Title: Statistical Parity with Exponential Weights
Venue: NeurIPS 2025
Accepted: yes
Keywords: bandits

statistical parity

fairness

privacy
Abstract: Statistical parity is one of the most foundational constraints in algorithmic fairness and privacy. In this paper, we show that statistical parity can be enforced efficiently in the adversarial contextual bandit setting while retaining strong performance guarantees. Specifically, we present a meta-algorithm that transforms any efficient implementation of Hedge (or, equivalently, any discrete Bayesian inference algorithm) into an efficient contextual bandit algorithm that guarantees exact statistical parity on every trial. Compared to any comparator that satisfies the same statistical parity constraint, the algorithm achieves the same asymptotic regret bound as running the equivalent instance of Exp4 for each group. We also address the scenario where the target parity distribution is unknown and must be estimated online. Finally, using online-to-batch conversion, we extend our approach to the batch classification setting.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe main contribution of this paper is developing a meta-algorithm called SPEW that translates an implementation of the HEDGE/EXP4 into a scheme that (i) ensures statistical parity, and (ii) achieves the same regret as EXP4 against the best parity-achieving policy in hindsight. The authors instantiate this general strategy for various examples, such as for graph valued contexts, finite metric spaces, statistical parity w.r.t. the empirical distribution, and for approximate statistical parity for hierarchical clustering. \nFinally, the authors conclude by discussing how SPEW can be applied to a fair classification problem via a online-to-batch conversion.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths \n\n* I think the main strength of the paper is that proposed idea of a wrapper around HEDGE algorithm is conceptually quite simple and elegant. Yet, this scheme seems to be applicable quite broadly to structured and unstructured problems, with known or unknown distribution $\\rho$. \n\nWeaknesses \n\n* One minor issue could be the fact that the reduction is tied to a very specific notion of fairness (i.e., statistical parity), and it doesn't seem obvious to extend it to other notions of fairness. \n\n* The paper only consists of theoretical results, and there is no empirical evaluation of practical issues like the effect of constant factors, the speed of convergence, any trade-offs between fairness and performance, scalability etc.\n\nQUESTIONS:\n**Q1:** Can you discuss about the possibility of constructing SPEW-like meta-algorithms for other notions of fairness, such as equalized odds for example. \n\n**Q2:** In Line 68 it is mentioned that the underlying methodology of SPEW can be generalized beyond HEDGE-based implementations. Can you expand upon this a bit.  \n\n**Q3:** Since both the time and space complexity of SPEW in each trial grows linearly with $M$, can you discuss potential ways of dealing with continuous or finite-but-large class of protected characteristics? What additional assumptions might we need to make? \n\n---\n### Minor Questions/Comments \n\nLine 23: The notation used in the display here is a bit confusing: if I understand correctly, a, c, v are random variables, and b, d, d' refer to realizations? \n\nLines 446, 659, 740: Broken cross-references.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper develops a novel algorithm for the contextual bandit setting, which is capable of producing no-regret policies that achieve guaranteed statistical parity with respect to protected attributes. The algorithmic proposal starts with Hedge (expressed in oracle-call format) and via reductions/tricks specific to the setting of obtaining statistical parity builds an algorithm entitled SPEW on top of it. The algorithm is then shown to provide regret bounds that have mild dependence on the dimensionality of the problem (rather than blow up when said dimension is exponential). \n\nThe algorithm's dimensionality properties are then showcased in several structured settings including: graphs with homophily; hierarchical settings; metric-induced settings. By way of straightforward extensions, it is furthermore observed that the proposed algorithm also gives a novel solution to the same problem even in the batch (offline i.i.d.) setting, as well as that an empirical-distribution variant of SPEW can be constructed that doesn't require full access to the underlying feature distribution (only to the observed samples).\n\nSTRENGTHS AND WEAKNESSES:\nThe main strength of the method is that it fills a niche that to my knowledge has not yet been addressed in the fairness-in-bandits literature; in particular,\n\n--- It enforces fundamental statistical parity guarantees, which have not been accomplished for this task even in the i.i.d. offline scenario;\n\n--- Said statistical parity guarantees are obtained and satisfied in an exact way, without the corresponding O(\\sqrt{T}) or similar regret term corresponding to constraint violation;\n\n--- In contrast to some other related strands of research such as many of the long-term constraints papers, the present work operates under bandit rather than e.g. full information feedback regime;\n\n--- The provided worked-out examples (and the general guarantees) show that the algorithm successfully deals with a-priori exponentially-high-dimensional settings by being able to rely on certain kinds of structure in them (while this is a pervasive theme throughout many online bandits literatures, it has not been instantiated in such setting before, to my knowledge).\n\nFor the main weakness, I have to point out the composition and writing of this paper; it is far from clearly or lucidly written, and has required a lot of parsing effort that could have been saved with a different organization/writing. To give some concrete pointers:\n\n--- First, the main algorithm (SPEW) is relegated to the depths of the paper (after an entire array of example constructions), which I couldn't get behind. \n\n--- Second, and very importantly, the algorithm SPEW that's the main contribution of the paper is not described insightfully in the main paper, nor even in the appendix! For instance, a vague promise is made that the meaning of the concretely set variables \\lambda can be understood from the algorithm analysis, but even in the corresponding appendix this is explained in a very murky way! This opacity could have absolutely been avoided --- e.g. along the lines of explaining that we are looking for suitably upper- and lower-bounding surrogate losses, which, in turn, leads to a loss of a particular form whose subgradient is of the form... etc etc.\n\n--- Third, the comparisons to prior literature are brief and incomplete in ways that make them rushed/not as insightful as they should be in this set of circumstances. To be sure, some effort is made in the intro --- by asking the readers to imagine the process of forming the Lagrangian for the corresponding parity-constrained problem and solving it for the primal and dual variables, and pointing out that this is inefficient to do in the \"brute-force\" way. Such a point is best understood by someone with a background in long-term constraints; but then for such readers, the following couple sentences hinting at the differences from existing long-term works (that most of them don't achieve exact constraint satisfaction and many of them are not applicable to the bandit setting) are not discussed deeply enough to explain the technical nuances. (In fact, some long-term constraints setups emphasize (near-)exact constraint satisfaction in general settings, and some other such works do target bandit settings; and yet other long-term constraints papers have some degree of dimensionality-avoiding oracle efficiency to them.) Also, some essential fairness in online learning references have been missed, such as works on individual fairness online (like Bechavod et al, Metric-free individual fairness).  Moreover, down the line this leads to the proofs of the algorithm's analysis in which long-term constraints influences are not invoked when appropriate. E.g. surrogate loss constructing techniques, which this paper's analysis has an instance of, could/should be mentioned at the right point.\n\nQUESTIONS:\nPlease see the Weaknesses section above for a list of concrete items that in my view would significantly improve readability of the paper. \n\nSpecifically, the following points are of primary importance:\n\n--- A more careful discussion of related work such as on long-term constraints intersect fairness in online learning; in particular emphasizing technical details compared to methods achieving cumulative constraint violation regret bounds with different tradeoffs in the long-term literature.\n\n--- A clearer reorganized structure where SPEW comes first, before the examples; and please consider throwing both online to batch and also the empirical version of the algorithm into a dedicated section called Extensions, to separate from Examples.\n\n--- SPEW should be re-discussed with a substantial degree of insight into why the particular elements of the pseudocode were chosen as they are (included but not limited to the \\lambda); for this one, please keep in mind first-time readers!\n\nI expect that the authors will be able to provide a careful list of patches along those lines, as well as concrete and detailed chunks of text to be later included in the revised manuscript, in the rebuttal. If this is not performed, then, for full transparency, I may downgrade my current (advance) borderline-accept to borderline-reject.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 1, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}

comments: SUMMARY:
In this paper, the authors propose a meta-algorithm that can transform any efficient implementation of Hedge (or discrete Bayesian inference algorithm) into a contextual bandit algorithm that guarantees exact statistical parity on every trial.

STRENGTHS AND WEAKNESSES:
***I have reviewed the paper with care, but evaluating the correctness of the theoretical analysis is beyond my current expertise. ***

QUESTIONS:
I am not familiar with the theory things about contextual bandits, so I only have some questions from the angle of fairness.
1. As statistical fairness focus on the "positive" action, in the presented examples in Sec 4, can a "positive" action always exist and be clearly defined, especially when |A|>2?
2. In the second example in Introduction, it says "the choice of blue agent depends on certain private attributes of the system" and "enforcing statistical parity ensures that the selected blue agent is independent of the sensitive attribute". In this sense, the correlation between the blue agent and private attributes is broken, which may hurt the model's performance (if any), as some useful features can no longer be utilized. How does the proposed method address this potential trade-off?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 4
DATE: 2025-07-03

comments: SUMMARY:
In this paper, the authors propose an algorithm for contextual bandits that enjoys statistical parity. The proposed algorithm uses a Hedge algorithm subroutine for each protected attribute.

STRENGTHS AND WEAKNESSES:
The paper makes an interesting contribution, IMO. However, I think this articulation is too dense for a non-expert. I had a hard time trying to understand the basic idea of how the statistical parity is achieved by the algorithms.

Even the examples in Section 3 are not covered in sufficient detail for a reader who has not encountered these problems before.

Overall, I think this paper is an instance of there being too much material being packed into too little space.

Minor suggestion: In the paragraph starting on Line 40 from the introduction, the authors describe the contextual bandit problem. It would help if the authors could also articulate what statistical parity means for this specific model (this is made clear later though).

QUESTIONS:
No specific questions from my side, but I would appreciate an accessible (to say someone familiar with a textbook treatment of Hedge/Exp4) and intuitive explanation on how SPEW achieves statistical parity in the present context.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 2
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-18