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We consider an online regression setting in which individuals adapt to theregression model: arriving individuals are aware of the current model, andinvest strategically in modifying their own features so as to improve thepredicted score that the current model assigns to them. Such featuremanipulation has been observed in various scenarios -- from credit assessmentto school admissions -- posing a challenge for the learner. Surprisingly, wefind that such strategic manipulations may in fact help the learner recover themeaningful variables -- that is, the features that, when changed, affect thetrue label (as opposed to non-meaningful features that have no effect). We showthat even simple behavior on the learner's part allows her to simultaneously i)accurately recover the meaningful features, and ii) incentivize agents toinvest in these meaningful features, providing incentives for improvement.

Gaming Helps! Learning from Strategic Interactions in Natural Dynamics