Should Decision-Makers Reveal Classifiers in Online Strategic Classification?

TL;DR

This paper investigates how hiding the classifier in online strategic classification impacts the decision-maker's performance, revealing that limited access can significantly increase mistakes due to agents' manipulation strategies.

Contribution

It introduces a new model where agents manipulate based on historical classifiers, and quantifies the performance degradation compared to full knowledge scenarios.

Findings

Limited access increases mistakes by a factor of $(1- ext{gamma})^{-1}$ or $k_{in}$.

Hiding classifiers can worsen decision accuracy in strategic settings.

Performance loss depends on agents' memory and manipulation graph complexity.

Abstract

Strategic classification addresses a learning problem where a decision-maker implements a classifier over agents who may manipulate their features in order to receive favorable predictions. In the standard model of online strategic classification, in each round, the decision-maker implements and publicly reveals a classifier, after which agents perfectly best respond based on this knowledge. However, in practice, whether to disclose the classifier is often debated -- some decision-makers believe that hiding the classifier can prevent misclassification errors caused by manipulation. In this paper, we formally examine how limiting the agents' access to the current classifier affects the decision-maker's performance. Specifically, we consider an extended online strategic classification setting where agents lack direct knowledge about the current classifier and instead manipulate based on a weighted average of historically implemented classifiers. Our main result shows that in this setting, the decision-maker incurs $(1-\gamma)^{-1}$ or $k_{\text{in}}$ times more mistakes compared to the full-knowledge setting, where $k_{\text{in}}$ is the maximum in-degree of the manipulation graph (representing how many distinct feature vectors can be manipulated to appear as a single one), and $\gamma$ is the discount factor indicating agents' memory of past classifiers. Our results demonstrate how withholding access to the classifier can backfire and degrade the decision-maker's performance in online strategic classification.