[Paper Review] Satisfying Real-world Goals with Dataset Constraints

Gabriel Goh, Andrew Cotter+2 more|arXiv (Cornell University)|Jun 24, 2016

Imbalanced Data Classification TechniquesComputer Science16 references79 citations

TL;DR

This paper proposes a constrained optimization framework using the ramp penalty to satisfy real-world machine learning goals—such as fairness, coverage, churn reduction, and recall—on multiple datasets. It introduces an efficient algorithm to approximately solve the resulting non-convex problem, demonstrating effectiveness on benchmark and industrial datasets.

ABSTRACT

The goal of minimizing misclassification error on a training set is often just one of several real-world goals that might be defined on different datasets. For example, one may require a classifier to also make positive predictions at some specified rate for some subpopulation (fairness), or to achieve a specified empirical recall. Other real-world goals include reducing churn with respect to a previously deployed model, or stabilizing online training. In this paper we propose handling multiple goals on multiple datasets by training with dataset constraints, using the ramp penalty to accurately quantify costs, and present an efficient algorithm to approximately optimize the resulting non-convex constrained optimization problem. Experiments on both benchmark and real-world industry datasets demonstrate the effectiveness of our approach.

Motivation & Objective

• Address the challenge of optimizing machine learning models for real-world objectives beyond standard accuracy, such as fairness, coverage, and model stability.
• Formulate diverse real-world goals—like demographic parity, recall, and churn rate—as rate constraints on multiple datasets.
• Develop a scalable optimization framework that handles multiple constraints simultaneously while maintaining computational efficiency.
• Ensure practical deployment by constraining model updates relative to a previously deployed model to reduce operational churn.
• Provide theoretical convergence guarantees for the proposed algorithm under realistic assumptions, including non-convexity and dataset heterogeneity.

Proposed method

• Represent real-world goals (e.g., fairness, coverage, recall) as constraints on positive and negative prediction rates across multiple datasets.
• Use the ramp penalty to accurately quantify misclassification costs, enabling precise control over constraint violations.
• Formulate the learning problem as a non-convex constrained optimization task with multiple dataset-specific constraints.
• Propose an iterative algorithm (Algorithm 2) that alternates between optimizing model weights and dual variables using a subgradient-based approach.
• Implement the inner SVM optimization via SDCA or kernelized SVM solvers, with a center-of-mass oracle for dual variable updates.
• Introduce a bias correction mechanism (Algorithm 3) to handle the unregularized bias term in linear classifiers, ensuring convergence.

Experimental results

Research questions

• RQ1 How can real-world machine learning objectives such as fairness, coverage, and churn be formally expressed as constraints in a training framework?
• RQ2 Can a single optimization framework effectively handle multiple, diverse real-world goals across different datasets simultaneously?
• RQ3 What is the convergence behavior of an algorithm that solves a non-convex, constrained optimization problem with multiple dataset constraints?
• RQ4 How does the use of the ramp penalty improve the accuracy of cost quantification compared to standard hinge loss in constrained learning?
• RQ5 To what extent can the proposed algorithm reduce model churn while maintaining or improving performance on primary objectives?

Key findings

• The proposed framework successfully handles diverse real-world goals—including fairness, coverage, recall, and churn—by formulating them as rate constraints on multiple datasets.
• Experiments on benchmark and real-world industrial datasets show that the method effectively satisfies user-specified constraints while maintaining competitive performance on primary objectives.
• Theoretical analysis shows that Algorithm 2 converges to an ϵ-suboptimal solution with a total cost of Õ(dnm + dm²k²/ϵ) arithmetic operations, where d is dimension, n is total data size, m is number of constraints, and k is number of datasets.
• The algorithm requires O(m ln²(k/ϵ)) calls to center-of-mass oracles and linear programming oracles, though these are computationally challenging in practice.
• Kernelization is supported, enabling the use of standard kernel SVM solvers (e.g., LIBSVM), which improves practical performance over SDCA in the kernel setting.
• The method provides a practical solution to the model churn problem by constraining the empirical disagreement rate between new and deployed models on unlabeled data.