Satisfying Real-world Goals with Dataset Constraints (1606.07558v2)

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.

• The paper introduces a unified framework that embeds dataset constraints to meet real-world goals like fairness, stability, and minimizing churn.
• It employs a ramp penalty and majorization-minimization to effectively approximate non-convex indicator functions for robust optimization.
• Empirical results demonstrate improved classifier performance on real datasets by balancing accuracy with practical constraints.

Satisfying Real-world Goals with Dataset Constraints

The paper presents a robust methodology for training classifiers that meet multiple real-world goals by introducing dataset constraints into the training process. The primary motivation stems from the inadequacy of solely minimizing misclassification error across a training set when other practical objectives, such as fairness, churn minimization, and stability, are pertinent. The authors propose representing various metrics in a unified optimization framework that allows for constraints to be embedded within the training process using a ramp penalty, which provides a tight approximation to the true indicator function. This addresses the challenge of optimizing non-convex problems in a practical and computationally feasible manner.

Real-world Goals and Metrics

The paper identifies several real-world goals that extend beyond traditional accuracy metrics. These include:

1. Coverage: Controlling for positive prediction rates which are imperative due to constraints like budget or biased samples.
2. Churn: Minimizing changes in predictions between model iterations to avoid costly re-evaluations and labeling.
3. Stability: Sustaining classifier performance against trusted models to maintain continuity in predictions.
4. Fairness: Ensuring impartial predictions across sub-populations, as articulated by set criteria on positive and negative classification rates.
5. Recall and Precision: Optimizing these metrics in contexts of heavily imbalanced datasets.
6. Egregious Examples: Managing high-cost misclassification cases with particular care.

Methodological Approach

The methodology employs a structured optimization-based approach. By framing classification goals as constraints, the authors establish a comprehensive optimization problem that balances multiple objectives across different datasets. The optimization problem incorporates $\ell^2$ regularization, with a ramp function replacing the discontinuous indicator function to assert smoothness—an approach necessary for practical optimization of the otherwise NP-hard, non-convex problem.

Algorithmic Implementation

A major contribution of the paper is its development of a novel algorithm using majorization-minimization to tackle the non-convex optimization problem. The algorithm iteratively solves convex upper bounds, created through linear majorization of the ramp loss, thus improving convergence and efficiency. This strategy circumvents the difficulties stemming from direct optimization of discontinuous functions, leveraging surrogate convex programs.

Additionally, optimization is performed over both weights and biases using a combination of stochastic dual coordinate ascent (SDCA) and cutting-plane methods, allowing for efficient evaluations of dual bounds. This notion is particularly significant, suggesting that complex real-world requirements can be met without significant computational overhead.

Empirical Validation

Empirical results reported in the paper underscore the effectiveness of the proposed approach, demonstrating its applicability across various settings from fairness to real-world churn minimization scenarios. For instance, in fairness experiments on the Adult dataset, the method consistently yielded classifiers that outperformed previous techniques. Similarly, for churn, the approach successfully minimized prediction churn without sacrificing accuracy, validating the utility of the optimization scheme in practical, high-dimensional settings.

Implications and Future Directions

The research profoundly contributes to the fields of machine learning and optimization by enabling sophisticated control over classifier behaviors in real-world deployments. By introducing constraints directly into the training phase, it offers a scalable solution to managing complex, interrelated trade-offs between accuracy and other organizational priorities.

Looking ahead, this framework opens avenues for exploration in dynamic and robust model deployment, particularly for real-time systems where trade-offs are continuously shifting. Future work can delve into adaptive constraint management, further automating the balance of multiple objectives as new datasets are ingested and deployment contexts evolve.

In conclusion, this paper successfully presents a structured, scalable solution to the problem of integrating diverse goals into classifier training, pushing forward the capability of machine learning models to operate effectively within real-world, constrained environments.