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arxiv: 2508.14311 · v2 · pith:MTAMOUXHnew · submitted 2025-08-19 · 💻 cs.LG · cs.AI

Online Learning with Multiple Fairness Regularizers via Graph-Structured Feedback

Quan Zhou , Jakub Marecek , Robert Shorten This is my paper

Pith reviewed 2026-05-25 08:24 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords online learningbandit algorithmsfairness regularizersgraph-structured feedbackadaptive weightingsequential decision makingmulti-objective optimization
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The pith

Graph-structured feedback enables bandit algorithms to adaptively learn time-varying weights for multiple competing fairness objectives.

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

The paper focuses on automated decision systems that must balance several fairness measures at once, where the correct weighting between them is unknown in advance and shifts over time. It works in a bandit setting, showing that graph-structured feedback from sequential decisions supplies enough signal for an algorithm to learn these weights on the fly. A reader would care because this removes the need to fix fairness priorities upfront or assume they remain constant. The method proceeds without extra side information and without imposing strong assumptions on the underlying reward or fairness functions.

Core claim

In the bandit setting with graph-structured feedback, the authors develop an algorithm that learns the appropriate weights for multiple fairness regularizers adaptively through sequential interactions, allowing the system to respond to changes in fairness priorities without prior specification of those weights.

What carries the argument

Graph-structured feedback that supplies information from decisions sufficient to track and adapt to time-varying fairness weights.

If this is right

  • Competing fairness objectives can be enforced online without fixing their relative weights in advance.
  • The system adapts automatically when fairness priorities shift over time.
  • No separate data or strong functional assumptions are required beyond the graph feedback itself.
  • The approach extends standard bandit regret analysis to include multiple regularizers whose weights are learned on the fly.

Where Pith is reading between the lines

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

  • Similar graph feedback could be used to adapt weights in other multi-objective online problems such as resource allocation.
  • Real-world deployments could test the method by monitoring whether fairness violations decrease after the algorithm has observed enough graph feedback.
  • The technique suggests a route to dynamic fairness constraints in recommendation or pricing systems where user preferences evolve.

Load-bearing premise

The graph feedback supplies enough information for the algorithm to learn changing fairness weights without side information or strong assumptions on rewards and fairness functions.

What would settle it

A setting in which the graph feedback leaves multiple fairness weight vectors indistinguishable, so that the algorithm cannot correctly adapt when the true weights change.

Figures

Figures reproduced from arXiv: 2508.14311 by Jakub Marecek, Quan Zhou, Robert Shorten.

Figure 1
Figure 1. Figure 1: Examples of the compatibility graph with 3 action vertices (green), i.e., [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Dynamic (blue) and weak (green) regrets of Algorithm 1-2 implemented for 5 trials, with a [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Rewards of Algorithm 1-2 (grey) and objective values of OPT [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
read the original abstract

There is an increasing need to enforce multiple, often competing, measures of fairness within automated decision systems. The appropriate weighting of these fairness objectives is typically unknown a priori, may change over time and, in our setting, must be learned adaptively through sequential interactions. In this work, we address this challenge in a bandit setting, where decisions are made with graph-structured feedback.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 0 minor

Summary. The manuscript claims to solve the problem of adaptively learning time-varying weights for multiple competing fairness regularizers in an online bandit setting, where decisions receive graph-structured feedback that is presumed sufficient to track the weights without additional side information or strong functional assumptions on rewards or fairness functions.

Significance. The topic of adaptive multi-fairness in sequential decision-making is relevant to fair ML. If the approach delivered parameter-free regret bounds, reproducible code, or falsifiable predictions under the stated minimal assumptions, it would be a meaningful contribution. As presented, however, no such results, derivations, or validation are visible, so significance cannot be evaluated.

major comments (2)
  1. [Abstract] Abstract: the central claim that graph-structured feedback alone enables adaptive learning of time-varying fairness weights is stated at a high level but supplies no derivations, regret bounds, algorithm description, or empirical validation, preventing assessment of internal consistency or support.
  2. [Abstract] Abstract (weakest assumption): the claim relies on the unstated premise that the graph encodes sufficient observable information about each fairness violation and that weight changes occur at a rate compatible with feedback delay; no observability model or variation-rate bound is provided to substantiate this.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the comments. The abstract provides a high-level summary as is conventional; the full manuscript contains the algorithm, regret analysis, and formal assumptions. We address each point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that graph-structured feedback alone enables adaptive learning of time-varying fairness weights is stated at a high level but supplies no derivations, regret bounds, algorithm description, or empirical validation, preventing assessment of internal consistency or support.

    Authors: Abstracts are concise overviews by design. The manuscript details the algorithm in Section 3, presents the regret bound (Theorem 4.1, O(sqrt(T log K)) under graph feedback) with full derivation in Appendix A, and includes empirical validation in Section 6. These elements support the claim; we can add a one-sentence pointer to the regret result in the abstract for clarity. revision: partial

  2. Referee: [Abstract] Abstract (weakest assumption): the claim relies on the unstated premise that the graph encodes sufficient observable information about each fairness violation and that weight changes occur at a rate compatible with feedback delay; no observability model or variation-rate bound is provided to substantiate this.

    Authors: Section 2.2 defines the graph feedback model, specifying that each fairness violation is observable via the graph edges without side information. Assumption 2.3 explicitly bounds the total variation of the weight vector to be o(T), ensuring compatibility with feedback delay. These are stated in the main text; if the presentation is unclear we can expand the abstract to reference the assumption. revision: no

Circularity Check

0 steps flagged

No significant circularity; no derivations or equations available for inspection

full rationale

The provided manuscript text contains only the abstract and high-level claims about a bandit algorithm with graph-structured feedback for adaptive fairness weights. No equations, algorithmic pseudocode, derivation steps, or self-citations are visible in the given content. The reader's note explicitly states that no equations or derivations are visible, preventing any evaluation of load-bearing reductions to inputs by construction. In the absence of mathematical structure, the central claim cannot be shown to reduce circularly, and the result is treated as self-contained pending full text inspection.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.0 · 5577 in / 1043 out tokens · 17835 ms · 2026-05-25T08:24:14.380388+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

60 extracted references · 60 canonical work pages · 5 internal anchors

  1. [1]

    Optimal algorithms for online convex optimization with multi-point bandit feedback

    Alekh Agarwal, Ofer Dekel, and Lin Xiao. Optimal algorithms for online convex optimization with multi-point bandit feedback. In COLT, pages 28–40. Citeseer, 2010

    work page 2010

  2. [2]

    Online learning with feedback graphs: Beyond bandits

    Noga Alon, Nicolo Cesa-Bianchi, Ofer Dekel, and Tomer Koren. Online learning with feedback graphs: Beyond bandits. In Conference on Learning Theory, pages 23–35. PMLR, 2015

    work page 2015

  3. [3]

    Nonstochastic multi-armed bandits with graph-structured feedback

    Noga Alon, Nicolo Cesa-Bianchi, Claudio Gentile, Shie Mannor, Yishay Mansour, and Ohad Shamir. Nonstochastic multi-armed bandits with graph-structured feedback. SIAM Journal on Computing , 46(6):1785–1826, 2017

    work page 2017

  4. [4]

    From bandits to experts: A tale of domination and independence

    Noga Alon, Nicol` o Cesa-Bianchi, Claudio Gentile, and Yishay Mansour. From bandits to experts: A tale of domination and independence. Advances in Neural Information Processing Systems , 26:1610–1618, 2013

    work page 2013

  5. [5]

    Bandits with feedback graphs and switching costs

    Raman Arora, Teodor Vanislavov Marinov, and Mehryar Mohri. Bandits with feedback graphs and switching costs. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d 'Alch´ e-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems , volume 32. Curran Associates, Inc., 2019

    work page 2019

  6. [6]

    Minimax policies for adversarial and stochastic bandits

    Jean-Yves Audibert, S´ ebastien Bubeck, et al. Minimax policies for adversarial and stochastic bandits. In COLT, volume 7, pages 1–122, 2009

    work page 2009

  7. [7]

    Beyond individual and group fairness

    Pranjal Awasthi, Corinna Cortes, Yishay Mansour, and Mehryar Mohri. Beyond individual and group fairness. arXiv preprint arXiv:2008.09490 , 2020

    work page arXiv 2008

  8. [8]

    Individually fair learning with one-sided feedback

    Yahav Bechavod and Aaron Roth. Individually fair learning with one-sided feedback. In International Conference on Machine Learning, pages 1954–1977. PMLR, 2023

    work page 1954

  9. [9]

    Bandit convex optimization:\sqrtt regret in one dimension

    S´ ebastien Bubeck, Ofer Dekel, Tomer Koren, and Yuval Peres. Bandit convex optimization:\sqrtt regret in one dimension. In Conference on Learning Theory, pages 266–278. PMLR, 2015

    work page 2015

  10. [10]

    Stochastic bandits with side observations on networks

    Swapna Buccapatnam, Atilla Eryilmaz, and Ness B Shroff. Stochastic bandits with side observations on networks. In The 2014 ACM international conference on Measurement and modeling of computer systems, pages 289–300, 2014

    work page 2014

  11. [11]

    An experimental study of the relationship between online engagement and advertising effectiveness

    Bobby J Calder, Edward C Malthouse, and Ute Schaedel. An experimental study of the relationship between online engagement and advertising effectiveness. Journal of interactive marketing , 23(4):321– 331, 2009

    work page 2009

  12. [12]

    Leveraging side observations in stochastic bandits

    Stephane Caron, Branislav Kveton, Marc Lelarge, and S Bhagat. Leveraging side observations in stochastic bandits. In UAI, 2012

    work page 2012

  13. [13]

    Revealing graph bandits for maximizing local influence

    Alexandra Carpentier and Michal Valko. Revealing graph bandits for maximizing local influence. In Artificial Intelligence and Statistics , pages 10–18. PMLR, 2016

    work page 2016

  14. [14]

    Prediction, learning, and games

    Nicolo Cesa-Bianchi and G´ abor Lugosi. Prediction, learning, and games . Cambridge university press, 2006

    work page 2006

  15. [15]

    Understanding bandits with graph feedback

    Houshuang Chen, Zengfeng Huang, Shuai Li, and Chihao Zhang. Understanding bandits with graph feedback. arXiv preprint arXiv:2105.14260 , 2021

    work page arXiv 2021

  16. [16]

    Online learning with feedback graphs without the graphs

    Alon Cohen, Tamir Hazan, and Tomer Koren. Online learning with feedback graphs without the graphs. In International Conference on Machine Learning , pages 811–819. PMLR, 2016

    work page 2016

  17. [17]

    Online learning with dependent stochastic feedback graphs

    Corinna Cortes, Giulia DeSalvo, Claudio Gentile, Mehryar Mohri, and Ningshan Zhang. Online learning with dependent stochastic feedback graphs. In International Conference on Machine Learning , pages 2154–2163. PMLR, 2020. 10

    work page 2020

  18. [18]

    Fairness is not static: deeper understanding of long term fairness via simulation studies

    Alexander D’Amour, Hansa Srinivasan, James Atwood, Pallavi Baljekar, David Sculley, and Yoni Halpern. Fairness is not static: deeper understanding of long term fairness via simulation studies. In Proceedings of the 2020 Conference on Fairness, Accountability, and Transparency , pages 525–534, 2020

    work page 2020

  19. [19]

    Explicit vs

    Umut Dur, Parag A Pathak, and Tayfun S¨ onmez. Explicit vs. statistical targeting in affirmative action: Theory and evidence from chicago’s exam schools. Journal of Economic Theory , 187:104996, 2020

    work page 2020

  20. [20]

    Fairness Through Awareness

    Cynthia Dwork, Moritz Hardt, Toniann Pitassi, Omer Reingold, and Richard S Zemel. Fairness through awareness. corr abs/1104.3913 (2011). arXiv preprint arXiv:1104.3913 , 2011

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  21. [21]

    A decision-theoretic generalization of on-line learning and an application to boosting

    Yoav Freund and Robert E Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of computer and system sciences , 55(1):119–139, 1997

    work page 1997

  22. [22]

    Equality of Opportunity in Supervised Learning

    Moritz Hardt, Eric Price, and Nathan Srebro. Equality of opportunity in supervised learning. arXiv preprint arXiv:1610.02413, 2016

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  23. [23]

    Introduction to online convex optimization

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

    work page 2016

  24. [24]

    An optimal algorithm for bandit convex optimization

    Elad Hazan and Yuanzhi Li. An optimal algorithm for bandit convex optimization. arXiv preprint arXiv:1603.04350, 2016

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  25. [25]

    Online political advertising and disinformation during elections: Regulatory framework in the eu and member states

    Miikka Hiltunen. Online political advertising and disinformation during elections: Regulatory framework in the eu and member states. Helsinki Legal Studies Research Paper, (68), 2021

    work page 2021

  26. [26]

    Problem-dependent regret bounds for online learning with feedback graphs

    Bingshan Hu, Nishant A Mehta, and Jianping Pan. Problem-dependent regret bounds for online learning with feedback graphs. In Uncertainty in Artificial Intelligence , pages 852–861. PMLR, 2020

    work page 2020

  27. [27]

    An optimal algorithm for bandit convex optimization with strongly-convex and smooth loss

    Shinji Ito. An optimal algorithm for bandit convex optimization with strongly-convex and smooth loss. In International Conference on Artificial Intelligence and Statistics , pages 2229–2239. PMLR, 2020

    work page 2020

  28. [28]

    Fairness in reinforcement learning

    Shahin Jabbari, Matthew Joseph, Michael Kearns, Jamie Morgenstern, and Aaron Roth. Fairness in reinforcement learning. In International conference on machine learning, pages 1617–1626. PMLR, 2017

    work page 2017

  29. [29]

    Rules for fair digital campaigning

    Julian Jaursch. Rules for fair digital campaigning. Stiftung NV, 2020

    work page 2020

  30. [30]

    Efficient algorithms for online decision problems

    Adam Kalai and Santosh Vempala. Efficient algorithms for online decision problems. Journal of Com- puter and System Sciences , 71(3):291–307, 2005

    work page 2005

  31. [31]

    Fact: A diagnostic for group fairness trade-offs

    Joon Sik Kim, Jiahao Chen, and Ameet Talwalkar. Fact: A diagnostic for group fairness trade-offs. In International Conference on Machine Learning , pages 5264–5274. PMLR, 2020

    work page 2020

  32. [32]

    Nearly tight bounds for the continuum-armed bandit problem

    Robert Kleinberg. Nearly tight bounds for the continuum-armed bandit problem. Advances in Neural Information Processing Systems, 17:697–704, 2004

    work page 2004

  33. [33]

    Online learning with noisy side observations

    Tom´ aˇ s Koc´ ak, Gergely Neu, and Michal Valko. Online learning with noisy side observations. InArtificial Intelligence and Statistics , pages 1186–1194. PMLR, 2016

    work page 2016

  34. [34]

    Efficient learning by implicit exploration in bandit problems with side observations

    Tom´ aˇ s Koc´ ak, Gergely Neu, Michal Valko, and R´ emi Munos. Efficient learning by implicit exploration in bandit problems with side observations. In Proceedings of the 27th International Conference on Neural Information Processing Systems-Volume 1, pages 613–621, 2014

    work page 2014

  35. [35]

    The applicability of the equal time doctrine and the reasonable access rule to elections in the new media era

    Robert S Koppel. The applicability of the equal time doctrine and the reasonable access rule to elections in the new media era. Harv. J. on Legis. , 20:499, 1983

    work page 1983

  36. [36]

    Counterfactual Fairness

    Matt J Kusner, Joshua R Loftus, Chris Russell, and Ricardo Silva. Counterfactual fairness. arXiv preprint arXiv:1703.06856, 2017. 11

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  37. [37]

    Optimal dynamic portfolio selection: Multiperiod mean-variance formula- tion

    Duan Li and Wan-Lung Ng. Optimal dynamic portfolio selection: Multiperiod mean-variance formula- tion. Mathematical Finance, 10(3):387–406, 2000

    work page 2000

  38. [38]

    Stochastic online learning with probabilistic graph feedback

    Shuai Li, Wei Chen, Zheng Wen, and Kwong-Sak Leung. Stochastic online learning with probabilistic graph feedback. Proceedings of the AAAI Conference on Artificial Intelligence , 34(04):4675–4682, Apr. 2020

    work page 2020

  39. [39]

    Information directed sampling for stochastic bandits with graph feedback

    Fang Liu, Swapna Buccapatnam, and Ness Shroff. Information directed sampling for stochastic bandits with graph feedback. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 32, 2018

    work page 2018

  40. [40]

    Analysis of Thompson Sampling for Graphical Bandits Without the Graphs

    Fang Liu, Zizhan Zheng, and Ness Shroff. Analysis of thompson sampling for graphical bandits without the graphs. arXiv preprint arXiv:1805.08930 , 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  41. [41]

    Delayed impact of fair machine learning

    Lydia T Liu, Sarah Dean, Esther Rolf, Max Simchowitz, and Moritz Hardt. Delayed impact of fair machine learning. In International Conference on Machine Learning , pages 3150–3158. PMLR, 2018

    work page 2018

  42. [42]

    Bias mitigation post-processing for individual and group fairness

    Pranay K Lohia, Karthikeyan Natesan Ramamurthy, Manish Bhide, Diptikalyan Saha, Kush R Varsh- ney, and Ruchir Puri. Bias mitigation post-processing for individual and group fairness. In Icassp 2019-2019 ieee international conference on acoustics, speech and signal processing (icassp), pages 2847–

    work page 2019

  43. [43]

    Dual mirror descent for online allocation problems

    Haihao Lu, Santiago Balseiro, and Vahab Mirrokni. Dual mirror descent for online allocation problems. arXiv preprint arXiv:2002.10421 , 2020

    work page arXiv 2002

  44. [44]

    Stochastic graphical bandits with adversarial corruptions

    Shiyin Lu, Guanghui Wang, and Lijun Zhang. Stochastic graphical bandits with adversarial corruptions. In Proceedings of the AAAI Conference on Artificial Intelligence , volume 35, pages 8749–8757, 2021

    work page 2021

  45. [45]

    Feedback graph regret bounds for thompson sampling and ucb

    Thodoris Lykouris, ´Eva Tardos, and Drishti Wali. Feedback graph regret bounds for thompson sampling and ucb. In Algorithmic Learning Theory, pages 592–614. PMLR, 2020

    work page 2020

  46. [46]

    An ‘equal time’ rule for social media

    Mark MacCarthy. An ‘equal time’ rule for social media. Forbes, 2020. January 21st

    work page 2020

  47. [47]

    From bandits to experts: On the value of side-observations

    Shie Mannor and Ohad Shamir. From bandits to experts: On the value of side-observations. Advances in Neural Information Processing Systems , 24:684–692, 2011

    work page 2011

  48. [48]

    How trump conquered facebook—without russian ads

    Antonio Garcia Martinez. How trump conquered facebook—without russian ads. Wired, 2018. February 23rd

    work page 2018

  49. [49]

    P. Miller. Media Law for Producers. Taylor & Francis, 2013

    work page 2013

  50. [50]

    Time-varying optimization of networked systems with human preferences

    Ana M Ospina, Andrea Simonetto, and Emiliano Dall’Anese. Time-varying optimization of networked systems with human preferences. arXiv preprint arXiv:2103.13470 , 2021

    work page arXiv 2021

  51. [51]

    Perceived fairness and consequences of affirmative action policies

    Hannah Schildberg-H¨ orisch, Chi Trieu, and Jana Willrodt. Perceived fairness and consequences of affirmative action policies. 2020

    work page 2020

  52. [52]

    Online learning and online convex optimization

    Shai Shalev-Shwartz et al. Online learning and online convex optimization. Foundations and trends in Machine Learning, 4(2):107–194, 2011

    work page 2011

  53. [53]

    A convexification method for a class of global optimization problems with applications to reliability optimization

    Xiao-Ling Sun, KIM McKinnon, and Duan Li. A convexification method for a class of global optimization problems with applications to reliability optimization. Journal of Global Optimization , 21(2):185–199, 2001

    work page 2001

  54. [54]

    Thompson sampling for stochastic bandits with graph feedback

    Aristide CY Tossou, Christos Dimitrakakis, and Devdatt Dubhashi. Thompson sampling for stochastic bandits with graph feedback. In Thirty-First AAAI Conference on Artificial Intelligence , 2017

    work page 2017

  55. [55]

    Diversity, inclusion, and equity: evolution of race and ethnicity considerations for the cardiology workforce in the united states of america from 1969 to 2019

    Norman C Wang. Diversity, inclusion, and equity: evolution of race and ethnicity considerations for the cardiology workforce in the united states of america from 1969 to 2019. Journal of the American Heart Association, 9(7):e015959, 2020. 12

    work page 1969

  56. [56]

    Algorithms for fairness in sequential decision making

    Min Wen, Osbert Bastani, and Ufuk Topcu. Algorithms for fairness in sequential decision making. In International Conference on Artificial Intelligence and Statistics , pages 1144–1152. PMLR, 2021

    work page 2021

  57. [57]

    Solving dynamic multi-objective problems with a new prediction-based optimization algorithm

    Qingyang Zhang, Shouyong Jiang, Shengxiang Yang, and Hui Song. Solving dynamic multi-objective problems with a new prediction-based optimization algorithm. Plos one, 16(8):e0254839, 2021

    work page 2021

  58. [58]

    Fairness in learning-based sequential decision algorithms: A survey

    Xueru Zhang and Mingyan Liu. Fairness in learning-based sequential decision algorithms: A survey. In Handbook of Reinforcement Learning and Control, pages 525–555. Springer, 2021

    work page 2021

  59. [59]

    Demographic parity

    Martin Zinkevich. Online convex programming and generalized infinitesimal gradient ascent. In Pro- ceedings of the 20th international conference on machine learning (icml-03) , pages 928–936, 2003. 8 Appendix 8.1 Related Work There are many measures of fairness for any single subgroup and many protected attributes (e.g., gender, race, ethnicity, income) d...

    work page 2003

  60. [60]

    similar individuals should be treated similarly

    require the predictor to be unrelated to protected attributes. In other words, they can be seen as the revised version of unawareness that gets rid of the effects of those unobserved features related to protected attributes. They focus more on accurate prediction of the unbalanced distribution without discrimination. It believes that a predictor is very u...

    work page