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Controlling Fairness and Bias in Dynamic Learning-to-Rank

Marco Morik, Ashudeep Singh, Jessica Hong, Thorsten Joachims

arXiv:2005.14713v1cs.IRcs.CYstat.ML

TL;DR

Dynamic learning-to-rank can amplify feedback bias and allocate provider exposure unfairly when optimizing user utility alone. The paper introduces FairCo, a controller using unbiased relevance and fairness estimators to enforce amortized merit-based exposure during learning. The authors report effective fairness, good ranking performance, theoretical guarantees, and practical robustness.

  • Problem

    Dynamic rankings can create rich-get-richer bias and unfair provider exposure because relevance and merit are learned from partial, position-biased feedback.

  • Method

    FairCo combines a control-based amortized fairness mechanism with unbiased cardinal relevance estimation using position-bias correction.

  • Results

    FairCo effectively enforces fairness while maintaining good ranking performance, with empirical evidence of substantially reduced unfairness at a small NDCG decrease versus D-ULTR(Glob).

  • Takeaways & Limitations

    FairCo provides a practical, efficient, robust approach for dynamic rankings that adaptively enforce merit-based exposure fairness.

  • Takeaways & Limitations

    The approach models examination with the Position-Based Model, where examination probability depends only on displayed rank.

Abstract

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Rankings are the primary interface through which many online platforms match users to items (e.g. news, products, music, video). In these two-sided markets, not only the users draw utility from the rankings, but the rankings also determine the utility (e.g. exposure, revenue) for the item providers (e.g. publishers, sellers, artists, studios). It has already been noted that myopically optimizing utility to the users, as done by virtually all learning-to-rank algorithms, can be unfair to the item providers. We, therefore, present a learning-to-rank approach for explicitly enforcing merit-based fairness guarantees to groups of items (e.g. articles by the same publisher, tracks by the same artist). In particular, we propose a learning algorithm that ensures notions of amortized group fairness, while simultaneously learning the ranking function from implicit feedback data. The algorithm takes the form of a controller that integrates unbiased estimators for both fairness and utility, dynamically adapting both as more data becomes available. In addition to its rigorous theoretical foundation and convergence guarantees, we find empirically that the algorithm is highly practical and robust.

1 INTRODUCTION

Dynamic learning-to-rank systems adapt rankings from user feedback, but rankings can create feedback bias and unfairly allocate provider exposure. FairCo addresses these issues with merit-based fairness control, unbiased relevance estimation, and empirical validation.

  • Dynamic LTR rankings adapt from user feedback, intertwining learning and prediction in online systems.
  • Rankings can amplify rich-get-richer feedback dynamics and allocate item-provider exposure unfairly relative to merit.
  • FairCo enforces configurable merit-based exposure allocation while learning relevance and merit in the dynamic setting.
  • FairCo uses a cardinal relevance estimator that supports both unbiased merit estimation for fairness and ranking.
  • FairCo is effective at enforcing fairness while providing good ranking performance, and is efficient, robust, and easy to implement.

2 MOTIVATION

The motivation develops from two failures of naive dynamic LTR: feedback counters are biased, and relevance-based rankings can distribute exposure unfairly. The desired alternative should be unbiased and merit-fair while adapting to learned relevance.

  • The naive algorithm initializes feedback counters, ranks articles by them, and increments counters for articles users read.
  • Early-read items receive more future exposure and feedback, creating a rich-get-richer dynamic because counters are inconsistent relevance estimators.
  • Ranking solely by true average relevance can give groups with similar merit disproportionately different exposure.
  • These deficiencies can produce poor ranking quality, economic disparity, unfairness, alienation, and polarization.
  • The proposed desiderata are unbiasedness against rich-get-richer dynamics and fairness through merit-based exposure allocation.
  • The paper develops amortized merit fairness, unbiased estimators, and a control-based algorithm for dynamic ranking.

3 RELATED WORK

Related work spans societal impacts and fairness in ranking, debiasing feedback from clicks, and conventional or online learning-to-rank. This paper extends these directions to dynamic ranking with explicit relevance estimation for merit.

  • Prior work studies societal consequences of ranking, exploration for utility, and fairness in recommendation and ranking systems.
  • Ranking fairness has been defined across binary classification, recommendation, and information-retrieval settings.
  • Debiasing approaches for click data include preference methods, click models, randomized interventions, and causal or missing-data techniques.
  • Unlike conventional LTR scores, merit-based fairness requires explicit relevance estimates with user-interpretable meaning.

4 DYNAMIC LEARNING-TO-RANK

Dynamic LTR presents rankings for incoming requests, observes partial feedback, and updates its policy over time. Ranking quality depends on estimating relevance despite examination and position bias, enabling sorting-based utility optimization.

  • At each time step, a request supplies visible features and hidden relevance ratings, after which a policy produces a presented ranking.
  • The system receives feedback after presentation and updates its ranking policy for the next time step.
  • Naive dynamic LTR aggregates feedback to form a new global ranking policy.
  • 4.1 Partial and Biased Feedback: Feedback is partial because users meaningfully respond only to examined items, while examination is unobserved and position-biased.
  • 4.1 Partial and Biased Feedback: The Position-Based Model represents examination probability as depending on an item's rank in the presented ranking.
  • 4.2 Evaluating Ranking Performance: Ranking quality is measured by user utility, commonly using DCG or normalized NDCG over request and relevance distributions.
  • Sorting policies optimize common information-retrieval utilities, so the key problem is estimating conditional or average item relevance.
  • Causal-inference and missing-data techniques provide unbiased and consistent relevance estimators using only observed feedback.

5 FAIRNESS IN DYNAMIC LTR

The paper extends merit-based fairness to dynamic learning-to-rank by allocating exposure across groups in proportion to relevance over time. It also considers impact-based allocation and allows alternative allocation strategies through different disparity definitions.

  • Motivation: Sorting items by relevance can maximize user utility while producing unfair exposure for item providers.The paper identifies exposure as the scarce resource allocated by ranking policies.
  • Exposure and merit: Exposure is defined as an item's marginal probability of examination and is aggregated over legally protected, seller-based, or individual groups.Exposure represents the probability that a user sees an item and can therefore read, buy, or interview it.
  • Exposure and merit: Merit is defined as expected average relevance, then aggregated over groups to formulate merit-based fairness criteria.The paper notes that unbiased group-merit estimates must be obtained from biased feedback data.
  • Fairness criteria: The exposure-based disparity measures whether amortized exposure over τ time steps is proportional to group relevance.A disparity farther from zero indicates a greater fairness violation.
  • Fairness criteria: An impact-based disparity can instead allocate exposure according to the impact implied by that exposure, and FairCo is designed to drive both disparities toward zero.Alternative allocation strategies can be implemented by changing the disparity definition.

6 UNBIASED ESTIMATORS

The paper develops unbiased estimators for the quantities required by dynamic ranking and fairness calculations from partial, position-biased feedback. Inverse propensity weighting makes the regression objective asymptotically equivalent to one using unobserved relevance labels, under stated conditions.

  • Required estimates: Dynamic ranking policies and fairness disparities require estimates of position bias, conditional relevance, and average relevance.These estimation problems are addressed before implementing the ranking policies and disparity measures.
  • Required estimates: Position-bias models are treated as inputs, with existing estimation techniques available and no restriction on which technique is used.In the simplest model, examination probabilities depend only on rank, as in a fixed Position-Based Click Model.
  • Conditional relevance: The central challenge is that true relevances are unobserved, leaving only partial and biased feedback for estimating conditional relevance.The paper therefore corrects selection bias using survey-sampling and causal-inference techniques.
  • Conditional relevance: Inverse Propensity Score weighting replaces unavailable relevance labels in a least-squares objective while correcting position bias.The resulting objective uses observed feedback and is asymptotically equivalent to the objective based on true relevances.
  • Estimator guarantees: The estimator's objective is unbiased, and concentration results imply convergence toward the least-squares regressor as the training sequence grows.The paper uses this regression objective to learn neural-network rankers.
  • Average relevance: An additional unbiased estimator supplies average relevance for fairness disparities and global ranking, provided propensities are bounded away from zero.The paper uses this estimator whenever a direct estimate of average relevance is needed.

7 DYNAMICALLY CONTROLLING FAIRNESS

FairCo treats dynamic fair ranking as a feedback-control problem, combining estimated relevance with correction terms for amortized fairness violations. Under the paper's assumptions, the controller converges toward merit-based exposure fairness while remaining practical to implement.

  • Controller design: FairCo is formulated as a controller that manages uncertainty in relevance and merit estimates early in the learning process.Its purpose is to compensate for initial estimation uncertainty while enforcing fairness conditions.
  • Controller design: The overall disparity metric aggregates pairwise fairness violations across groups and can represent exposure-based or impact-based disparity.Optimal fairness corresponds to D_τ = 0.
  • Controller design: FairCo uses a proportional-controller error term that increases with a group's exposure or impact disparity relative to its merit.The error is zero for the group with the maximum exposure or impact relative to merit.
  • Controller design: The estimated merit in the error term converges to true merit as sample size increases, with a minimum constant available to avoid division by zero.This implementation safeguard applies when estimated group merit is too small.
  • FairCo policy: The correction term pushes underexposed groups upward while the ranking sorts items using both estimated relevance and fairness error.FairCo is a sort-based policy whose positive parameter λ controls finite-sample behavior.
  • Practical behavior: A larger λ can cause oscillation whereas a smaller λ produces smoother but slower convergence, and λ = 0.01 works across the reported experiments.The controller is also described as agnostic to the error metric, easy to implement, and efficient.
  • Convergence: For any λ > 0 under the stated group, merit, relevance, and exposure assumptions, FairCo(Exp)'s disparity relative to target merits converges to zero.The theorem applies from any time point τ0, including when estimated merits changed substantially beforehand.

8 EMPIRICAL EVALUATION

The evaluation tests FairCo on semi-synthetic news data under controlled dynamic-ranking conditions and on real-world movie data. Across robustness experiments, FairCo substantially reduces unfairness while maintaining good ranking quality and remaining practical.

  • Experimental setup: Experiments use semi-synthetic news rankings with 30 articles divided into polarity-based groups, simulated user polarities, and position-based clicking.At each step, an unpersonalized ranking is presented; the algorithm observes click feedback but not true relevance.
  • Metrics: Ranking quality is measured by average cumulative NDCG, while fairness is measured using Exposure Unfairness.
  • Overall comparison: FairCo substantially reduces unfairness with only a small NDCG decrease relative to D-ULTR(Glob), whereas Naive retains high unfairness and D-ULTR(Glob) achieves the best NDCG.The comparison tracks convergence as the number of user interactions increases across 100 trials.
  • Estimator evaluation: The IPS relevance estimator’s error approaches zero as users increase, while Naive’s error stagnates around 0.25.This supports using IPS estimates for both fairness and ranking criteria because they correct position bias.
  • Initial-condition robustness: Under adversarial initial user blocks, FairCo remains robust and achieves low unfairness across the tested range, unlike Naive and high-unfairness D-ULTR(Glob).The experiment uses 3000 users and varies the size of an initial right-leaning block before balanced arrivals.

8.2 Evaluation on Real-World Preference Data

On ML-20M movie data, FairCo learns personalized rankings from simulated user interactions while targeting fair exposure across five production-company groups. Personalization improves NDCG, FairCo controls exposure and impact unfairness, and the fairness gains require only a small NDCG reduction.

  • Dataset and setup: The evaluation uses 104 users and 100 movies from five production companies, with matrix factorization filling missing ratings for simulated preference feedback.The companies are MGM, Warner Bros, Paramount, 20th Century Fox, and Columbia.
  • Dataset and setup: FairCo learns personalized ranking policies that maximize NDCG while providing fair exposure to production companies.Users are sampled at each time step, and rankings are evaluated through simulated position-based interactions.
  • Ranking performance: Personalized unbiased regression substantially improves NDCG over D-ULTR(Glob) and Naive, tracking the unobserved-relevance Skyline asymptotically.The comparison uses 10 trials on the Movie data.
  • Fairness-performance trade-off: FairCo(Exp) controls Exposure Unfairness and FairCo(Imp) controls Impact Unfairness, unlike methods that do not actively consider fairness.The corresponding evaluations track NDCG and the relevant unfairness measure as user interactions increase.
  • Fairness-performance trade-off: The fairness improvement comes with a small reduction in NDCG.The trade-off is reported for both exposure- and impact-oriented FairCo evaluations.
  • Fairness criteria: Exposure fairness and impact fairness are substantially different criteria, so optimizing one can increase unfairness under the other.The choice of fairness criterion should match application requirements.

9 CONCLUSIONS

The paper identifies biased feedback and uncontrolled exposure allocation as sources of unfairness in dynamic learning-to-rank systems. It proposes FairCo to enforce amortized merit-based fairness during learning while remaining robust, efficient, and practical.

  • Conclusions: Biased feedback and uncontrolled exposure allocation can produce unfairness and undesirable behavior in dynamic LTR.The conclusion frames these as the central problems addressed by the paper.
  • Conclusions: FairCo adaptively enforces amortized merit-based fairness constraints while item relevances are still being learned.The method is designed for the dynamic learning setting rather than assuming known merits.
  • Conclusions: FairCo is robust to presentation bias, avoids rich-get-richer dynamics, and is easy to implement and computationally efficient.These properties are presented as making the algorithm suitable for practical applications.

A LINEAR PROGRAMMING BASELINE

The linear-programming baseline represents stochastic rankings with a doubly-stochastic matrix and optimizes estimated ranking utility together with fairness disparity. Its fairness-utility balance is controlled by λ, but computational cost can become substantial for large item sets.

  • Baseline formulation: The baseline solves a linear program using current relevance and disparity estimates to obtain a stochastic ranking policy satisfying fairness constraints in expectation.It is adapted to the dynamic LTR setting and evaluated against FairCo.
  • Optimization objective: The objective maximizes estimated DCG while minimizing estimated cumulative fairness disparity.The formulation provides the optimal ranking policy for the chosen trade-off.
  • Baseline formulation: A doubly-stochastic matrix P represents the ranking policy, with P_y,j giving the probability of placing item y at position j.Both DCG and impact disparity are linear functions of P.
  • Optimization objective: λ controls the trade-off between DCG and fairness.Its effect is explored empirically in the evaluation.
  • Implementation: The optimized stochastic policy is converted into a deterministic ranking by Birkhoff von Neumann decomposition, preserving the optimized DCG and fairness in expectation.The implementation uses an LP solver to obtain P*.
  • Implementation: The LP has O(n^2 + |G|^2) variables, creating substantial computation costs for large practical ranking problems.This is the principal stated scalability limitation of the baseline.

B CONVERGENCE OF FAIRCO-CONTROLLER

The convergence analysis proves that FairCo’s exposure unfairness approaches zero under stated feasibility, boundedness, and positive-merit conditions. The proof uses lemmas that bound disparity and show corrective ranking behavior when group exposure is imbalanced.

  • Proof strategy: The convergence proof establishes FairCo’s exposure-fairness theorem through a sequence of supporting lemmas.The paper conjectures that analogous proofs apply to other fairness criteria.
  • Proof strategy: Under the main-theorem conditions, a disparity above a threshold triggers a corrective term that changes the ranking order between groups.The induction argument bounds disparity across subsequent time steps.
  • Conditions and guarantee: The analysis assumes exposure is not available in overabundance, requiring a feasibility condition on group rankings and target merits.Without this condition, some groups may receive more exposure than their merits warrant even when ranked at the bottom.
  • Conditions and guarantee: Theorem B.3 applies to disjoint groups with positive fixed target merits, relevance estimates in [0, 1], bounded exposure, and λ > 0.These assumptions define the scope of the convergence guarantee.
  • Conditions and guarantee: Exposure unfairness relative to the target merits converges to zero at rate O(…).The supplied theorem statement gives the asymptotic rate but does not include the completed expression.
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