We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest. Examples of such problems include optimizing the false negative rate at a fixed false positive rate, optimizing precision at a fixed recall, optimizing the area under the precision-recall or ROC curves, etc. Our key idea is to formulate a rate-constrained optimization that expresses the threshold parameter as a function of the model parameters via the Implicit Function theorem. We show how the resulting optimization problem can be solved using standard gradient based methods. Experiments on benchmark datasets demonstrate the effectiveness of our proposed method over existing state-of-the art approaches for these problems. The code for the proposed method is available at https://github.com/google-research/google-research/tree/master/implicit_constrained_optimization .

Fairness is a highly subjective concept and is not different when comes to machine learning. We typically feels that the referees are "unfair" to our favorite team when they lose a close match or that any outcome is extremely "fair" when it goes our way. Given that machine learning models cannot rely on subjectivity, we need an efficient way to quantify fairness. A lot of research has been done in this area mostly framing fairness as an outcome optimization problem. Recently, Google AI research open sourced the Tensor Flow Constrained Optimization Library(TFCO), an optimization framework that can be used for optimizing different objectives of a machine learning model including fairness.

Google AI today released TensorFlow Constrained Optimization (TFCO), a supervised machine learning library built for training machine learning models on multiple metrics and "optimizing inequality-constrained problems." The library is designed to help address issues like fairness constraints and predictive parity and help machine learning practitioners better understand things like true positive rates on residents of certain countries, or recall illness diagnoses depending on age and gender. In tests with a Wikipedia data set, the library achieved lower false-positive rates when predicting whether a comment on a Wiki is toxic based on race, religion, gender identity, or sexuality, while maintaining similar accuracy rates. TFCO is made to "take into account the societal and cultural factors necessary to satisfy real-world requirements," said Andrew Zaldivar on behalf of the TFCO team today in a Google AI blog post. "The ability to express many fairness goals as rate constraints can help drive progress in the responsible development of machine learning, but it also requires developers to carefully consider the problem they are trying to address," he said.