Learning with Statistical Equality Constraints
This work addresses the problem of handling equality constraints in machine learning for practitioners in fairness and boundary value applications, offering a more efficient alternative to hyperparameter tuning, though it is incremental as it builds on constrained optimization methods.
The paper tackles the challenge of incorporating statistical equality constraints, such as fairness requirements, into machine learning without needing hyperparameter tuning, by developing a generalization theory and proposing a practical algorithm that solves a sequence of unconstrained problems, demonstrating effectiveness in applications like fair learning and boundary value problems.
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement violation penalties into the training objective. To be effective, this approach requires careful tuning of these hyperparameters (weights), involving trial-and-error and cross-validation, which becomes ineffective even for a moderate number of requirements. These issues are exacerbated when the requirements involve parities or equalities, as is the case in fairness and boundary value problems. An alternative technique uses constrained optimization to formulate these learning problems. Yet, existing approximation and generalization guarantees do not apply to problems involving equality constraints. In this work, we derive a generalization theory for equality-constrained statistical learning problems, showing that their solutions can be approximated using samples and rich parametrizations. Using these results, we propose a practical algorithm based on solving a sequence of unconstrained, empirical learning problems. We showcase its effectiveness and the new formulations enabled by equality constraints in fair learning, interpolating classifiers, and boundary value problems.