When users can benefit from certain predictive outcomes, they may be prone to
act to achieve those outcome, e.g., by strategically modifying their features.
The goal in strategic classification is therefore to train predictive models
that are robust to such behavior. However, the conventional framework assumes
that changing features does not change actual outcomes, which depicts users as
"gaming" the system. Here we remove this assumption, and study learning in a
causal strategic setting where true outcomes do change. Focusing on accuracy as
our primary objective, we show how strategic behavior and causal effects
underlie two complementing forms of distribution shift. We characterize these
shifts, and propose a learning algorithm that balances between these two forces
and over time, and permits end-to-end training. Experiments on synthetic and
semi-synthetic data demonstrate the utility of our approach