Migration as Submodular Optimization

TL;DR

This paper improves migration matching algorithms by modeling competition effects as submodular functions, leading to better optimization and higher employment outcomes through theoretical guarantees and simulation results.

Contribution

It introduces a novel submodular optimization framework for migration matching that explicitly accounts for competition effects, extending classic greedy algorithm guarantees.

Findings

Models competition effects as submodular functions

Proves greedy algorithm guarantees extend to this setting

Simulation results show significant performance gains

Abstract

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.