Implicit Rate-Constrained Optimization of Non-decomposable Objectives

• URL: http://arxiv.org/abs/2107.10960v1
• Date: Fri, 23 Jul 2021 00:04:39 GMT
• Title: Implicit Rate-Constrained Optimization of Non-decomposable Objectives
• Authors: Abhishek Kumar, Harikrishna Narasimhan, Andrew Cotter
• Abstract summary: We consider a family of constrained optimization problems arising in machine learning. Our key idea is to formulate a rate-constrained optimization that expresses the threshold parameter as a function of the model parameters. We show how the resulting optimization problem can be solved using standard gradient based methods.
• Score: 37.43791617018009
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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