通过对偶方法分析带f散度正则的算法泛化误差，提升理论可解释性。
Generalization Error of $f$-Divergence Stabilized Algorithms via Duality
- 利用对偶框架与变分法推导正则化解的归一化函数
- 在温和条件下显式刻画一般算法的泛化误差界
- 适用于需要理论保证的机器学习模型设计场景
将带f散度正则的经验风险最小化（ERM-$f$DR）解推广至约束优化问题，建立了其与约束条件等价的充要条件。提出ERM-$f$DR的对偶形式，借助Legendre-Fenchel变换和隐函数定理，实现了对ERM-$f$DR解归一化函数的高效计算。该对偶方法在较弱假设下，可显式表征一般算法的泛化误差，以及ERM-$f$DR解本身的泛化误差界。
原文摘要 · Abstract (English)
The solution to empirical risk minimization with $f$-divergence regularization (ERM-$f$DR) is extended to constrained optimization problems, establishing conditions for equivalence between the solution and constraints. A dual formulation of ERM-$f$DR is introduced, providing a computationally efficient method to derive the normalization function of the ERM-$f$DR solution. This dual approach leverages the Legendre-Fenchel transform and the implicit function theorem, enabling explicit characterizations of the generalization error for general algorithms under mild conditions, and another for ERM-$f$DR solutions.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。