On Learning with a Concurrent Verifier: Convexity, Improving Bounds, and Complex Requirements

Abstract

Machine learning technologies have been used in a wide range of practical applications. In them, it is preferable to guarantee that the input-output pairs of a model satisfy the given requirements. The recently proposed concurrent verifier (CV) is a module combined with machine learning models to guarantee that the model's input-output pairs satisfy the given requirements. The previous paper provides a generalization analysis of learning with a CV to show how the model's learnability changes using a CV. Although the paper provides basic learnability results, many CV properties remain unrevealed. Moreover, the previous work assumed a CV always works correctly, and requirements are imposed on a single input-output pair, which limits the situation where we can use a CV. We show the learning algorithms that preserve convexity when using a CV. We also show conditions that using a CV improves the generalization error bound. Moreover, we analyze the learnability when a CV is incorrect, or requirements are imposed on the combination of multiple input-output pairs.