Strategic Classification with Randomised Classifiers

TL;DR

This paper explores the use of randomized classifiers in strategic classification, demonstrating they can outperform deterministic ones in accuracy without added downsides, especially with limited data.

Contribution

It introduces a theoretical analysis of randomized classifiers in strategic classification, showing their potential advantages over deterministic classifiers.

Findings

Randomized classifiers can achieve better accuracy than deterministic ones under certain conditions.

The excess risk of strategic empirical risk minimization is similarly bounded for both randomized and deterministic classifiers.

Classifier risk converges to the optimal at the same rate as data volume increases.

Abstract

We consider the problem of strategic classification, where a learner must build a model to classify agents based on features that have been strategically modified. Previous work in this area has concentrated on the case when the learner is restricted to deterministic classifiers. In contrast, we perform a theoretical analysis of an extension to this setting that allows the learner to produce a randomised classifier. We show that, under certain conditions, the optimal randomised classifier can achieve better accuracy than the optimal deterministic classifier, but under no conditions can it be worse. When a finite set of training data is available, we show that the excess risk of Strategic Empirical Risk Minimisation over the class of randomised classifiers is bounded in a similar manner as the deterministic case. In both the deterministic and randomised cases, the risk of the classifier produced by the learner converges to that of the corresponding optimal classifier as the volume of available training data grows. Moreover, this convergence happens at the same rate as in the i.i.d. case. Our findings are compared with previous theoretical work analysing the problem of strategic classification. We conclude that randomisation has the potential to alleviate some issues that could be faced in practice without introducing any substantial downsides.