这篇论文解决了非线性策略分类的计算难题，用拉格朗日对偶和隐函数定理做出了实用算法，比线性方法更准，值得做对抗性机器学习的人看。
该论文提出一种利用拉格朗日对偶性近似策略分类中最佳响应的方法，将策略行为重构为约束优化问题，使得一阶优化方法可直接适用。在线性分类器上能复现封闭解，并自然扩展到非线性分类器。作者进一步结合隐函数定理，在分类器训练中计算损失的全梯度，从而将模型参数与策略行为直接关联。在多个常见机器学习数据集上，新方法训练出的模型显著提升了策略准确率（strategic accuracy）。
Non-Linear Strategic Classification Made Practical
Algorithmic developments in Strategic Classification have been mostly limited to linear classifiers in settings where the best response has a closed-form solution or can be easily approximated. While some work has explored the role of non-linear classifiers in strategic settings, progress in this direction is impeded by the computational intractability of the strategic behaviour. Addressing this, we present a novel method for approximating the best response by exploiting Lagrangian duality. By reformulating the strategic response as a constrained optimisation problem, we can construct a Lagrangian that is amenable to first order optimisation methods. This approach reproduces closed-form strategic behaviour in linear settings and can be straight-forwardly applied to non-linear settings. We show how the Implicit Function Theorem can be used in conjunction with our proposed response formulation during classifier learning to compute the total gradient of the loss. This connects the classifier parameters directly to the consequent strategic behaviour, yielding a novel training algorithm that can exploit this relationship. Experimental evaluation shows that the resulting models achieve improved strategic accuracy on common machine learning datasets.