Pith. sign in

REVIEW 3 major objections 4 minor 108 references

Performative Learning Theory

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper proves that performative predictions—models that change the data they learn from—carry a fundamental trade-off: the more units that react, the weaker the generalization guarantees, and it shows when retraining still helps.

desk verdict A useful conceptual framework for performative generalization, but the central finite-sample bounds are invalidated by a proof error in Lemma 3.5; the paper needs major revision before its advertised results can be trusted. read the letter →

arxiv 2602.04402 v3 pith:GTRD6JX4 submitted 2026-02-04 stat.ML cs.AIcs.CYcs.LGmath.STstat.TH

Julian Rodemann , Unai Fischer-Abaigar , James Bailie , Krikamol Muandet This is my paper · ORCID
classification stat.MLcs.AIcs.CYcs.LGmath.STstat.TH MSC 68T0562G0562G20
keywords performativepredictiongeneralizationboundsWassersteindistanceempiricalriskminimizationexcessself-fulfillingpredictionssampleperformativitypopulation
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 embeds performative prediction—where a model's predictions change the distribution it is trying to learn from—into statistical learning theory. It proves finite-sample generalization and excess-risk bounds when the performative effect hits the training sample, the whole population, or both. The core result is a trade-off: the larger the share of units that react to predictions, the weaker the guarantees a learner can extract from data. The paper also shows that although retraining on shifted samples worsens the model's own bound, it can sharpen estimates of the population's response rate, so the initial model plus pooled shift observations gives the tightest guarantee. A case study on job-training assignments illustrates how the bounds grow with the intervention rate.

What carries the argument

The central object is the unknown transition map Tr(θ,d) that maps a deployed model and the current data distribution to the next distribution; it is assumed (ε,p)-jointly sensitive in Wasserstein distance. Around it, the paper builds: (i) the observed response rate m/n as an estimator of the population response rate s via a Bernoulli/Wald confidence bound; (ii) Wasserstein-p distance bounds on sample and population shifts; and (iii) covering-number entropy integrals plus dual characterizations of distributionally robust (sup) and 'favorable' (inf) risk functionals, which turn worst-case self-negating populations and self-fulfilling samples into computable bounds.

What would settle it

Take a performative system in which the training sample is deliberately unrepresentative—say 50% of sample units react while 90% of the population reacts. Under the paper's Lemma 3.9, the Wald interval centered at m/n would severely understate s, and the Theorem 3.10 or 3.13 bound could fall below the observed generalization gap. Equivalently, simulate a deterministic transition map that changes exactly m fixed sample units but nearly the whole population; if the gap exceeds the bound, the stochastic-independence reading of m/n is falsified.

Watch

Extended reading notes

Core claim

The central discovery is that generalization under performativity can be bounded with only compactness, strong convexity of the loss, regularity of the loss/hypothesis class, and joint Lipschitz sensitivity of the unknown transition map. In the worst case, the population works against the predictions (self-negation) while the sample appears to confirm them (self-fulfillment), and the paper casts these as min-max and min-min risk functionals in Wasserstein space. The resulting bounds—on performative excess risk, generalization gap, and cumulative risk—grow with the observed performative response rate m/n, formalizing a fundamental trade-off between changing the world and learning from it.

Load-bearing premise

The bounds rest on Lemma 3.9, which treats the observed fraction m/n of changed sample units as a Bernoulli estimate of the population response rate s; if units do not react independently with equal probability, or the sample is not representative of the population, the population-shift estimate and the bounds built on it can fail.

Editorial extensions

If this is right

  • If a model alters a larger fraction of the units it observes, the finite-sample generalization guarantee degrades; helping more people (e.g., assigning more job trainings) directly widens the bound.
  • Excess risk converges as n grows only when the response rate grows slowly enough; the condition needed here is weaker than the stability condition for performative predictions.
  • With full performativity, the initial empirical-risk minimizer yields the tightest bound; retraining hurts the model's guarantee but observing shifts over T rounds gives a pooled estimate of the response rate that tightens the bound.
  • The generalization gap splits into a sampling term, a hypothesis-complexity term, and a performative term, with the performative term proportional to the response rate.
  • Repeated empirical risk minimization under performativity amounts to fitting models in an echo chamber where the sample fulfills predictions and the population negates them.

Reading between the lines

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

  • Editorial inference: the response rate m/n could be monitored in deployment as a practical early warning—when it climbs, out-of-sample guarantees shrink even if in-sample accuracy looks fine.
  • Editorial inference: the Bernoulli/Wald estimate of the population response rate is the fragile link; extending the result to heterogeneous or non-representative responses (e.g., propensity-weighted estimators) would harden the bounds.
  • Editorial inference: the 'retrain to estimate the shift' idea should transfer to any feedback-loop setting—adaptive experiments, recommender systems, or policy rollouts—where the shift is unknown but observable.
  • Editorial inference: a direct simulation with a known linear transition map could test whether the empirical excess risk grows at the predicted m/n rate, which would validate or reject the theory's quantitative shape.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a statistical learning theory for performative prediction when the transition map can affect the training sample, the population, or both. It introduces a taxonomy of research questions (RQ1–RQ4), formalizes repeated ERM/RRM in Wasserstein space, and states finite-sample bounds: Theorem 3.7 (excess risk under sample performativity), Theorem 3.10 (performative excess risk), Theorems 3.13 and 3.15 (generalization gaps), and Theorem 3.16 (cumulative excess risk), together with a case study on German jobseekers. The headline insight is a trade-off: a larger observed response rate m/n leads to larger bounds. The proof strategy combines Wasserstein concentration, the Kantorovich-Rubinstein lemma, Rademacher/Dudley bounds, and a Bernoulli/Wald model for the population response rate.

Significance. The paper is well motivated, and the taxonomy together with the Wasserstein min-max/min-min interpretation are useful. If the bounds were correct, the work would be a significant step toward finite-sample learnability under performativity with minimal assumptions. The authors also provide code and a real-data illustration, which are strengths. However, the current manuscript contains a major error in the in-sample shift lemma and an unstated stochastic assumption in the population-shift lemma; the main generalization bounds are therefore not proved under the stated assumptions. In its present form the central claim cannot be accepted.

major comments (3)
  1. [Appendix C.1, Lemma 3.5] The recursion in Eq. (22) is delta_{t+1} <= epsilon delta_t + epsilon eta_t. Instead of solving this recurrence, the proof iterates delta_t <= epsilon^{T-1}(delta_1 + eta_1) for every t, which drops the terms epsilon eta_j for j>=2. Using eta_t <= L_a delta_t gives the correct recurrence delta_{t+1} <= epsilon(1+L_a) delta_t and hence W_p(hat d0, hat dT) <= ((q^T - 1)/(q - 1)) (m/n)^{1/p} D_Z with q = epsilon(1+L_a), with the usual modification for q <= 1. The stated bound (epsilon^T - 1)/(epsilon - 1) (m/n)^{1/p} D_Z / (1+L_a) is smaller and even decreases with L_a, which is not plausible. Since Lemma 3.5 is applied in Corollary 3.8 and Theorems 3.10, 3.13, 3.15, and 3.16, these results are not established by the current proofs.
  2. [Lemma 3.9 / Appendix C.4] Lemma 3.9 asserts a Wald confidence interval for the population response rate s from the observed fraction m/n. This requires that each unit reacts independently with probability s, i.e., that m is Binomial(n,s). Condition 3.2 is a deterministic Lipschitz condition on Tr; it supplies no Bernoulli/Binomial structure, and no independence or identical response probability is stated. Therefore the high-probability bound on s, and its use in Theorems 3.10, 3.13, 3.15, and 3.16, does not follow from the stated assumptions. This is an added modeling assumption, not a consequence of the 'minimal assumptions' advertised in Section 3.
  3. [Section 4 / Appendices B.2 and B.3] In the case study, the sensitivity constant epsilon is set to the observed m/n ('Further using epsilon = m/n', Appendix B.2), and the radius R in Appendix B.3 Eq. (9) omits the additive m/n term and the 1/(1+L_a) factor present in the definition of R in Theorem 3.13. Condition 3.2 defines epsilon as a worst-case sensitivity constant; an observed response rate is not the same object. The plotted bounds therefore do not evaluate the theorems as stated. This does not affect the theoretical contribution, but it invalidates the numerical illustration as a demonstration of the stated results.
minor comments (4)
  1. [Corollary 3.8] The displayed formula has a typo: L^{-1}_ell (epsilon - 1) should be L_ell / (epsilon - 1), as in the proof in Appendix C.3. The case-study calculation in Appendix B.2 appears to use the corrected form, so the displayed theorem and the appendix disagree.
  2. [Condition 3.3] The condition 'kappa-continuously differentiable' is not defined, and the proofs only seem to use Lipschitzness of the argmin map G. Please clarify the precise smoothness assumption and state the resulting Lipschitz constant.
  3. [Throughout] The phrase 'w.p. over d0' is imprecise: probabilities are over the training sample drawn from d0, not over the distribution d0 itself. This matters because some bounds are stated as holding 'pointwise in hat d0' while others require high-probability statements over the draw.
  4. [Corollary 3.11] Part (II) contains a typesetting error in the displayed Wald bound, and the proof assumes that the per-iteration counts m_t/n are independent Bernoulli estimates. This is the same extra stochastic assumption as in Lemma 3.9 and should be stated as an explicit condition if it is used.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the bounds are derived from stated assumptions and external results, with self-citations only in non-load-bearing contexts.

full rationale

The paper's derivation chain is self-contained relative to its stated assumptions. The main bounds (Theorems 3.7, 3.10, 3.13, 3.15, 3.16) are obtained by combining (i) an external Wasserstein concentration result (Lemma 3.4, Fournier & Guillin), (ii) transport-based bounds on the in-sample shift using the observable count m of changed units (Lemma 3.5), (iii) Lipschitz properties of the risk minimizer G derived from Conditions 3.1 and 3.3 via standard implicit-function and mean-value arguments, and (iv) standard empirical-process/Rademacher/Dudley bounds. Lemma 3.9 is an application of Wald's binomial interval treating the observed m/n as an estimator of a population response rate s; this is an explicit extra Bernoulli modeling assumption, not a hidden identification of the target with the input. The case study's choice ε=m/n is an illustrative numerical assignment in the application section, not a step in the proof of the theorems, and the theoretical bounds are not defined in terms of that choice. The self-citations to Rodemann et al. (2024) and Rodemann & Bailie (2025) appear in related-work positioning and as a 'see also' reference; the load-bearing Lipschitz/contraction facts are attributed to Brown et al. (2022) and Ross & Nyström (2018), so no claim reduces to a self-citation chain. The skeptic's objections concern the correctness of the recursion in Lemma 3.5, the unproven population analog, and the validity of the Bernoulli/Wald step; these are mathematical-validity concerns, not circularity in the sense of a prediction being equivalent by construction to a fitted input or a defined quantity. Accordingly, no circular step is exhibited, and the circularity score is 0.

Assumptions & free parameters 6 free parameters · 9 assumptions · 0 invented entities

The theoretical claims rest on standard learning-theoretic tools plus the Lipschitz/smoothness conditions of the performative prediction literature. The most fragile additions are the Bernoulli sampling model for m/n and the treatment of ε as an observed response rate, neither of which is justified by the stated transition-map framework.

free parameters (6)
  • ε (joint sensitivity constant) = m/n = 1816/60147 in the case study; unspecified in the theory
    Condition 3.2 introduces ε as a Lipschitz constant of the unknown transition map. The bounds depend on it, but the paper never estimates it except in the case study where it is set to the observed fraction of changed units, which is not a valid estimator of a worst-case constant.
  • Wasserstein order p = 2 in the case study
    The theory allows any p ∈ [1,2]; the case study fixes p=2 to compute numeric bounds.
  • Lipschitz constant L_a of the risk minimizer map G = ≈2 in the case study (computed as D_X/γ)
    Used in Lemma 3.5 and Theorem 3.7 to translate Wasserstein distribution shifts into parameter shifts. The case study estimates it crudely; the theory only assumes existence.
  • Strong convexity constant γ = γ=1 in the case study (L2 regularization strength C=1)
    Condition 3.1 requires γ-strong convexity. The case study chooses the regularizer strength, which sets γ.
  • C∞(F) entropy integral = ≈7.3855 in the case study
    Numerical value used to instantiate Theorem 3.13. The paper states it results from a Lipschitz covering argument but does not show the computation.
  • B (Condition 3.14 constant) = =10^{-3} 'exemplarily' in the case study
    Theorem 3.15 uses B from Condition 3.14; the case study chooses B=10^{-3} for the plot without empirical justification.
assumptions (9)
  • standard math Fournier-Guillin empirical Wasserstein convergence bound (Lemma 3.4)
    Invoked to bound W_p(bd0, d0). Standard result for empirical measures on bounded spaces.
  • standard math Kantorovich-Rubinstein duality
    Used to convert Wasserstein distances into loss expectation differences for Lipschitz loss.
  • standard math Rademacher complexity / Dudley entropy integral and Talagrand's contraction lemma
    Used in the proofs of Theorems 3.7, 3.13 and 3.15 to bound empirical-process terms.
  • standard math Dual characterization of Wasserstein distributionally robust risk (Gao & Kleywegt 2023; Lee & Raginsky 2018)
    Used in Theorem 3.13 and 3.15 proofs for supremum risk over Wasserstein balls.
  • standard math Implicit function theorem / Lipschitzness of the risk minimizer map G
    Used to justify that G(d) is L_a-Lipschitz under Conditions 3.1 and 3.3.
  • domain assumption Condition 3.2: Tr is (ε,p)-jointly sensitive
    The entire framework requires the unknown transition map to satisfy a Lipschitz condition with a known constant ε. This is a substantive assumption about the world, not a consequence of the setup.
  • domain assumption Conditions 3.1 and 3.3: strong convexity and κ-smoothness of the loss
    Required for the Lipschitzness of G and the contraction used in Theorem 3.7. The paper notes this is restrictive.
  • domain assumption Conditions 3.12 or 3.14: Lipschitzness or a local-growth condition on the hypothesis class
    Needed for the tighter bounds in Theorems 3.13 and 3.15.
  • ad hoc to paper The observed sample change count m/n is a Bernoulli estimate of the population response rate s, with Wald confidence interval (Lemma 3.9)
    This is not implied by the deterministic transition map Tr. It introduces an unstated stochastic model for how units react, and is load-bearing for the bounds in Theorem 3.10, Corollary 3.11 and Theorem 3.16.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Performative Learning Theory." pith.science (2026). https://pith.science/paper/GTRD6JX4

@misc{pith2026260204402,
  author       = {Pith},
  title        = {Pith review of: Performative Learning Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GTRD6JX4}},
  note         = {Machine review of arXiv:2602.04402}
}
read the original abstract

Performative predictions influence the very outcomes they aim to forecast. We study performative predictions that affect a sample (e.g., only existing users of an app) and/or the whole population (e.g., all potential app users). This raises the question of how well models generalize under performativity. For example, how well can we draw insights about new app users based on existing users when both of them react to the app's predictions? We address this question by embedding performative predictions into statistical learning theory. We prove generalization bounds under performative effects on the sample, on the population, and on both. A key intuition behind our proofs is that in the worst case, the population negates predictions, while the sample deceptively fulfills them. We cast such self-negating and self-fulfilling predictions as min-max and min-min risk functionals in Wasserstein space, respectively. Our analysis reveals a fundamental trade-off between performatively changing the world and learning from it: the more a model affects data, the less it can learn from it. Moreover, our analysis results in a surprising insight on how to improve generalization guarantees by retraining on performatively distorted samples. We illustrate our bounds in a case study on prediction-informed assignments of unemployed German residents to job trainings, drawing upon administrative labor market records from 1975 to 2017 in Germany.

Figures

Figures reproduced from arXiv: 2602.04402 by the authors.

Figure 1
Figure 1. 1.1 Example (A): Route predictions are known to have performative effects: Drivers avoid routes with predicted congestion, thereby rendering these predictions less accurate. Can routing apps still generalize from San Francisco (sample) to the whole Bay Area (population)? 1.2 Example (B): A job center in Bavaria assigns job training programs to those among the unemployed that have high risks of long-term unemployment… view at source ↗
Figure 2
Figure 2. Generalization gap bound from Theorem 3.15 and its decomposition as a function of ξ (fraction of jobseekers receiving training). The total bound (blue) is decomposed into complexity term CompB(ξ), sampling term Samp(ξ), and performative term Perf(ξ) (see details in Appendix B. All values are in logistic loss units. Parameters: n training samples, B = 10−3 , δ = 0.05, p = 2. B.4 Further Results from the Semi-Simulati… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

108 extracted references · 4 linked inside Pith

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry add.period write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTIO...

  2. [2]

    Allhutter, D., Cech, F., Fischer, F., Grill, G., & Mager, A. (2020). Algorithmic profiling of job seekers in Austria : How austerity politics are made effective. Frontiers in Big Data , 3, 5

    2020

  3. [3]

    L., Kern, C., Mautner, H., & Kreuter, F

    Bach, R. L., Kern, C., Mautner, H., & Kreuter, F. (2023). The impact of modeling decisions in statistical profiling. Data & Policy , 5, e32

    2023

  4. [4]

    R., Gan, Q., Bayen, A

    Bagabaldo, A. R., Gan, Q., Bayen, A. M., & Gonz \'a lez, M. C. (2024). Impact of navigation apps on congestion and spread dynamics on a transportation network. Data science for Transportation , 6(2), 12

    2024

  5. [5]

    Balcan, M.-F., Hanneke, S., & Vaughan, J. W. (2010). The true sample complexity of active learning. Machine learning , 80(2), 111--139

    2010

  6. [6]

    Bartlett, P. L. & Mendelson, S. (2002). Rademacher and G aussian complexities: Risk bounds and structural results. Journal of Machine Learning Research , 3(Nov), 463--482

    2002

  7. [7]

    Bastani, H. (2021). Predicting with proxies: Transfer learning in high dimension. Management Science , 67(5), 2964--2984

    2021

  8. [8]

    & Grammatico, S

    Benenati, E. & Grammatico, S. (2024). Probabilistic game-theoretic traffic routing. IEEE Transactions on Intelligent Transportation Systems , 25(10), 13080--13090

    2024

Show all 108 references
  1. [9]

    Besbes, O., Gur, Y., & Zeevi, A. (2015). Non-stationary stochastic optimization. Operations Research , 63(5), 1227--1244

    2015

  2. [10]

    Bian, H., Li, E., Liu, L., & Wang, Z. (2023). The influencer copycats. PBCSF-NIFR Research Paper

    2023

  3. [11]

    A., Dogan, \"U ., Lee, G., & Scott, C

    Blanchard, G., Deshmukh, A. A., Dogan, \"U ., Lee, G., & Scott, C. (2021). Domain generalization by marginal transfer learning. Journal of Machine Learning Research , 22(2), 1--55

    2021

  4. [12]

    Boeken, P., Zoeter, O., & Mooij, J. M. (2025). Conditional forecasts and proper scoring rules for reliable and accurate performative predictions. NeurIPS

    2025

  5. [13]

    & Elisseeff, A

    Bousquet, O. & Elisseeff, A. (2002). Stability and generalization. The Journal of Machine Learning Research , 2, 499--526

    2002

  6. [14]

    Bracale, D., Maity, S., et al. (2025). Microfoundation inference for strategic prediction. In Y. Li, S. Mandt, S. Agrawal, & E. Khan (Eds.), Proceedings of The 28th International Conference on Artificial Intelligence and Statistics , volume 258 of Proceedings of Machine Learni...

    2025

  7. [15]

    Brown, G., Hod, S., & Kalemaj, I. (2022). Performative prediction in a stateful world. In International conference on artificial intelligence and statistics (pp.\ 6045--6061).: PMLR

    2022

  8. [16]

    D., Cai, T

    Brown, L. D., Cai, T. T., & DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical science , 16(2), 101--133

    2001

  9. [17]

    Cabannes, T. (2019). Capturing the impact of navigational app usage on road traffic from a game theory point of view . PhD thesis, UC Berkeley

    2019

  10. [18]

    & Lugosi, G

    Cesa-Bianchi, N. & Lugosi, G. (2006). Prediction, learning, and games . Cambridge University Press

    2006

  11. [19]

    Chaney, A. J. B., Stewart, B. M., & Engelhardt, B. E. (2018). How algorithmic confounding in recommendation systems increases homogeneity and decreases utility. In Proceedings of the 12th ACM Conference on Recommender Systems , RecSys '18 (pp.\ 224--232). New York, NY, USA: As...

    2018

  12. [20]

    Chewi, S., Niles-Weed, J., & Rigollet, P. (2025). Statistical Optimal Transport: \'E cole d' \'E t \'e de Probabilit \'e s de Saint-Flour XLIX -- 2019 , volume 2364 of Lecture Notes in Mathematics . Springer

    2025

  13. [21]

    Cutler, J., D \' az, M., & Drusvyatskiy, D. (2024). Stochastic approximation with decision-dependent distributions: Asymptotic normality and optimality. Journal of Machine Learning Research , 25, 90:1--90:49

    2024

  14. [22]

    de Moivre, A. (1738). The Doctrine of Chances: Or, a Method of Calculating the Probabilities of Events in Play . London: H. Woodfall, 2 edition

  15. [23]

    Dong, J., Roth, A., Schutzman, Z., Waggoner, B., & Wu, Z. S. (2018). Strategic classification from revealed preferences. In Proceedings of the 2018 ACM Conference on Economics and Computation (pp.\ 55--70)

    2018

  16. [24]

    Dudley, R. (1987). Universal Donsker classes and metric entropy. The Annals of Probability , 15(4), 1306--1326

    1987

  17. [25]

    I., & Spinnewijn, J

    Ernst, S., Mueller, A. I., & Spinnewijn, J. (2024). Risk scores for long-term unemployment and the assignment to job search counseling. AEA Papers and Proceedings , 114, 572--576

    2024

  18. [26]

    Fischer-Abaigar, U., Kern, C., & Perdomo, J. C. (2025). The value of prediction in identifying the worst-off. In Forty-second International Conference on Machine Learning

    2025

  19. [27]

    & Guillin, A

    Fournier, N. & Guillin, A. (2015). On the rate of convergence in Wasserstein distance of the empirical measure. Probability theory and related fields , 162(3), 707--738

    2015

  20. [28]

    Gama, J., Z liobait \.e , I., Bifet, A., Pechenizkiy, M., & Bouchachia, A. (2014). A survey on concept drift adaptation. ACM Computing Surveys , 46(4), 1--37

    2014

  21. [29]

    & Kleywegt, A

    Gao, R. & Kleywegt, A. (2023). Distributionally robust stochastic optimization with Wasserstein distance. Mathematics of Operations Research , 48(2), 603--655

    2023

  22. [30]

    & Modigliani, F

    Grunberg, E. & Modigliani, F. (1954). The predictability of social events. Journal of Political Economy , 62(6), 465--478

    1954

  23. [31]

    A., Zhan, R., Wager, S., & Athey, S

    Hadad, V., Hirshberg, D. A., Zhan, R., Wager, S., & Athey, S. (2021). Confidence intervals for policy evaluation in adaptive experiments. Proceedings of the National Academy of Sciences , 118(15)

    2021

  24. [32]

    Hanneke, S. (2007). A bound on the label complexity of agnostic active learning. In Proceedings of the 24th international conference on Machine learning (pp.\ 353--360)

    2007

  25. [33]

    Hanneke, S. (2014). Theory of disagreement-based active learning. Foundations and Trends in Machine Learning , 7(2-3), 131--309

    2014

  26. [34]

    Hardt, M., Megiddo, N., Papadimitriou, C., & Wootters, M. (2016). Strategic classification. In Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science (pp.\ 111--122)

    2016

  27. [35]

    & Mendler-D \"u nner, C

    Hardt, M. & Mendler-D \"u nner, C. (2025). Performative prediction: Past and future. Statistical Science , 40(3), 417--436

    2025

  28. [36]

    Hazan, E. (2016). Introduction to online convex optimization. Foundations and Trends in Optimization , 2(3-4), 157--325

    2016

  29. [37]

    S., & Srebro, N

    Hazan, E., Shwartz, S. S., & Srebro, N. (2025). Research program: Theory of learning in dynamical systems. arXiv preprint arXiv:2512.19410

    2025

  30. [38]

    Jia, Z., Wang, Y., Dong, R., & Hanasusanto, G. A. (2025). Distributionally robust performative optimization. In The Thirty-ninth Annual Conference on Neural Information Processing Systems

    2025

  31. [39]

    & Xie, W

    Jiang, N. & Xie, W. (2025). On tractability, complexity, and mixed-integer convex programming representability of distributionally favorable optimization. Mathematical Programming , (pp.\ 1--38)

    2025

  32. [40]

    Junquera, \'A . F. & Kern, C. (2025). From rules to forests: Rule-based versus statistical models for jobseeker profiling. Journal for Labour Market Research , 59(1), 26

    2025

  33. [41]

    Kallus, N. (2018). Balanced policy evaluation and learning. Advances in neural information processing systems , 31

    2018

  34. [42]

    Kantorovich, L. V. & Rubinstein, S. (1958). On a space of totally additive functions. Vestnik of the St. Petersburg University: Mathematics , 13(7), 52--59

    1958

  35. [43]

    L., Mautner, H., & Kreuter, F

    Kern, C., Bach, R. L., Mautner, H., & Kreuter, F. (2021). Fairness in algorithmic profiling: A German case study. arXiv preprint arXiv:2108.04134

    2021 arXiv

  36. [44]

    E., Kim, A

    Khandani, A. E., Kim, A. J., & Lo, A. W. (2010). Consumer credit-risk models via machine-learning algorithms. Journal of Banking & Finance , 34(11), 2767--2787

    2010

  37. [45]

    Kirev, I., Baltadzhiev, L., & Konstantinov, N. (2025). PAC learnability in the presence of performativity. arXiv preprint arXiv:2510.08335

    2025

  38. [46]

    Kleinberg, J., Lakkaraju, H., Leskovec, J., Ludwig, J., & Mullainathan, S. (2018). Human decisions and machine predictions. The quarterly journal of economics , 133(1), 237--293

    2018

  39. [47]

    Kleinberg, J., Ludwig, J., Mullainathan, S., & Obermeyer, Z. (2015). Prediction policy problems. American Economic Review , 105(5), 491--495

    2015

  40. [48]

    Kolmogorov, A. N. & Tikhomirov, V. M. (1959). -entropy and -capacity of sets in function spaces. Uspekhi Matematicheskikh Nauk , 14(2), 3--86

    1959

  41. [49]

    o nig, G., Fokkema, H., Freiesleben, T., Mendler-D \

    K \"o nig, G., Fokkema, H., Freiesleben, T., Mendler-D \"u nner, C., & von Luxburg, U. (2025). Performative validity of recourse explanations. In The Thirty-ninth Annual Conference on Neural Information Processing Systems

    2025

  42. [50]

    & Szepesv \'a ri, C

    Lattimore, T. & Szepesv \'a ri, C. (2020). Bandit algorithms . Cambridge University Press

    2020

  43. [51]

    & Raginsky, M

    Lee, J. & Raginsky, M. (2018). Minimax statistical learning with Wasserstein distances. Advances in Neural Information Processing Systems , 31

    2018

  44. [52]

    Li, V., Chen, B., Mao, Y., Lei, Q., & Deng, Z. (2025a). Performative risk control: Calibrating models for reliable deployment under performativity. NeurIPS

  45. [53]

    Li, X., Li, Y., Zhong, H., Lei, L., & Deng, Z. (2025b). Statistical inference under performativity. In The Thirty-ninth Annual Conference on Neural Information Processing Systems

  46. [54]

    T., Raji, I

    Liu, L. T., Raji, I. D., et al. (2025). Bridging prediction and intervention problems in social systems. arXiv preprint arXiv:2507.05216

    2025

  47. [55]

    Lu, Y., Meisami, A., Tewari, A., & Yan, W. (2021). Regret analysis of bandit problems with causal background knowledge. In Conference on Uncertainty in Artificial Intelligence (pp.\ 1351--1361).: PMLR

    2021

  48. [56]

    MacKenzie, D. (2008). An engine, not a camera: How financial models shape markets . MIT Press

    2008

  49. [57]

    McDiarmid, C. et al. (1989). On the method of bounded differences. Surveys in combinatorics , 141(1), 148--188

    1989

  50. [58]

    Mendler-D \"u nner, C., Ding, F., & Wang, Y. (2022). Anticipating performativity by predicting from predictions. Advances in neural information processing systems , 35, 31171--31185

    2022

  51. [59]

    Miller, J., Milli, S., & Hardt, M. (2020). Strategic classification is causal modeling in disguise. In International Conference on Machine Learning (pp.\ 6917--6926).: PMLR

    2020

  52. [60]

    P., Perdomo, J

    Miller, J. P., Perdomo, J. C., & Zrnic, T. (2021). Outside the echo chamber: Optimizing the performative risk. In International Conference on Machine Learning (pp.\ 7710--7720).: PMLR

    2021

  53. [61]

    Mofakhami, M., Mitliagkas, I., & Gidel, G. (2023). Performative prediction with neural networks. In International Conference on Artificial Intelligence and Statistics (pp.\ 11079--11093).: PMLR

    2023

  54. [62]

    O konomie und Wirtschaftsinformatik, Deutscher Universit \

    Morgenstern, O. (1928). Wirtschaftsprognose: Eine Untersuchung ihrer Voraussetzungen und M \"o glichkeiten , Wien 1928, cited after: G. betz (2004), Empirische und aprioristische Grenzen von Wirtschaftsprognosen : Oskar Morgenstern nach 70 Jahren . Wissenschaftstheorie in \"O ...

    1928

  55. [63]

    Muandet, K., Balduzzi, D., & Sch \"o lkopf, B. (2013). Domain generalization via invariant feature representation. In International Conference on Machine Learning (pp.\ 10--18)

    2013

  56. [64]

    Muandet, K., Fukumizu, K., Sriperumbudur, B., & Sch \"o lkopf, B. (2017). Kernel mean embedding of distributions: A review and beyond. Foundations and Trends in Machine Learning , 10(1-2), 1--141

    2017

  57. [65]

    Muandet, K., Kanagawa, M., Saengkyongam, S., & Marukata, S. (2021). Counterfactual mean embeddings. In International Conference on Machine Learning (pp.\ 7107--7117).: PMLR

    2021

  58. [66]

    Nagler, T. (2024). Statistical Learning Theory -- Lecture Notes . Technical report, LMU Munich

    2024

  59. [67]

    Neurath, O. (1911). National \"o konomie und Wertlehre: eine systematische Untersuchung , volume 20

    1911

  60. [68]

    Nisan, N., Roughgarden, T., Tardos, E., & Vazirani, V. V. (2007). Algorithmic game theory . Cambridge University Press

    2007

  61. [69]

    Pearl, J. (2009). Causality . Cambridge University Press

    2009

  62. [70]

    Perdomo, J. (2023). Performative Prediction: Theory and Practice . PhD thesis, UC Berkeley

    2023

  63. [71]

    Perdomo, J., Zrnic, T., Mendler-D \"u nner, C., & Hardt, M. (2020). Performative prediction. In International Conference on Machine Learning (pp.\ 7599--7609).: PMLR

    2020

  64. [72]

    Perdomo, J. C. (2024). The relative value of prediction in algorithmic decision making. In Proceedings of the 41st International Conference on Machine Learning (pp.\ 40439--40460)

    2024

  65. [73]

    Perdomo, J. C. (2025). Revisiting the predictability of performative, social events. arXiv preprint arXiv:2503.11713

    2025 arXiv

  66. [74]

    C., Britton, T., Hardt, M., & Abebe, R

    Perdomo, J. C., Britton, T., Hardt, M., & Abebe, R. (2025). Difficult lessons on social prediction from Wisconsin public schools. In Proceedings of the 2025 ACM Conference on Fairness, Accountability, and Transparency (pp.\ 2682--2704)

    2025

  67. [75]

    Peters, J., Janzing, D., & Sch \"o lkopf, B. (2017). Elements of causal inference: foundations and learning algorithms . MIT Press

    2017

  68. [76]

    Quionero-Candela, J., Sugiyama, M., Schwaighofer, A., & Lawrence, N. D. (2009). Dataset shift in machine learning . MIT Press

    2009

  69. [77]

    & Augustin, T

    Rodemann, J. & Augustin, T. (2024). Imprecise bayesian optimization. Knowledge-Based Systems , 300, 112186

    2024

  70. [78]

    & Bailie, J

    Rodemann, J. & Bailie, J. (2025). Generalization bounds and stopping rules for learning with self-selected data. arXiv preprint arXiv:2505.07367

    2025 arXiv

  71. [79]

    Rodemann, J., Jansen, C., & Schollmeyer, G. (2024). Reciprocal learning. Advances in Neural Information Processing Systems , 37

    2024

  72. [80]

    & Nystr \"o m, D

    Ross, J. & Nystr \"o m, D. W. (2018). Differentiability of the argmin function and a minimum principle for semiconcave subsolutions. arXiv preprint arXiv:1808.04402

    2018 arXiv

  73. [81]

    Roughgarden, T. (2016). Twenty lectures on algorithmic game theory . Cambridge University Press

    2016

  74. [82]

    Russac, Y., Vernade, C., & Cappe, O. (2019). Weighted linear bandits for non-stationary environments. In Advances in Neural Information Processing Systems , volume 32

    2019

  75. [83]

    & vom Berge, P

    Schmucker, A. & vom Berge, P. (2023a). Factually anonymous version of the sample of integrated labour market biographies ( SIAB-Regional File ) -- version 7521 v1. Research Data Centre of the Federal Employment Agency (BA) at the Institute for Employment Research (IAB). Research data

  76. [84]

    & vom Berge, P

    Schmucker, A. & vom Berge, P. (2023b). Sample of integrated labour market biographies regional file (siab-r) 1975--2021. FDZ-Datenreport. FDZ-Datenreport, 07/2023 (en), N \"u rnberg

    1975

  77. [85]

    Settles, B. (2009). Active learning literature survey. University of Wisconsin-Madison Department of Computer Sciences

    2009

  78. [86]

    & Ben-David, S

    Shalev-Shwartz, S. & Ben-David, S. (2014a). Part I : Foundations. Understanding Machine Learning: From Theory to Algorithms , (pp.\ 11–86)

  79. [87]

    & Ben-David, S

    Shalev-Shwartz, S. & Ben-David, S. (2014b). Understanding machine learning: From theory to algorithms . Cambridge university press

  80. [88]

    Shapiro, A., Dentcheva, D., & Ruszczynski, A. (2021). Lectures on stochastic programming: modeling and theory . SIAM

    2021

  81. [89]

    Shimodaira, H. (2000). Improving predictive inference under covariate shift by weighting the log-likelihood function. Journal of Statistical Planning and Inference , 90(2), 227--244

    2000

  82. [90]

    Slivkins, A. et al. (2019). Introduction to multi-armed bandits. Foundations and Trends in Machine Learning , 12(1-2), 1--286

    2019

  83. [91]

    Soros, G. (1994). The Alchemy of Finance: Reading the Mind of the Market . John Wiley & Sons

    1994

  84. [92]

    & Zakynthinou, L

    Steinke, T. & Zakynthinou, L. (2020). Reasoning about generalization via conditional mutual information. In Conference on Learning Theory (pp.\ 3437--3452).: PMLR

    2020

  85. [93]

    Talagrand, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Publications Math \'e matiques de l'Institut des Hautes Etudes Scientifiques , 81, 73--205

    1995

  86. [94]

    Talagrand, M. (2014). Upper and lower bounds for stochastic processes , volume 60. Springer

    2014

  87. [95]

    Vapnik, V. (1991). Principles of risk minimization for learning theory. Advances in neural information processing systems , 4

    1991

  88. [96]

    Vapnik, V. (1998). Statistical learning theory. John Wiley & Sons , 2, 831--842

    1998

  89. [97]

    Vapnik, V. (1999). The Nature of Statistical Learning Theory . Springer Science & Business Media

    1999

  90. [98]

    Vapnik, V. N. & Chervonenkis, A. Y. (1968). The uniform convergence of frequencies of the appearance of events to their probabilities. Doklady Akademii Nauk , 181(4), 781--783

    1968

  91. [99]

    Q., Aadil, M., Chau, S

    Vo, K. Q., Aadil, M., Chau, S. L., & Muandet, K. (2024). Causal strategic learning with competitive selection. In Proceedings of the AAAI Conference on Artificial Intelligence , volume 38 (pp.\ 15411--15419)

    2024

  92. [100]

    & Sch \"o lkopf, B

    Von Luxburg, U. & Sch \"o lkopf, B. (2011). Statistical learning theory: Models, concepts, and results. In Handbook of the History of Logic , volume 10 (pp.\ 651--706). Elsevier

    2011

  93. [101]

    & Welle, P

    Wilder, B. & Welle, P. (2025). Learning treatment effects while treating those in need. In Proceedings of the 26th ACM Conference on Economics and Computation (pp.\ 448--473)

    2025

  94. [102]

    & Sun, Y

    Xue, S. & Sun, Y. (2024). Distributionally robust performative prediction. In The Thirty-eighth Annual Conference on Neural Information Processing Systems

    2024

  95. [103]

    Zalouk, S., Marx, C., Belakaria, S., De Sa, C., & Ermon, S. (2025). Multivariate calibration is performative: A perspective on pitfalls and progress. In 1st ICML Workshop on Foundation Models for Structured Data

    2025

  96. [104]

    A., & Athey, S

    Zhan, R., Hadad, V., Hirshberg, D. A., & Athey, S. (2021). Off-policy evaluation via adaptive weighting with data from contextual bandits. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining (pp.\ 2125--2135)

    2021

  97. [105]

    & Conitzer, V

    Zhang, H. & Conitzer, V. (2021). Incentive-aware PAC learning. In Proceedings of the AAAI Conference on Artificial Intelligence , volume 35 (pp.\ 5797--5804)

    2021

  98. [106]

    & Bareinboim, E

    Zhang, J. & Bareinboim, E. (2020). Designing optimal dynamic treatment regimes: A causal reinforcement learning approach. In International Conference on Machine Learning (pp.\ 11012--11022).: PMLR

    2020

  99. [107]

    Zhang, K., Janson, L., & Murphy, S. (2021). Statistical inference with m-estimators on adaptively collected data. Advances in neural information processing systems , 34, 7460--7471

    2021

  100. [108]

    Zhang, K., Sch \"o lkopf, B., Muandet, K., & Wang, Z. (2013). Domain adaptation under target and conditional shift. In International Conference on Machine Learning (pp.\ 819--827)

    2013

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.