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

↗ arXiv ↗ Hugging Face

TL;DR

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Key Takeaways

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Why does it matter?

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This paper is crucial for researchers working on multi-objective optimization, fair machine learning, and human-AI collaboration. It offers a novel framework for solving complex real-world problems where multiple objectives need to be balanced while adhering to various constraints. The generalizability of the proposed approach beyond learn-to-defer problems to broader decision-making scenarios makes it particularly impactful for various AI applications. This new methodology provides a significant advancement in handling problems with NP-Hard complexities.

Visual Insights

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🔼 This figure illustrates the process of applying the d-dimensional generalized Neyman-Pearson (d-GNP) lemma to solve multi-objective learn-to-defer (L2D) problems. The training phase involves a learning algorithm to estimate the probability of deferral for each input data point, based on multiple constraints (e.g. accuracy, fairness, cost). The validation phase takes the trained model and uses it to make predictions for new data points. Depending on the trained model and whether the constraints are satisfied, the prediction is made either by the machine learning algorithm or deferred to a human expert.

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Figure 1: Diagram of applying d-GNP to solve multi-objective L2D problem. The role of randomness is neglected due to simplicity of presentation.

🔼 This table lists the embedding functions used in the paper for various constraints in the multi-objective learn-to-defer problem. Each row represents a specific constraint (e.g., accuracy, expert intervention budget, demographic parity) and provides the corresponding embedding function, which maps input features to a vector used in the optimization process. The embedding functions are derived from conditional probability distributions and incorporate features relevant to each constraint, such as demographic information where applicable.

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Table 1: A list of embedding functions corresponding to the constraints that are discussed in Section 3. This list is a version of the results in Appendix D when we assume that the input feature contains demographic group identifier A. To simplify the notations, we define t(A, y) := IA=1 IA=0 Pr(Y=y,A=1) Pr(Y=y,A=0)

In-depth insights

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Multi-objective L2D

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The concept of “Multi-objective L2D” integrates the Learn-to-Defer (L2D) paradigm with the complexities of multi-objective optimization. Traditional L2D focuses on improving overall system accuracy by strategically deferring certain tasks to human experts. However, real-world applications often involve multiple, potentially conflicting, objectives. For instance, a medical diagnosis system might aim to maximize accuracy while simultaneously minimizing bias, cost, or the need for human intervention. Multi-objective L2D addresses this challenge by formulating the problem as a constrained optimization, where the primary goal (e.g., accuracy) is optimized subject to constraints representing the secondary objectives. This framework offers a more nuanced and practical approach to AI systems collaboration with human experts, enabling systems to consider various practical and ethical implications of automated decision-making.

d-GNP solution

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The core of the proposed methodology hinges on a d-dimensional generalization of the Neyman-Pearson Lemma (d-GNP). This novel approach elegantly solves multi-objective learn-to-defer problems by framing them as a functional linear program. The d-GNP solution provides a closed-form solution that determines the optimal deterministic classifier and rejection function under various constraints. Randomness is incorporated to address computational challenges posed by NP-hard deterministic solutions. The framework’s strength lies in its ability to manage multiple constraints simultaneously, providing control over issues like algorithmic fairness, expert intervention budget, and anomaly deferral. Post-processing is employed, thus avoiding potential complications of in-processing methods. The resulting algorithm efficiently estimates the d-GNP solution, showcasing improved constraint violation control compared to existing baselines across diverse datasets. The generalizability of the d-GNP framework extends beyond learn-to-defer applications, offering a powerful tool for various decision-making scenarios involving controlled expected performance measures.

Post-processing

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Post-processing in this context refers to a two-stage machine learning approach. The first stage involves training a model to estimate probability scores for inputs. The second stage uses these scores, applying a carefully designed algorithm, to make the final prediction or decision. This post-processing step allows for the incorporation of constraints and multiple objectives that might not be easily handled during the initial model training. For instance, the framework optimizes accuracy while simultaneously addressing fairness concerns or managing the budget for human intervention. The method’s strength lies in its flexibility and ability to control multiple constraint violations, demonstrated through its application to real-world datasets. A key component is a generalization of the Neyman-Pearson Lemma, which provides the theoretical foundation for optimal decision-making under constraints. The effectiveness of post-processing is highlighted through experiments showing improvements over existing single-objective approaches.

Generalization

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The concept of generalization is central to the success of any machine learning model, and this research is no exception. The authors explicitly address generalization in the context of their multi-objective learn-to-defer framework. A key challenge is ensuring that the algorithm’s performance on unseen data reflects its performance on training data. This is particularly important for fairness constraints. They introduce a post-processing algorithm and use the d-GNP lemma to estimate the optimal solution under various constraints. This approach tackles the complex NP-Hard nature of the problem through the introduction of randomness. The statistical analysis provides generalization error bounds, demonstrating that the algorithm’s performance on unseen data is close to its optimal performance on training data. This rigorous analysis is crucial for demonstrating the practical applicability of the developed framework. The empirical results on multiple datasets further support the claim of effective generalization and the ability to control constraint violations. The authors emphasize that in-processing methods might not generalize well, unlike their post-processing approach. Therefore, the post-processing method coupled with the theoretical generalization bounds is a significant contribution to robust multi-objective learn-to-defer systems.

Fairness tradeoffs

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In many real-world applications of machine learning, particularly those involving sensitive attributes like race or gender, achieving fairness is crucial. However, striving for fairness often necessitates trade-offs. Simply maximizing accuracy can lead to unfair outcomes, where certain groups are disproportionately disadvantaged. Therefore, a balance must be struck. Different fairness metrics present their own trade-offs. For example, demographic parity might improve one type of fairness but worsen another. Algorithmic approaches for achieving fairness, such as pre-processing, in-processing, or post-processing, each offer unique tradeoffs. Pre-processing techniques, while potentially beneficial, can also lead to information loss and reduced model accuracy. In-processing methods are more complex and require substantial modifications to learning algorithms, and might not be feasible in all settings. Finally, post-processing approaches can maintain accuracy but may be limited in their ability to correct severe biases present in the data. It’s critical to carefully consider these inherent trade-offs when designing and implementing fair machine learning systems and to choose the approach best suited for the specific context and objectives. The best strategy for fairness will depend on the specific problem and available data. Ultimately, the goal is not necessarily to achieve perfect fairness across all metrics, but rather to understand and mitigate the negative consequences of unfair bias in a principled manner.

More visual insights

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More on figures

🔼 This figure presents the performance of the proposed d-GNP algorithm compared to two baselines (Madras et al. 2018 and Mozannar et al. 2020) on the COMPAS and ACSIncome datasets. The left panel shows the demographic parity and test accuracy on the COMPAS dataset, illustrating how d-GNP achieves better fairness while maintaining comparable accuracy. The center and right panels display the test accuracy and constraint violation, respectively, on the ACSIncome dataset. These panels demonstrate d-GNP’s ability to control constraint violations effectively and improve accuracy when tolerance for violations increases. The shaded areas in the center panel represent confidence intervals around the test accuracy.

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Figure 2: Performance of d-GNP on COMPAS dataset (left), and ACSIncome (center and right)

🔼 This figure shows the performance comparison of the proposed d-GNP method against other baselines on the Hatespeech dataset. The leftmost panel displays the classification performance for tweets predicted to contain African-American dialect, showing the ground truth, human predictions, classifier predictions, HAI predictions (Human-AI integration), and predictions from d-GNP with different demographic parity constraints (DP-O and DP-HS). The center panel shows the same metrics for tweets not predicted to contain African-American dialect, and the rightmost panel shows the difference in performance between the two groups, highlighting the control of demographic disparity achieved by d-GNP.

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Figure 3: Prediction of d-GNP on Hatespeech dataset [22] and for tweets with predicted African-American (left), and Non-African-American (center) dialect and the disparity between groups (right).

🔼 This figure is a geometric illustration to support the proof of Theorem 4.1 in the paper. It shows two convex sets, M and N, in a multi-dimensional space. The set M represents the space of achievable objective and constraint values for a multi-objective optimization problem. The set N is a subset of M representing the space of solutions that satisfy the constraints exactly (tightly). The figure demonstrates that if a point (v) in N has a corresponding point in M, then all points in the interior of N have corresponding points in M. This property is crucial to proving the sufficiency of the proposed d-GNP solution for solving the multi-objective learn-to-defer problem.

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Figure 4: If an interior point of N has one corresponding point at M, then so are all interior points of N

Full paper

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