Pith. sign in

REVIEW 2 major objections 6 minor 49 references

Algorithmic Fairness: A Runtime Perspective

T0 review · 2 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Fairness can be studied as a runtime property of sequential decisions, and the feasibility of monitoring or enforcing it is determined entirely by the environment dynamics, prediction horizon, and confidence threshold.

desk verdict Useful survey and two new algorithms, but the monitoring problem is trivially solvable by the constant [0,1] monitor, so the central impossibility claim is false as stated. read the letter →

arxiv 2507.20711 v1 pith:YPSGIEVO submitted 2025-07-28 cs.AI

Filip Cano , Thomas A. Henzinger , Konstantin Kueffner This is my paper · ORCID
classification cs.AI MSC 68Q6060J2068T01
keywords runtimefairnessmonitoringenforcementbiasedcoinprocessesMarkovchainsconfidenceintervalsconditionalexpectationalgorithmic
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

This paper argues that fairness in AI is not a one-time static property but a runtime property of a sequential process, and it models each decision as a coin toss whose bias can evolve over time. Within this model it poses two problems: monitoring fairness by outputting a high-confidence interval, and enforcing fairness by intervening to keep it in a target interval. The paper's central finding is that neither problem has a universal solution; whether a monitor or enforcer exists, and how to build one, is fully determined by the environment dynamics, the prediction horizon, and the confidence level. Under no assumptions, infinite-horizon outcome fairness cannot be monitored at all, while finite-horizon outcome fairness is trivial; under static, Markovian, hidden-Markovian, or additive dynamics, monitoring becomes possible, and under weak interval assumptions, enforcement is always feasible. The payoff is a roadmap and a unified parameter space in which existing results are placed and new algorithms are given.

What carries the argument

The central object is a sequence $w=(p_t,x_t)_{t\in\mathbb{N}^+}$ of coin biases and outcomes, together with a dynamics function $\theta:W^*\to\Delta(P)$ that samples the next bias from the history. Runtime fairness is the conditional expectation $\rho_t^h(W;\varphi)=\mathbb{E}_\theta(\varphi(W_{1:t+h})\mid w_{1:t})$ of one of three measures (outcome average, bias average, current bias) over a prediction horizon $h$. The machinery carries the argument in two ways: monitoring reduces to maintaining a register that estimates the relevant expectation and wrapping it in confidence intervals obtained from concentration inequalities (Hoeffding-type bounds for pointwise soundness, time-uniform confidence sequences for uniform soundness); enforcement reduces to a shield that decides whether to overwrite a bias or outcome, with cost measured by a history-dependent cost function. The examples show that the same register-and-interval template specializes to static, Markovian, hidden-Markovian, and additive dynamics by changing only the error-bound computation.

What would settle it

Take a real logged decision stream, such as loan acceptances over several years, and estimate at each step the next-decision probability from the full history; if two prefixes with approximately the same scalar bias $p_t$ yield systematically different next-outcome probabilities, or if the monitor's confidence intervals exclude the empirical acceptance rate more often than $\delta$, the coin-process representation of runtime fairness is falsified.

Watch

Extended reading notes

Core claim

Runtime fairness should be understood as the conditional expectation, given the observed history, of a fairness measure over a prediction horizon, rather than as a static average over a fixed dataset. In the coin setting, a stochastic process $W=(P_t,X_t)_{t\in\mathbb{N}^+}$ is generated by a dynamics function $\theta:W^*\to\Delta(P)$; at each step the bias is drawn from $\theta$ conditioned on history and the outcome is a Bernoulli trial. The paper claims that for the two core problems—monitoring (output an interval containing $\rho_t^h(W;\varphi)$ with probability $1-\delta$) and enforcement (intervene to keep the property inside target intervals)—feasibility is determined by the class of dynamics, fairness measure, horizon, and confidence threshold. It exhibits the boundary cases: with unrestricted dynamics, infinite-horizon outcome fairness is unmonitorable, whereas with a single static coin, every measure and horizon is monitorable; for enforcement, any fairness property can be enforced with high confidence under mild interval assumptions, and cost-optimal enforcement is achievable in static known-dynamics settings. The paper thereby unifies scattered results into one taxonomy and adds a probabilistic finite-window enforcer with fewer restrictions than prior work.

Load-bearing premise

The load-bearing premise is that real-world fairness dynamics can be represented as a history-dependent sequence of independent biased coin tosses, with the fairness-relevant quantity being a function of the biases or outcomes; the paper explicitly notes that full generality would require the bias to depend on the entire process including the customer, group, and classifier decision.

Editorial extensions

If this is right

  • For deployed systems, the impossibility result means that asking for a monitor of long-run outcome fairness in an unconstrained environment is asking for something that cannot exist; constraints on the environment are a prerequisite, not an optimization.
  • When the environment is a single unknown coin, every fairness measure and every horizon can be monitored with the same register update, so simple deployed systems can get runtime fairness verdicts inexpensively.
  • Under observable or hidden Markovian dynamics, fairness monitoring is sound but has an explicit cost in waiting time, since the hidden-chain error bound depends on the mixing time and verdicts must be delayed until the chain has mixed.
  • For enforcement, weak conditions on the target intervals suffice: bias fairness can be enforced by pinning the bias to a common intersection point, and outcome fairness by a threshold rule that flips outcomes when the running average drifts the wrong way.
  • In static systems with known bias, finite-window enforcement can be made cost-optimal, and the paper's new probabilistic enforcer works under a less restricted setting than previous cost-optimal enforcers, at the price of a confidence guarantee rather than an almost-sure one.

Reading between the lines

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

  • Read as a design principle, the paper implies that a runtime fairness system should first classify its environment (static, Markovian, hidden, additive, or unknown) and only then select an algorithm; the taxonomy effectively serves as a decision tree for practitioners.
  • The paper's own future-work suggestion points to discounting as a way to interpolate between current fairness and cumulative bias fairness; a concrete testable extension would be a discounted measure $\sum\gamma^{t-i}p_i$ and a monitor whose error bound depends on $\gamma$.
  • The claim that group fairness properties reduce to differences of coin biases suggests a practical falsification test: run the proposed monitors on logged data from a real lending or hiring pipeline and check whether the confidence intervals cover the acceptance-probability gap; failures would indicate that per-decision Bernoulli independence is the wrong model.
  • Combining monitoring and enforcement for unknown dynamics, which the paper lists as open, could be approached by treating the monitor's confidence intervals as a partial observation for the enforcer, yielding an adaptive shield with self-tuned intervention thresholds.
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

2 major / 6 minor

Summary. The paper proposes a runtime perspective on algorithmic fairness, modeling each step as a biased coin toss whose bias evolves under a history-dependent dynamics function. It defines three fairness measures (outcome, bias, and current fairness), lifts them to stochastic processes via conditional expectations, and poses two problems: monitoring fairness within a confidence interval and enforcing fairness within target intervals. The paper surveys existing monitoring results for static, Markovian, hidden Markovian, and additive dynamics, and existing enforcement results for static known dynamics, adding new results: a static-coin monitor with uniform confidence sequences, process-agnostic enforcement theorems (Theorems 1 and 2), and a probabilistic finite-window enforcer (Theorem 7). The central claim is that feasibility of monitoring and enforcement is fully determined by environment dynamics, prediction horizon, and confidence threshold, with no one-size-fits-all solution.

Significance. If the framework and taxonomy are made rigorous, the paper would provide a useful unified presentation of runtime fairness monitoring and enforcement, with clearly parametrized problem statements and a structured survey of recent results. The paper's strengths include explicit problem definitions, self-contained proofs for the new lemmas and theorems, correct use of established concentration inequalities (Hoeffding, Howard et al.) for static-coin monitoring, and honest discussion of scope limitations, including the admission in Section 7.1 that full generality of group fairness requires a richer state space. The paper also includes a valuable comparison of pointwise versus uniform soundness and of finite versus periodic enforcement windows. However, the formal monitoring problem as stated is currently degenerate: the constant monitor returning [0,1] solves every instance, so the claimed impossibility results and the associated taxonomy are not yet supported.

major comments (2)
  1. [Sec. 3.1 and Sec. 4] Problem 1 is trivially solvable in full generality by the constant monitor M(u)=[0,1]. For every φ∈{φ_O,φ_B,φ_C}, the runtime fairness value ρ^h_t(W;φ) is a conditional expectation of a [0,1]-valued random variable, hence lies in [0,1] almost surely under every dynamics θ, every t, h, and δ. Therefore both pointwise soundness (Eq. 7) and uniform soundness (Eq. 8) are satisfied. Section 3.3 explicitly states that aggregating interval quality is out of scope, so no nontriviality or tightness constraint is part of Problem 1. The counterexample in Section 3.4.2 shows only that no monitor can converge to the limit fairness value from finite prefixes, not that no sound interval can be produced. Consequently, the opening claim of Section 4 that "There does not exist a monitor capable of solving Problem 1 in full generality" and the ✗ entries in Table 1 are false as stated. The problem definition must be modified, for example by requiring the monitor to produce intervals that shrink with t, or by adding an explicit quality objective, before the infeasibility taxonomy can be sustained.
  2. [Sec. 5.1.1 and App. A.6] Theorem 7 is stated under Assumptions 5, 9, and 10, but its proof in Appendix A.6 states that it holds under Assumptions 10 and 12, where Assumption 12 fixes δ=0. This is a substantive inconsistency: the main text presents Theorem 7 as a probabilistic guarantee for general δ∈(0,1), while the proof as written claims an almost-sure setting. The proof itself actually establishes a stronger statement for arbitrary δ under a feasibility condition P(t,h)>0, so the mismatch is fixable by aligning the assumption list and clarifying the quantifier over δ in both the statement and the proof.
minor comments (6)
  1. [Sec. 2.2] In the sentence "P ⊆ [0,1] is a subset set of all coins," the word "set" is duplicated; it should read "a subset of all coins."
  2. [Sec. 3.3] The sentence "we only consider enforcers that overwrite bias our outcome, but not both" contains a typo: "our" should be "or."
  3. [Sec. 4.2, Example 1] The expression ψ = p(1)θ(p,x)(p(1)) + p(2)θ(p,x)(p(1)) repeats p(1) in the second term; it should be p(2)θ(p,x)(p(2)).
  4. [App. A.1, Proof of Theorem 2] The proof lists the two dangerous cases as "φO(x1:(t−1)) ≤ p and xt = 0, or with φO(x1:(t−1)) ≤ p and xt = 0"; the second case should be φO(x1:(t−1)) > p and xt = 1. In the same proof, the final displayed inequality in the second case should be φO(x1:t) ≤ p + 1/t, not > p + 1/t.
  5. [Sec. 3.1] Problem 1 defines the prediction horizon as h∈N, while the runtime fairness definition in Eq. (6) and several assumptions such as Assumption 2 allow h=∞. The definition of Problem 1 should be aligned to h∈N∪{∞}.
  6. [App. A.6, Eq. (20)] The sentence "for a sequence w1:t with t coins and h tails" uses h for tails, but h was defined earlier as the number of heads; please correct the terminology to avoid confusion.

Circularity Check

2 steps flagged · score 6.0 of 10

Formal monitoring impossibility collapses to a trivial interval monitor, and a periodic-enforcement theorem is imported from a self-citation that the paper admits does not support it.

  1. self definitional [Sec. 3.1 (Problem 1, Eqs. (7)-(8)), Sec. 3.3, Sec. 3.4.2, Sec. 4 opening]
    "Problem 1. Given a problem instance (Θ, φ, h, δ), synthesise a pointwise sound or uniformly sound monitor. ... Intuitively, we want the monitor to output the tightest interval possible while remaining sound. ... There does not exist a monitor capable of solving Problem 1 in full generality."

    The claimed non-existence theorem is not entailed by the stated Problem 1. Eqs. (7)-(8) only require ρ^h_t(W;φ) ∈ M(U1:t) with probability ≥ 1−δ. Because the fairness measures in Eqs. (1)-(3) are averages or biases in [0,1], every ρ^h_t is a.s. in [0,1]; hence M(u)=[0,1] satisfies both soundness conditions by construction. Thus the paper's own soundness definition supplies a universal solution, and the Sec. 4 impossibility can hold only under an unstated 'tightest interval' requirement, which Sec. 3.3 explicitly leaves out of scope. The impossibility is therefore an artifact of a definitional omission rather than a consequence of the formal problem.

  2. self citation load bearing [Sec. 5.2 (Theorem 9 and the following note)]
    "Theorem 9 ([13]). The enforcer described in Eq.(16) solves Problem 2 under Assumptions 5, 9, 11, and 12. ... Theorem 9 is a direct consequence of [13, Thm. 5]. Note that the original result is stated in terms of more general group fairness properties, and as a result, the produced enforcers are not sound for δ = 0, but they are pointwise sound for a confidence value δ > 0 dependent on the input distribution."

    Theorem 9 is stated under Assumption 12, which sets δ=0. The only support offered is a citation to the authors' own [13, Thm. 5], and the very next sentence concedes that the original result's enforcers are not sound for δ=0 and provide only pointwise soundness for δ>0. Thus the uniform, almost-sure periodic-enforcement claim is not implied by the cited self-work; the theorem's conclusion is imported from a self-citation that, by the paper's own admission, does not state it. This is load-bearing for the periodic enforcement row of Table 2.

full rationale

The paper's genuinely new technical results — the process-agnostic enforcers of Section 3.4.3, the static-coin monitor of Section 4.1, and the probabilistic finite-window enforcer of Section 5.1.1 — are self-contained and do not derive their conclusions from the surveyed self-citations. The concentration-based monitor rests on Hoeffding and Howard et al., which are external. However, the central monitoring impossibility is not a valid consequence of Problem 1: the soundness definition allows the constant [0,1] monitor, so the claimed nonexistence of a general monitor depends on an unformalized tightness criterion that Section 3.3 explicitly defers. Separately, Theorem 9's periodic enforcement guarantee is attributed to the authors' own prior work while the paper simultaneously admits that work gives only pointwise soundness for δ>0, not the stated δ=0 uniform guarantee. These are two load-bearing circular or definitional failures in the claimed taxonomy, although the rest of the surveyed and new material retains independent mathematical content. Score 6 reflects partial circularity: one central result reduces to a definitional artifact and one result is carried by an insupportable self-citation.

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

No free parameters are fitted to data; the error bounds are derived from concentration inequalities with user-specified confidence δ. The only invented notions are formal definitions (runtime fairness ρ, monitors, enforcers), not entities requiring independent evidence. The axioms are standard math plus domain assumptions about the coin-process model and observability, which the paper states explicitly.

assumptions (6)
  • domain assumption The stochastic process W is defined by a dynamics function θ: W* to Δ(P) mapping histories to distributions over biases, with outcomes drawn as Bernoulli(p_t).
    Sec. 2.3, Eq. (5). This is the modeling foundation; it assumes the environment can be described by history-dependent coin biases, which the paper motivates but does not validate against real systems.
  • domain assumption The monitor observes only outcomes x_t, not biases p_t, in the monitoring problem.
    Sec. 3.1, monitor M: X* to I([0,1]). This restricts evidence to outcomes, which is realistic for many systems but is a modeling choice that drives the impossibility results.
  • domain assumption For hidden Markov chains, the monitor knows a bound on the mixing time τmix and the process starts in the stationary distribution.
    Sec. 4.3, Assumption 7. The soundness of the monitor depends on this knowledge; without it, the error bound is not valid.
  • domain assumption For additive dynamics, the bias remains within [0,1] and the change function β is known to the monitor.
    Sec. 4.4, Remark 1 and Assumption 8. The paper acknowledges the original paper's bound-keeping assumption and adopts it without proof of how it interacts with monitoring.
  • standard math Concentration inequalities of Hoeffding and Howard et al. are valid and applicable.
    Sec. 4.1 and Theorem 3. The static-coin monitor's soundness is 'a direct consequence of known concentration inequalities'; these are standard results.
  • standard math The ergodic theorem for Markov chains holds for the constructed chain.
    Appendix A.4, proof of Theorem 5, citing Norris Theorem 1.10.2.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Algorithmic Fairness: A Runtime Perspective." pith.science (2026). https://pith.science/paper/YPSGIEVO

@misc{pith2026250720711,
  author       = {Pith},
  title        = {Pith review of: Algorithmic Fairness: A Runtime Perspective},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YPSGIEVO}},
  note         = {Machine review of arXiv:2507.20711}
}
read the original abstract

Fairness in AI is traditionally studied as a static property evaluated once, over a fixed dataset. However, real-world AI systems operate sequentially, with outcomes and environments evolving over time. This paper proposes a framework for analysing fairness as a runtime property. Using a minimal yet expressive model based on sequences of coin tosses with possibly evolving biases, we study the problems of monitoring and enforcing fairness expressed in either toss outcomes or coin biases. Since there is no one-size-fits-all solution for either problem, we provide a summary of monitoring and enforcement strategies, parametrised by environment dynamics, prediction horizon, and confidence thresholds. For both problems, we present general results under simple or minimal assumptions. We survey existing solutions for the monitoring problem for Markovian and additive dynamics, and existing solutions for the enforcement problem in static settings with known dynamics.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

49 extracted references · 44 canonical work pages

  1. [1]

    In: Proceedings of the International Conference on Machine Learning (ICML)

    Alamdari, P.A., Klassen, T.Q., Creager, E., Mcilraith, S.A.: Remembering to be fair: Non-Markovian fairness in sequential decision making. In: Proceedings of the International Conference on Machine Learning (ICML). vol. 235, pp. 906–920. PMLR (21–27 Jul 2024)

    work page 2024

  2. [2]

    Proceedings of the ACM on Programming Lan- guages 1(OOPSLA), 1–30 (2017) Algorithmic Fairness: A Runtime Perspective 19

    Albarghouthi, A., D’Antoni, L., Drews, S., Nori, A.V.: Fairsquare: probabilistic verification of program fairness. Proceedings of the ACM on Programming Lan- guages 1(OOPSLA), 1–30 (2017) Algorithmic Fairness: A Runtime Perspective 19

    work page 2017

  3. [3]

    In: Proceedings of the Conference on Fairness, Accountability, and Transparency

    Albarghouthi, A., Vinitsky, S.: Fairness-aware programming. In: Proceedings of the Conference on Fairness, Accountability, and Transparency. pp. 211–219 (2019)

    work page 2019

  4. [4]

    Ab initio properties of the NaLi molecule in the $a^3\Sigma^+$ electronic state

    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-checking algorithms for continuous-time markov chains. IEEE Transactions on Software Engineering 29(6), 524–541 (2003). https://doi.org/10.1109/TSE.2003.1205180

    work page Pith review arXiv 2003

  5. [5]

    In: International Conference on Learning Representations (2021)

    Balunovic, M., Ruoss, A., Vechev, M.: Fair normalizing flows. In: International Conference on Learning Representations (2021)

    work page 2021

  6. [6]

    MIT Press (2023)

    Barocas, S., Hardt, M., Narayanan, A.: Fairness and Machine Learning Limitations and Opportunities. MIT Press (2023)

    work page 2023

  7. [7]

    In: Lectures on Runtime Verification, pp

    Bartocci, E., Deshmukh, J., Donzé, A., Fainekos, G., Maler, O., Ničković, D., Sankaranarayanan, S.: Specification-based monitoring of cyber-physical systems: a survey on theory, tools and applications. In: Lectures on Runtime Verification, pp. 135–175. Springer (2018)

    work page 2018

  8. [8]

    Proceedings of the ACM on Programming Languages 3(OOPSLA), 1–27 (2019)

    Bastani, O., Zhang, X., Solar-Lezama, A.: Probabilistic verification of fairness properties via concentration. Proceedings of the ACM on Programming Languages 3(OOPSLA), 1–27 (2019)

    work page 2019

Show all 49 references
  1. [9]

    IBM Journal of Research and Development 63(4/5), 4–1 (2019)

    Bellamy, R.K., Dey, K., Hind, M., Hoffman, S.C., Houde, S., Kannan, K., Lohia, P., Martino, J., Mehta, S., Mojsilović, A., et al.: Ai fairness 360: An extensible toolkit for detecting and mitigating algorithmic bias. IBM Journal of Research and Development 63(4/5), 4–1 (2019)

    2019

  2. [10]

    Sociological Methods & Research50(1), 3–44 (2021)

    Berk, R., Heidari, H., Jabbari, S., Kearns, M., Roth, A.: Fairness in criminal justice risk assessments: The state of the art. Sociological Methods & Research50(1), 3–44 (2021)

    2021

  3. [11]

    Microsoft, Tech

    Bird, S., Dudik, M., Edgar, R., Horn, B., Lutz, R., Milan, V., Sameki, M., Wallach, H., Walker, K.: Fairlearn: A toolkit for assessing and improving fairness in ai. Microsoft, Tech. Rep. MSR-TR-2020-32 (2020)

    2020

  4. [12]

    In: International Conference on Formal Structures for Computation and Deduction (FSCD)

    Cano, F., Henzinger, T.A., Könighofer, B., Kueffner, K., Mallik, K.: Abstraction- based decision making for statistical properties. In: International Conference on Formal Structures for Computation and Deduction (FSCD). LIPIcs, vol. 299, pp. 2:1–2:17. Schloss Dagstuhl - Leibni...

    2024

  5. [13]

    Proceedings of the AAAI Conference on Artificial Intelligence39(15), 15659–15668 (2025)

    Cano, F., Henzinger, T.A., Könighofer, B., Kueffner, K., Mallik, K.: Fairness shields: Safeguarding against biased decision makers. Proceedings of the AAAI Conference on Artificial Intelligence39(15), 15659–15668 (2025)

    2025

  6. [14]

    In: Proceedings of the Conference on Fairness, Accountability, and Trans- parency (FAccT)

    D’Amour, A., Srinivasan, H., Atwood, J., Baljekar, P., Sculley, D., Halpern, Y.: Fairness is not static: deeper understanding of long term fairness via simulation studies. In: Proceedings of the Conference on Fairness, Accountability, and Trans- parency (FAccT). pp. 525–534 (2020)

    2020

  7. [15]

    In: International Conference on Formal Modeling and Analysis of Timed Systems

    Donzé, A., Maler, O.: Robust satisfaction of temporal logic over real-valued signals. In: International Conference on Formal Modeling and Analysis of Timed Systems. pp. 92–106. Springer (2010)

    2010

  8. [16]

    Science advances 4(1), eaao5580 (2018)

    Dressel, J., Farid, H.: The accuracy, fairness, and limits of predicting recidivism. Science advances 4(1), eaao5580 (2018)

    2018

  9. [17]

    In: Proceedings of the 3rd Innovations in Theoretical Computer Science Con- ference (ITCS)

    Dwork, C., Hardt, M., Pitassi, T., Reingold, O., Zemel, R.: Fairness through aware- ness. In: Proceedings of the 3rd Innovations in Theoretical Computer Science Con- ference (ITCS). p. 214–226. ACM, New York, NY, USA (2012)

    2012

  10. [18]

    In: Proceedings of the 3rd innovations in theoretical computer science con- ference

    Dwork, C., Hardt, M., Pitassi, T., Reingold, O., Zemel, R.: Fairness through aware- ness. In: Proceedings of the 3rd innovations in theoretical computer science con- ference. pp. 214–226 (2012)

    2012

  11. [19]

    arXiv preprint arXiv:1711.03829 (2017) 20 F

    Faymonville,P.,Finkbeiner,B.,Schwenger,M.,Torfah,H.:Real-timestream-based monitoring. arXiv preprint arXiv:1711.03829 (2017) 20 F. Cano, T. A. Henzinger, and K. Kueffner

    2017 arXiv

  12. [20]

    arXiv preprint arXiv:2109.09447 (2021)

    Ghosh, B., Basu, D., Meel, K.S.: Algorithmic fairness verification with graphical models. arXiv preprint arXiv:2109.09447 (2021)

    2021 arXiv

  13. [21]

    In: Proceedings of the AAAI Conference on Artificial Intelligence (AAAI)

    Ghosh, B., Basu, D., Meel, K.S.: Justicia: A stochastic sat approach to formally verify fairness. In: Proceedings of the AAAI Conference on Artificial Intelligence (AAAI). vol. 35, pp. 7554–7563 (2021)

    2021

  14. [22]

    In: Advances in Neural Information Processing Systems (NeurIPS)

    Hardt, M., Price, E., Srebro, N.: Equality of opportunity in supervised learning. In: Advances in Neural Information Processing Systems (NeurIPS). pp. 3315–3323 (2016)

    2016

  15. [23]

    arXiv preprint arXiv:1903.01209 (2019)

    Heidari, H., Nanda, V., Gummadi, K.P.: On the long-term impact of algorithmic decision policies: Effort unfairness and feature segregation through social learning. arXiv preprint arXiv:1903.01209 (2019)

    2019 arXiv

  16. [24]

    In: Proceedings of the International Computer Aided Verification (CAV)

    Henzinger, T.A., Karimi, M., Kueffner, K., Mallik, K.: Monitoring algorithmic fairness. In: Proceedings of the International Computer Aided Verification (CAV). p. 358–382. Springer-Verlag (2023)

    2023

  17. [25]

    In: Proceedings of the ACM Conference on Fairness, Accountability, and Transparency (FAccT)

    Henzinger, T.A., Karimi, M., Kueffner, K., Mallik, K.: Runtime mon- itoring of dynamic fairness properties. In: Proceedings of the ACM Conference on Fairness, Accountability, and Transparency (FAccT). pp. 604–614. ACM (2023). https://doi.org/10.1145/3593013.3594028, https://do...

    2023

  18. [26]

    Henzinger, T.A., Karimi, M., Kueffner, K., Mallik, K.: Runtime monitoring of dynamic fairness properties (2025), (To appear)

    2025

  19. [27]

    In: International Conference on Runtime Verification (RV)

    Henzinger, T.A., Kueffner, K., Mallik, K.: Monitoring algorithmic fairness under partial observations. In: International Conference on Runtime Verification (RV). pp. 291–311. Springer (2023)

    2023

  20. [28]

    Henzinger, T.A., Kueffner, K., Mallik, K.: Runtime monitoring of static fairness properties (2025), (To appear)

    2025

  21. [29]

    Journal of the American Statistical Association58(301), 13–30 (1963)

    Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association58(301), 13–30 (1963)

    1963

  22. [30]

    The Annals of Statistics49(2), 1055–1080 (2021)

    Howard, S.R., Ramdas, A., McAuliffe, J., Sekhon, J.: Time-uniform, nonparamet- ric, nonasymptotic confidence sequences. The Annals of Statistics49(2), 1055–1080 (2021)

    2021

  23. [31]

    In: International Conference on Machine Learning

    Jagielski, M., Kearns, M., Mao, J., Oprea, A., Roth, A., Sharifi-Malvajerdi, S., Ullman, J.: Differentially private fair learning. In: International Conference on Machine Learning. pp. 3000–3008. PMLR (2019)

    2019

  24. [32]

    In: Conference on Uncertainty in Artificial Intelligence

    John, P.G., Vijaykeerthy, D., Saha, D.: Verifying individual fairness in machine learning models. In: Conference on Uncertainty in Artificial Intelligence. pp. 749–

  25. [33]

    In: International Conference on Computer Aided Verification

    Junges, S., Torfah, H., Seshia, S.A.: Runtime monitors for markov decision pro- cesses. In: International Conference on Computer Aided Verification. pp. 553–576. Springer (2021)

    2021

  26. [34]

    In: International Conference on Machine Learning

    Kearns, M., Neel, S., Roth, A., Wu, Z.S.: Preventing fairness gerrymandering: Au- diting and learning for subgroup fairness. In: International Conference on Machine Learning. pp. 2564–2572. PMLR (2018)

    2018

  27. [35]

    Journal of Machine Learning Research23 (2022)

    Konstantinov,N.H.,Lampert,C.:Fairness-awarepaclearningfromcorrupteddata. Journal of Machine Learning Research23 (2022)

    2022

  28. [36]

    Advances in neural information processing systems30 (2017)

    Kusner, M.J., Loftus, J., Russell, C., Silva, R.: Counterfactual fairness. Advances in neural information processing systems30 (2017)

    2017

  29. [37]

    In: International Conference on Machine Learning

    Liu, L.T., Dean, S., Rolf, E., Simchowitz, M., Hardt, M.: Delayed impact of fair machine learning. In: International Conference on Machine Learning. pp. 3150–

  30. [38]

    In: International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems

    Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems. pp. 152–166. Springer (2004)

    2004

  31. [39]

    ACM Computing Surveys (CSUR)54(6), 1–35 (2021)

    Mehrabi, N., Morstatter, F., Saxena, N., Lerman, K., Galstyan, A.: A survey on bias and fairness in machine learning. ACM Computing Surveys (CSUR)54(6), 1–35 (2021)

    2021

  32. [40]

    Advances in Neural Information Processing Systems (NeurIPS) 34, 26276–26288 (2021)

    Meyer, A., Albarghouthi, A., D’Antoni, L.: Certifying robustness to programmable data bias in decision trees. Advances in Neural Information Processing Systems (NeurIPS) 34, 26276–26288 (2021)

    2021

  33. [41]

    Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press (1997)

    Norris, J.R.: Markov Chains. Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press (1997)

    1997

  34. [42]

    Science366(6464), 447–453 (2019)

    Obermeyer, Z., Powers, B., Vogeli, C., Mullainathan, S.: Dissecting racial bias in an algorithm used to manage the health of populations. Science366(6464), 447–453 (2019)

    2019

  35. [43]

    Proceed- ings of the ACM on Human-Computer Interaction3(CSCW), 1–33 (2019)

    Scheuerman, M.K., Paul, J.M., Brubaker, J.R.: How computers see gender: An evaluation of gender classification in commercial facial analysis services. Proceed- ings of the ACM on Human-Computer Interaction3(CSCW), 1–33 (2019)

    2019

  36. [44]

    Advances in Neural Information Process- ing Systems 32 (2019)

    Sharifi-Malvajerdi, S., Kearns, M., Roth, A.: Average individual fairness: Algo- rithms, generalization and experiments. Advances in Neural Information Process- ing Systems 32 (2019)

    2019

  37. [45]

    In: International conference on runtime verification

    Stoller, S.D., Bartocci, E., Seyster, J., Grosu, R., Havelund, K., Smolka, S.A., Zadok, E.: Runtime verification with state estimation. In: International conference on runtime verification. pp. 193–207. Springer (2011)

    2011

  38. [46]

    In: International Symposium on Formal Methods

    Sun, B., Sun, J., Dai, T., Zhang, L.: Probabilistic verification of neural networks against group fairness. In: International Symposium on Formal Methods. pp. 83–

  39. [47]

    IEEE transac- tions on visualization and computer graphics26(1), 56–65 (2019)

    Wexler, J., Pushkarna, M., Bolukbasi, T., Wattenberg, M., Viégas, F., Wilson, J.: The what-if tool: Interactive probing of machine learning models. IEEE transac- tions on visualization and computer graphics26(1), 56–65 (2019)

    2019

  40. [48]

    In: International conference on machine learning

    Zemel, R., Wu, Y., Swersky, K., Pitassi, T., Dwork, C.: Learning fair representa- tions. In: International conference on machine learning. pp. 325–333. PMLR (2013) A Proofs A.1 Process-agnostic enforcement (Proof of Lemma 1 and Theorems 1 and 2) Lemma (1). Let w = (pt, xt)t∈N ...

    2013

  41. [3158]

    PMLR (2018) Algorithmic Fairness: A Runtime Perspective 21

    2018

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.