Causal Strategic Linear Regression
Yonadav Shavit,u00a0Benjamin Edelman,u00a0Brian Axelrod
In many predictive decision-making scenarios, such as credit scoring and academic testing, a decision-maker must construct a model that accounts for agentsu2019 propensity to u201cgameu201d the decision rule by changing their features so as to receive better decisions. Whereas the strategic classification literature has previously assumed that agentsu2019 outcomes are not causally affected by their features (and thus that strategic agentsu2019 goal is deceiving the decision-maker), we join concurrent work in modeling agentsu2019 outcomes as a function of their changeable attributes. As our main contribution, we provide efficient algorithms for learning decision rules that optimize three distinct decision-maker objectives in a realizable linear setting: accurately predicting agentsu2019 post-gaming outcomes (prediction risk minimization), incentivizing agents to improve these outcomes (agent outcome maximization), and estimating the coefficients of the true underlying model (parameter estimation). Our algorithms circumvent a hardness result of Miller et al. (2019) by allowing the decision maker to test a sequence of decision rules and observe agentsu2019 responses, in effect performing causal interventions through the decision rules.
