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A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems

Mohammad-Amin Charusaie, Samira Samadi

TL;DR

This work tackles multi-objective Learn-to-Defer (L2D) by casting it as a constrained decision problem and deriving a Bayes-optimal solution via a $d$-dimensional Neyman-Pearson generalization ($d$-GNP). By jointly learning the classifier and a randomized deferral rule, it reframes the problem as a linear program on score embeddings, enabling a post-processing algorithm that handles arbitrary constraint sets (e.g., demographic parity, equality of opportunity, expert budgets). The authors provide an empirical plug-in method with generalization guarantees and demonstrate improved constraint satisfaction on datasets like COMPAS and ACSIncome, while maintaining competitive accuracy. The framework offers a unified, scalable approach for constrained multiclass L2D and suggests broader usefulness for constrained vanilla classification as well.

Abstract

Learn-to-Defer is a paradigm that enables learning algorithms to work not in isolation but as a team with human experts. In this paradigm, we permit the system to defer a subset of its tasks to the expert. Although there are currently systems that follow this paradigm and are designed to optimize the accuracy of the final human-AI team, the general methodology for developing such systems under a set of constraints (e.g., algorithmic fairness, expert intervention budget, defer of anomaly, etc.) remains largely unexplored. In this paper, using a $d$-dimensional generalization to the fundamental lemma of Neyman and Pearson (d-GNP), we obtain the Bayes optimal solution for learn-to-defer systems under various constraints. Furthermore, we design a generalizable algorithm to estimate that solution and apply this algorithm to the COMPAS and ACSIncome datasets. Our algorithm shows improvements in terms of constraint violation over a set of baselines.

A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems

TL;DR

This work tackles multi-objective Learn-to-Defer (L2D) by casting it as a constrained decision problem and deriving a Bayes-optimal solution via a -dimensional Neyman-Pearson generalization (-GNP). By jointly learning the classifier and a randomized deferral rule, it reframes the problem as a linear program on score embeddings, enabling a post-processing algorithm that handles arbitrary constraint sets (e.g., demographic parity, equality of opportunity, expert budgets). The authors provide an empirical plug-in method with generalization guarantees and demonstrate improved constraint satisfaction on datasets like COMPAS and ACSIncome, while maintaining competitive accuracy. The framework offers a unified, scalable approach for constrained multiclass L2D and suggests broader usefulness for constrained vanilla classification as well.

Abstract

Learn-to-Defer is a paradigm that enables learning algorithms to work not in isolation but as a team with human experts. In this paradigm, we permit the system to defer a subset of its tasks to the expert. Although there are currently systems that follow this paradigm and are designed to optimize the accuracy of the final human-AI team, the general methodology for developing such systems under a set of constraints (e.g., algorithmic fairness, expert intervention budget, defer of anomaly, etc.) remains largely unexplored. In this paper, using a -dimensional generalization to the fundamental lemma of Neyman and Pearson (d-GNP), we obtain the Bayes optimal solution for learn-to-defer systems under various constraints. Furthermore, we design a generalizable algorithm to estimate that solution and apply this algorithm to the COMPAS and ACSIncome datasets. Our algorithm shows improvements in terms of constraint violation over a set of baselines.
Paper Structure (20 sections, 16 theorems, 129 equations, 2 figures, 1 table, 2 algorithms)

This paper contains 20 sections, 16 theorems, 129 equations, 2 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Problem Setting
  4. $d$-dimensional Generalization of Neyman-Pearson Lemma
  5. Empirical $d$-GNP and its Statistical Generalization
  6. Experiments
  7. Conclusion
  8. Acknowledgment
  9. Lack of Compositionality of Fairness Criteria
  10. Extended Related Works
  11. Rephrasing \ref{['eqn: optem']} into Linear Functional Programming
  12. Derivation of Embedding Functions
  13. Limitations of Cost-Sentitive Methods
  14. On Failure of In-Processing Methods
  15. Proof of Theorem \ref{['thm: np']}
  16. ...and 5 more sections

Key Result

Theorem 3.1

Let the human expert and the classifier induce $0-1$ losses and assume $\mathcal{X}$ to be finite. Finding an optimal deterministic classifier and rejection function for a bounded expert intervention budget is an NP-Hard problem.

Figures (2)

  • Figure 1: Diagram of applying $d$-GNP to solve multi-objective L2D problem via Algorithm \ref{['alg:bayes']}. The role of randomness is neglected due to simplicity of presentation.
  • Figure 2: Performance of $d$-GNP on COMPAS dataset (left), and ACSIncome (center and right)

Theorems & Definitions (29)

  • Theorem 3.1: NP-Hardness of \ref{['eqn: optem']}
  • Theorem 4.1: $d$-GNP
  • Example 1: L2D with Demographic Parity
  • Example 2: L2D with Equality of Opportunity
  • Example 3: Algorithmic Fairness for Multiclass Classification
  • Theorem 4.2: $d$-GNP with a single constraint
  • Theorem 5.1: Generalization of the Constraints
  • Definition 5.2
  • Theorem 5.3: Generalization of Objective
  • Proposition 5.4: Impossibility of generalization of deferral labels
  • ...and 19 more