Causal Feature Discovery through Strategic Modification

We consider an online regression setting in which individuals adapt to the regression model: arriving individuals may access the model throughout the process, and invest strategically in modifying their own features so as to improve their assigned score. We find that this strategic manipulation may help a learner recover the causal variables, in settings where an agent can invest in improving impactful features that also improve his true label. We show that even simple behavior on the learner's part (i.e., periodically updating her model based on the observed data so far, via least-square regression) allows her to simultaneously i) accurately recover which features have an impact on an agent's true label, provided they have been invested in significantly, and ii) incentivize agents to invest in these impactful features, rather than in features that have no effect on their true label.