks, B., and Morris, S. Informa- tionally robust optimal auction design. Cowles Foun- dation Discussion Papers 2065, Cowles Foundation for Research in Economics, Yale University, 2016. Brückner, M., Kanzow, C., and Scheffer, T. Static p...

    work page arXiv 2022

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    Milli, S., Miller, J., Dragan, A

    PMLR, 2020. Milli, S., Miller, J., Dragan, A. D., and Hardt, M. The social cost of strategic classification. In Proceedings of the Conference on Fairness, Accountability, and Transparency, pp. 230–239, 2019. Nair, V., Ghalme, G., Talgam-Cohen, I., and Rosen- feld, N. Strategic representation. In International Conference on Machine Learning , pp. 16331–163...

    2020

  3. [3]

    That is, there exists w2 [ ¯w, ¯w] such that w⊤x′ + b < 0

    Suppose by contradiction that x′ /2S cont. That is, there exists w2 [ ¯w, ¯w] such that w⊤x′ + b < 0. Based on this w, we will construct w′ which yields even lower score than w, such that w′2 Ω. Recall that w⊤x′ = Σ iwix′ i. Then for each i:

  4. [4]

    It holds that w′ i x′ i wi x′ i, since w′ i wi

    If x′ i < 0, pick w′ i = ¯wi. It holds that w′ i x′ i wi x′ i, since w′ i wi

  5. [5]

    It holds that w′ i x′ i wi x′ i, since w′ i wi

    If x′ i 0, pick w′ i = ¯wi. It holds that w′ i x′ i wi x′ i, since w′ i wi. 13 Therefore, we get that w′⊤x′ + b < 0 also. This is a contradiction, since w′2 Ω and hence x′ /2 Sdisc. Eq. (7) and Eq. ( 9) minimize the same objective. Hence, from the equivalence of their feasibility sets we get that they share the same optimal solutions. Proof of Lemma 4. We...

  6. [6]

    It holds that w∗′ i xi < 0 and is smaller than ¯wi xi

    If xi < 0, pick w∗′ i = ¯wi. It holds that w∗′ i xi < 0 and is smaller than ¯wi xi

  7. [7]

    It holds that w∗′ i xi < 0 and is smaller than ¯wi xi

    If xi < 0, pick w∗′ i = ¯wi. It holds that w∗′ i xi < 0 and is smaller than ¯wi xi. Therefore, w∗⊤x + b = argminw∈Ω w⊤x + b, and since x is non feasible, w∗⊤x + b < 0. Hence, w∗ separates x from the feasible set defined by Ω and b. A.3. Projection algorithm (Algo. 1) Proof of Theorem 1. First, if by the end of the algorithm C = Ω then correctness is trivi...

  8. [8]

    For the positive class, µ+ = [1, 0, 0, ..., 0] and Σ+ = diag(0.5, 0.3, ..., 0.3)

Show all 15 references
  1. [9]

    Results were averaged over twenty random instances of the data

    For the negative class, µ− = [0.5, 0, 0, ..., 0] and Σ− = diag(2, 8, 2, 2, ..., 2) The label prior was set to P (y = 1) = p(y =1) = 0 .5, and the cost scale in ∆ was set to α = 1. Results were averaged over twenty random instances of the data. B.1.3. Optimization Parameter ini...

  2. [10]

    rounded” polytope with ball segments instead of vertices. The approximation eF outer-bounds these “corner

    and ’MIL’- Military Service (ordinal from 0 to 4). All features where scaled to [0, 1]. Labeled were set by binarizing the attribute ’ESR’ - employment status. Data generation. For each experimental instance we sampled 9,000 random class-balanced example. These were split 40:3...

  3. [11]

    If it derives from the outer min, return EXACT

    Compute et. If it derives from the outer min, return EXACT

  4. [12]

    If only one constraint is tight, return EXACT

    Compute x′ and its projection to the AoP. If only one constraint is tight, return EXACT

  5. [13]

    Note all steps above are implementable via the tools we provide in the paper

    Return APX. Note all steps above are implementable via the tools we provide in the paper. Empirical Distortion. We next examine R for non exact points. Note that computing the distortion requires computing t∗. For this, we use two properties:

  6. [14]

    The distance of points z on the line between x and x′ to the center c of C is convex in z

  7. [15]

    Together, this implies we can use line search to find t∗

    t∗ is exactly at distance 2 α from c. Together, this implies we can use line search to find t∗. Importantly, we would like to emphasize again that the ability to compute t∗ (for reasonably sized sets) does not imply that learning with t∗ is tractable. Results. We applied the a...

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