Abstract
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.
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