Title: Online Multi-Class Selection with Group Fairness Guarantee
Venue: NeurIPS 2025
Accepted: yes
Keywords: Online Selection

Group Fairness

Randomized Rounding

Learning-Augmented Algorithms
Abstract: We study the online multi-class selection problem with group fairness guarantees, where limited resources must be allocated to sequentially arriving agents. Our work addresses two key limitations in the existing literature. First, we introduce a novel lossless rounding scheme that ensures the integral algorithm achieves the same expected performance as any fractional solution. Second, we explicitly address the challenges introduced by agents who belong to multiple classes. To this end, we develop a randomized algorithm based on a relax-and-round framework. The algorithm first computes a fractional solution using a resource reservation approach---referred to as the *set-aside* mechanism---to enforce fairness across classes. The subsequent rounding step preserves these fairness guarantees without degrading performance. Additionally, we propose a learning-augmented variant that incorporates untrusted machine-learned predictions to better balance fairness and efficiency in practical settings.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors study the problem of online muti-class selection, where agents are arriving one at a time and based on each agent’s value, the algorithm must determine whether to allocate a resource to each agent. The goal is to allocate these resources ‘fairly’ to the agents by group, where each agent can be a member of multiple groups. The authors study two natural notions of fairness, Group Fairness by Quantity (guaranteeing a specific quantity to every group) and \\beta-proportional fairness (guaranteeing a form of approximate proportional fairness for each group). The authors present a series of deterministic and randomized algorithms that solve the multi-class selection problem with these two notions of fairness, proving that for GFQ they achieve the optimal competitive ratio. The authors also provide some results of augmenting the algorithms with machine learning predictions.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- The extension of group fairness to the multi-class setting is a natural question, as is the question of finding integral solutions rather than fractional solutions\n- The algorithm techniques of rounding seem to be novel compared to the literature on this topic and the concepts are interesting and may generalize beyond the scope of this problem.\n- The fairness notions studied in the paper are natural for the problem and are well-motivated by the authors\n- While the writing is a bit dense at times, the paper is overall well-written\n\nWeaknesses \n- The work builds off of two related works [JZST24] and [ZJST25] that study the same problem with slightly different variations (studying single-labeled groups among other differences). While the multi-group setting is natural, it is not obvious to me that the advancements in this paper are interesting enough to the general machine learning for this conference. More specifically, I feel that the problem is somewhat specific and the improvements in this paper are somewhat incremental on previous works.\n- This work is primarily a theoretical contribution, however it could be interesting to motivate with some applications of this problem and the authors' algorithm.\n\nMinor presentation comments\n- K seems to be reused on line 142 to be different than the K on line 118\n- What is the definition of  \\beta-NSW on line 168?\n- It would be helpful if FRAC-GFQ is presented in the main body\n-Would be helpful to define/explain what \\kappa_i is for algorithm 1\n- The description of algorithm 1 doesn’t quite match the algorithm, so would be helpful to clarify the description\n- Could be helpful to have pseudocode given the significant amount of algorithm-specific notation\n- When presenting LILA, please link to the appendix where the algorithm is formally presented\n\nQUESTIONS:\n1. Can you describe in detail how the results and techniques in this paper differ from the most closely related works (namely [JZST24] and [ZJST25])? \n\n2. Are there any specific settings or applications where the authors believe this algorithm could be useful or in which the new setting additions (multigroup, integral) would be especially useful?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies the online multiclass selection problem  OMcS) under two fairness constraints namely group fairness by quantity (GFQ) and $\\beta$ proportionality. Unlike the usual setting, here the agents arrive online and make a request for 1 unit of finite indivisible resources for a price and the algorithm(seller) has to make an irrevocable decision to allocate the resource or reject the request. The goal is to maximize the utility while also adhering to the mentioned group fairness notion. Here the agents may belong to more than one protected group simultaneously and one allocation may lead to simultaneously satisfying multiple constraints. \n\nThe authors give \n1) An optimal deterministic algorithm and a rounding based randomized algorithm for the problem with GFQ constraints. The rounding scheme is lossless and may be applied to other online settings\n2) Rounding based randomized algorithm for problem the $\\beta$- proportionality fairness constraint\n3) A learning augmented framework to improve the algorithm in practice in presence of 'fair' advice. \n\nThe paper is theoretical in nature. However, authors have provided proof of concept experiments in the appendix.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1) The paper studies multi labeled group fairness in online setting with theoretical guarantees. The question is important both theoretically and practically and the paper can be simultaneously of interest to multiple communities.\n2) The problem setting is clearly defined and there are multiple contributions in terms of algorithms and guarantees. I did not check the proofs in detail, but the paper appears sound in its arguments.\n3) Proof of concept experiments are given in the appendix. \n\nWeakness And Suggestions: \nThough, as mentioned in the strengths, the problem setting is well defined and clear; my main concern with the paper is with the overall writing and structure of the paper. The paper is too dense to read and is not easily accessible.\nI think the authors have tried to cram in a lot in the main body of the paper and have missed out on some more important things (in my opinion)\n1. The most important thing I would like to see in the paper is more intuitive explanation of the algorithms, more insights and discussions on the definitions, algorithms and probably a section on proof ideas. For example, intuitively, what do the thresholds mean in theorem 3.1 and are constructed the way they are? what do the conditions signify in a practical setting? Some explanation of these kinds of things will make the paper much more readable.\n2. Though the paper is theoretical in nature, since Neurips is a venue which caters to a broader audience, I think paper with strong theory with a good mix of empirical results will be better appreciated. I would suggest bringing some of the experiments to the main paper from the appendix. \n3. I understand that there are space constraints for the main body of the paper, however I can suggest a couple of things\n         i) Your related work is too detailed, make it crisper and move the bulk of it to the appendix\n        ii)I think the main algorithms with the worst-case assumptions are themselves decent enough and the learning augmented framework may be mentioned in very brief in the main paper and rest of it can be moved to appendix. \n4.  Do provide LiLA in the algorithm box format (may be in appendix). I find it difficult to follow it exactly in the current descriptive version\n\nI do believe the paper is strong however in the current form I found it harder to parse. It is very mechanical and dry. I think these suggestions, if incorporated, might make it more readable and accessible to a broader audience.\n\nQUESTIONS:\nSee Weakness and Suggestions\n\nLIMITATIONS:\nSee Weakness and Suggestions", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

comments: SUMMARY:
This paper tackles improving group fairness in the Online Multi-Class Selection (OMcS) problem, which allocates limited integer resources to sequentially arriving multi-class agents. To this end, the authors introduce a threshold-based algorithm and theoretically prove that it satisfies the group-fairness constraints while attaining the tight competitive ratio in utility maximization.

STRENGTHS AND WEAKNESSES:
-C1. The authors mathematically formalize the fundamental trade-off between group fairness and utility maximization in an online setting. On top of that, they propose a threshold-based algorithm that achieves a tight solution. As one of the pioneering works on this task, I believe that  this work will serve as an important foundation for future research.

-C2. The paper is well-written and logically structured, and the proposed algorithm is supported by rigorous theoretical guarantees, including tight competitive-ratio bounds.

-C3. Compared to the ADV baseline, the proposed method achieves more robust fairness guarantees while incurring only a marginal loss in total utility.

-W1. The current experiments are limited to a single task, limiting the reliability of empirical evaluations.

-W2 The current draft lacks implementation details, experimental setup, and results. They are included only in supplementary material.

QUESTIONS:
Please refer to the weaknesses above.

1. Could you provide additional experimental results on other domains or datasets?

2. How about including some implementation details or a concise summary of the experimental setup and results within the main text?

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

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nAuthors study the following problem setting.\n- Agents arrive in a sequential patter onto the platform and query for an item (from the finite inventory). Each agent has an associated set of labels (categories that the agent belongs to), and a valuation for the item.\n- The platform has to determine to either allocate or reject the agents' query as soon as they arrive. The platform is aware of the variance of valuations for different categories apriori, but does not know the distribution of labels of agents yet to arrive. \n\nAuthors attempt to solve a utility (summation of valuations where items get allocated to the agents) maximization under fairness constraints. They define competitive ratio of their proposed approach in form of a robust (min-max) formulation comparing the allocation output by their approach with that of optimal algorithm. \n\nAuthors define two fairness metrics (1) Group Fairness by Quantity (GFQ) (2) $\\beta$-proportional Fairness (BPF). They propose an optimal deterministic algorithm for GFQ followed by a randomized variant. For BFP, authors propose another randomized st-aside algorithm and provide analysis for its performance.\n\nAuthors then comment on the overly pessimistic output of their proposed algorithm on account of the min-max formulation and propose a hybrid approach that probabilistically samples from either the output of their algorithm or from an \"advice\" allocation from a blackbox ML algorithm. Authors provide performance guarantees for the hybrid approach.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. Overall, the presentation of content is very high quality. Even for a reader with very limited background in the related works, it was easy to parse and understand the problem setting and the contributions of the work.\n2. I appreciated the inclusion of Section 5, wherein the authors acknowledge the limited practicality of their proposed approach and suggest an approach that overcomes some of those limitations.\n3. Throughout the paper, authors place their mathematical results in context of the results from the related works and broader literature on the topic.\n\nWeaknesses:\n\n1. Section 5 could be made clearer by providing pseudocode.\n2. Lack of complexity analysis.\n\nQUESTIONS:\n1. Could the authors make Section 5 (learning augmented algorithm) clearer by creating sub-sections for limitation of Algorithm 3, athe proposed learning augmented algorithm (with pesudocode), the 2 definitions of fairness of allocation and analysis. [ I am leaning towards improving the score based on this relatively minor change]\n\n2. Please include complexity analysis for each of the proposed approaches in the main manuscript. \n\n3. [Minor] Authors have included experimental evaluation in the Appendix. I understand the limitation of page limit, but it would be valuable if the authors could include the evaluation in the main manuscript.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-07"}