用精确优化方法训练公平且准确的回归模型，显著缩短训练时间。
Fair and Accurate Regression: Strong Formulations and Algorithms
- 基于混合整数优化构建公平回归的精确公式
- 通过子问题凸包描述提升求解效率，支持快速生成公平模型
- 适合需要兼顾公平性与计算效率的研究者和工程师
本文提出利用混合整数优化求解包含公平性度量的回归问题。我们建立了训练公平回归模型的精确公式。为应对该问题的计算复杂性，研究了多项式可解的单因子和单观测子问题，并推导出其闭凸包描述。由此获得的强形式化公式被用于分支定界算法中精确求解，或作为松弛快速生成公平且准确的模型。此外，为处理大规模实例，我们基于单因子公平回归问题的凸包表示，设计了一种坐标下降算法，可高效改进现有解。在公平最小二乘和公平逻辑回归问题上的数值实验表明，该方法在统计性能上媲美当前最优方法，同时显著降低训练时间。
原文摘要 · Abstract (English)
This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we study the polynomially-solvable single-factor and single-observation subproblems as building blocks and derive their closed convex hull descriptions. Strong formulations obtained for the general fair regression problem in this manner are utilized to solve the problem with a branch-and-bound algorithm exactly or as a relaxation to produce fair and accurate models rapidly. Moreover, to handle large-scale instances, we develop a coordinate descent algorithm motivated by the convex-hull representation of the single-factor fair regression problem to improve a given solution efficiently. Numerical experiments conducted on fair least squares and fair logistic regression problems show competitive statistical performance with state-of-the-art methods while significantly reducing training times.
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