Should Humans Lie to Machines?  The Incentive Compatibility of Lasso and General Weighted Lasso

We consider situations where a user feeds her attributes to a machine learning method that tries to predict her best option based on a random sample of other users. The predictor is incentive-compatible if the user has no incentive to misreport her covariates. Focusing on the popular Lasso estimation technique, we borrow tools from high-dimensional statistics to characterize sufficient conditions that ensure that Lasso is incentive compatible in large samples. We extend our results to the Conservative Lasso estimator and provide new moment bounds for this generalized weighted version of Lasso. Our results show that incentive compatibility is achieved if the tuning parameter is kept above some threshold. We present simulations that illustrate how this can be done in practice.

Introduction. Rapid advances in machine learning methods for analyzing big data have given rise to au- tomated systems that employ these methods to predict the best fitting outcomes for users based on their personal characteristics. For example, many online platforms try to predict which content - a song, a video, a post, or an article - is the best fit for each user. Medical providers have also begun using machine learning techniques to automate check-ups and test appointments for patients based on their medical history. Typically, these automated systems use data from past users to estimate a model that relates the best fit for a user (such as the most preferred content or the appropriate medical test) to her characteristics. These estimates are then applied to a new user’s characteristics, which she discloses either actively or passively via her past online behavior (which may be reflected in her cookies or collected by her browser). Given the growing interaction of users with such automated systems, it is only natural to ask whether a user should truthfully disclose her characteristics?

Discussion / Conclusion. The growing reliance on machine learning in automating decisions previously made by peo- ple raises the question of how people would interact with these automated systems. In particular, would people have an incentive to act strategically in order to manipulate such automated systems? This strategic interaction will become particularly important when these automated systems start playing a more prominent role in medical decision-making or even in driving. This paper takes only a small preliminary step towards addressing this question by study- ing whether a user would want to lie to an automated system that uses Lasso or Conservative Lasso to predict that user’s ideal outcome based on her reported attributes. Our main con- tribution is showing that truthful reporting can be ensured by appropriately adjusting the tuning parameter to be larger than what is required for consistency. Our result is also sig- nificant from a pure econometrics point of view: just concentrating on oracle inequalities and post-selection inference can lead to a small tuning parameter, which in turn, can lead to model overfitting, which then introduces an incentive to misreport.