Causal Strategic Linear Regression
Abstract
When machine learning systems are deployed in high-stakes domains, agents may have incentives to manipulate their observable features in order to receive more favorable predictions. Such strategic behavior can undermine the accuracy and fairness of the deployed model. In this work, we study the problem of learning in the presence of strategic agents who can modify their features. We focus on the linear regression setting and ask: when can a learner achieve both statistical accuracy and incentive compatibility?
We introduce a causal framework for strategic classification that explicitly models the strategic agents’ ability to modify features. Our key insight is that agents’ strategic responses can be viewed through a causal lens, where agents intervene on their features to influence the model’s predictions. We show that under certain conditions, it is possible to learn predictors that are both accurate and robust to strategic manipulation. We provide both positive and negative results: we identify settings where robust learning is possible and prove impossibility results for other scenarios.
Our approach combines ideas from causal inference and strategic classification, providing new theoretical insights into the fundamental limits of learning from strategic agents.