Supervised learning models have been used in various domains such as lending,
college admission, face recognition, natural language processing, etc. However,
they may inherit pre-existing biases from training data and exhibit
discrimination against protected social groups. Various fairness notions have
been proposed to address unfairness issues. In this work, we focus on Equalized
Loss (EL), a fairness notion that requires the expected loss to be
(approximately) equalized across different groups. Imposing EL on the learning
process leads to a non-convex optimization problem even if the loss function is
convex, and the existing fair learning algorithms cannot properly be adopted to
find the fair predictor under the EL constraint. This paper introduces an
algorithm that can leverage off-the-shelf convex programming tools (e.g.,
CVXPY) to efficiently find the global optimum of this non-convex optimization.
In particular, we propose the ELminimizer algorithm, which finds the optimal
fair predictor under EL by reducing the non-convex optimization to a sequence
of convex optimization problems. We theoretically prove that our algorithm
finds the global optimal solution under certain conditions. Then, we support
our theoretical results through several empirical studies.

通过使用现成的凸规划工具（如 CVXPY），本文提出了 ELminimizer 算法，通过将非凸优化问题转化为一系列凸优化问题，高效地找到满足等效损失约束条件下的全局最优公平预测器，并通过多个实证研究支持我们的理论结果。