用改进的拉格朗日法解决非凸约束学习问题，保证收敛和公平性。
AL-CoLe: Augmented Lagrangian for Constrained Learning
- 基于增广拉格朗日法处理非凸约束，只需少量修改即可应用。
- 在温和条件下证明强对偶性与算法收敛到最优解。
- 适用于需要公平性的分类任务，如性别、种族公平建模。
尽管现代机器学习参数化通常是非凸的，拉格朗日对偶性仍是解决约束学习问题的常用工具。本文重新审视增广拉格朗日方法，该方法旨在缓解非凸情形下的对偶间隙，且仅需最小改动，在约束学习中仍较少被研究。本文在温和条件下建立了强对偶性结果，证明了对偶上升算法可收敛至可行且最优的原始解，并提供了类似PAC的泛化保证。最后，我们在公平性约束分类任务中验证了其有效性。
原文摘要 · Abstract (English)
Despite the non-convexity of most modern machine learning parameterizations, Lagrangian duality has become a popular tool for addressing constrained learning problems. We revisit Augmented Lagrangian methods, which aim to mitigate the duality gap in non-convex settings while requiring only minimal modifications, and have remained comparably unexplored in constrained learning settings. We establish strong duality results under mild conditions, prove convergence of dual ascent algorithms to feasible and optimal primal solutions, and provide PAC-style generalization guarantees. Finally, we demonstrate its effectiveness on fairness constrained classification tasks.
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