Migration presents sweeping societal challenges that have recently attracted
significant attention from the scientific community. One of the prominent
approaches that have been suggested employs optimization and machine learning
to match migrants to localities in a way that maximizes the expected number of
migrants who find employment. However, it relies on a strong additivity
assumption that, we argue, does not hold in practice, due to competition
effects; we propose to enhance the data-driven approach by explicitly
optimizing for these effects. Specifically, we cast our problem as the
maximization of an approximately submodular function subject to matroid
constraints, and prove that the worst-case guarantees given by the classic
greedy algorithm extend to this setting. We then present three different models
for competition effects, and show that they all give rise to submodular
objectives. Finally, we demonstrate via simulations that our approach leads to
significant gains across the board.Comment: Simulation code is available at https://github.com/pgoelz/migration
