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Fair Classification with Partial Feedback: An Exploration-Based Data Collection Approach

Vijay Keswani, Anay Mehrotra, L. Elisa Celis

TL;DR

This work tackles partial feedback in high‑stakes classification by introducing an exploration‑based data collection framework that partitions the domain into Exploit and Explore regions and jointly learns predictions while collecting outcomes for previously ignored subpopulations. It provides strong guarantees: per‑iteration $oldsymbol{α}$‑FDR feasibility, monotone improvement of group‑wise utility, and convergence of the learned policy to the $oldsymbol{f_{ ext{opt}}^{oldsymbol{α}}}$, with convergence rates depending on exploration design and distributional properties. The method supports explicit fairness through exploitation and exploration strategies and demonstrates empirically that data quality and true positive rates improve across protected groups with minimal loss in overall utility. These results have practical impact for lending, policing, and other domains where ground truth is observed only after initial positive classifications, offering a principled balance between performance, fairness, and informative data collection.

Abstract

In many predictive contexts (e.g., credit lending), true outcomes are only observed for samples that were positively classified in the past. These past observations, in turn, form training datasets for classifiers that make future predictions. However, such training datasets lack information about the outcomes of samples that were (incorrectly) negatively classified in the past and can lead to erroneous classifiers. We present an approach that trains a classifier using available data and comes with a family of exploration strategies to collect outcome data about subpopulations that otherwise would have been ignored. For any exploration strategy, the approach comes with guarantees that (1) all sub-populations are explored, (2) the fraction of false positives is bounded, and (3) the trained classifier converges to a ``desired'' classifier. The right exploration strategy is context-dependent; it can be chosen to improve learning guarantees and encode context-specific group fairness properties. Evaluation on real-world datasets shows that this approach consistently boosts the quality of collected outcome data and improves the fraction of true positives for all groups, with only a small reduction in predictive utility.

Fair Classification with Partial Feedback: An Exploration-Based Data Collection Approach

TL;DR

This work tackles partial feedback in high‑stakes classification by introducing an exploration‑based data collection framework that partitions the domain into Exploit and Explore regions and jointly learns predictions while collecting outcomes for previously ignored subpopulations. It provides strong guarantees: per‑iteration ‑FDR feasibility, monotone improvement of group‑wise utility, and convergence of the learned policy to the , with convergence rates depending on exploration design and distributional properties. The method supports explicit fairness through exploitation and exploration strategies and demonstrates empirically that data quality and true positive rates improve across protected groups with minimal loss in overall utility. These results have practical impact for lending, policing, and other domains where ground truth is observed only after initial positive classifications, offering a principled balance between performance, fairness, and informative data collection.

Abstract

In many predictive contexts (e.g., credit lending), true outcomes are only observed for samples that were positively classified in the past. These past observations, in turn, form training datasets for classifiers that make future predictions. However, such training datasets lack information about the outcomes of samples that were (incorrectly) negatively classified in the past and can lead to erroneous classifiers. We present an approach that trains a classifier using available data and comes with a family of exploration strategies to collect outcome data about subpopulations that otherwise would have been ignored. For any exploration strategy, the approach comes with guarantees that (1) all sub-populations are explored, (2) the fraction of false positives is bounded, and (3) the trained classifier converges to a ``desired'' classifier. The right exploration strategy is context-dependent; it can be chosen to improve learning guarantees and encode context-specific group fairness properties. Evaluation on real-world datasets shows that this approach consistently boosts the quality of collected outcome data and improves the fraction of true positives for all groups, with only a small reduction in predictive utility.
Paper Structure (26 sections, 7 theorems, 69 equations, 9 figures, 2 tables, 1 algorithm)

This paper contains 26 sections, 7 theorems, 69 equations, 9 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related Works
  4. Model, Stakeholders, and Classification
  5. Partial Feedback, False Discovery Rate, and Optimal Offline Classifier
  6. Stakeholders and Iterative Model
  7. Our Framework
  8. Theoretical Results
  9. Empirical Results
  10. Adult Income Dataset
  11. German Credit Dataset
  12. Proofs
  13. Proof of \ref{['thm:feasibility']}
  14. Proof of \ref{['lem:conc_inequality']}
  15. Discussion of techniques.
  16. ...and 11 more sections

Key Result

Theorem 4.1

Suppose $f_0$ is $(\alpha,\lambda)$-feasible (assump:f0_is_feasible). For any $\varepsilon,\delta,\tau \in (0,1]$, alg:main_algorithm satisfies the following at every iteration $t$: If $n\geq \left| D \right|\cdot\mathop{\hbox{\rm poly}}(1/\lambda,$$1/\tau, 1/\min\left\{\varepsilon,\alpha-\varepsilo

Figures (9)

  • Figure 1: Pipeline of the process undertaken at time-step $t$ to classify unlabeled samples $S_t$. The institution learns a classifier $f_t$ using past labeled data. It also creates exploitation-exploration partitions to decide which elements in $S_t$ will be classified using $f_t$ and which elements will compose the exploration set, over which the exploration strategy $g$ will be employed.
  • Figure 2: Iteration-wise performance of Algorithm \ref{['alg:main_algorithm']} (with explore and/or exploit fairness) on Adult (protected attribute is race). Parameters $\alpha = 0.15$ with $\alpha_{\textrm{exploit}} = 0.075 {\cdot} t^{0.2}$ and $\alpha_{\textrm{explore}} = \alpha - \alpha_{\textrm{exploit}}$, $\tau = 0.5, \lambda = 0, \varepsilon = 10^{-3}$.
  • Figure 3: Iteration-wise performance of Algorithm \ref{['alg:main_algorithm']} (with explore and/or exploit fairness) on German (protected attribute is gender). Parameters $\alpha{=}0.15$ with $\alpha_{\textrm{exploit}} {=} 0.075 {\cdot} t^{0.2}$ and $\alpha_{\textrm{explore}} {=} \alpha {-} \alpha_{\textrm{exploit}}$, $\tau{=}0.5, \lambda {=} 0, \varepsilon{=}10^{-3}$.
  • Figure 4: Iteration-wise performance of all variants of Algorithm \ref{['alg:main_algorithm']} (with or without each of explore and exploit fairness constraints) on the Adult dataset with gender as the protected attribute. All algorithms can be seen to improve TPR for both groups.
  • Figure 5: Performance of all versions of Algorithm \ref{['alg:main_algorithm']} (with or without each of explore and exploit fairness constraints) and baselines on the Adult dataset with race as the protected attribute.
  • ...and 4 more figures

Theorems & Definitions (12)

  • Definition 2.1: Utility Metrics
  • Definition 2.2: False-discovery Rate Constraint
  • Theorem 4.1: Feasibility with respect to FDR constraint
  • Theorem 4.2: Fairness: Improvement in group-wise utility
  • Theorem 4.3: Group-wise convergence to $\optOffline^\alpha$
  • Theorem 6.1: Feasibility with respect to FDR constraint
  • Lemma 6.1
  • Definition 6.2
  • proof : Proof of \ref{['thm:feasibility']} assuming \ref{['lem:conc_inequality']}
  • Remark 6.3
  • ...and 2 more