Learning Fair Policies for Multi-stage Selection Problems from
  Observational Data
Zhuangzhuang Jia Grani A. Hanasusanto Phebe Vayanos Weijun Xie
We consider the problem of learning fair policies for multi-stage selection
problems from observational data. This problem arises in several high-stakes
domains such as company hiring, loan approval, or bail decisions where outcomes
(e.g., career success, loan repayment, recidivism) are only observed for those
selected. We propose a multi-stage framework that can be augmented with various
fairness constraints, such as demographic parity or equal opportunity. This
problem is a highly intractable infinite chance-constrained program involving
the unknown joint distribution of covariates and outcomes. Motivated by the
potential impact of selection decisions on people's lives and livelihoods, we
propose to focus on interpretable linear selection rules. Leveraging tools from
causal inference and sample average approximation, we obtain an asymptotically
consistent solution to this selection problem by solving a mixed binary conic
optimization problem, which can be solved using standard off-the-shelf solvers.
We conduct extensive computational experiments on a variety of datasets adapted
from the UCI repository on which we show that our proposed approaches can
achieve an 11.6% improvement in precision and a 38% reduction in the measure of
unfairness compared to the existing selection policy.