  In many predictive decision-making scenarios, such as credit scoring and
academic testing, a decision-maker must construct a model that accounts for
agents' propensity to "game" the decision rule by changing their features so as
to receive better decisions. Whereas the strategic classification literature
has previously assumed that agents' outcomes are not causally affected by their
features (and thus that strategic agents' goal is deceiving the
decision-maker), we join concurrent work in modeling agents' 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
agents' 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. (2020) by allowing the
decision maker to test a sequence of decision rules and observe agents'
responses, in effect performing causal interventions through the decision
rules.
