论文标题
将非滑动解决方案与参数单调包容问题区分开
Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems
论文作者
论文摘要
我们利用路径可不同的性能和对非平滑隐式分化演算的最新结果，以提供足够的条件，以确保解决单调包含问题的解决方案将是可区分的，并具有计算其广义梯度的公式。我们结果的直接结果是这些解决方案几乎到处都是可区分的。我们的方法与自动差异完全兼容，并带有易于检查的假设，大概是：半gebraicity和强烈的单调性。我们通过考虑三个基本的综合问题设置来说明结果的范围：强烈凸出问题，凸出最小化问题的双重解决方案以及针对Min-Max问题的原始二重解决方案。
We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for computing its generalized gradient. A direct consequence of our result is that these solutions happen to be differentiable almost everywhere. Our approach is fully compatible with automatic differentiation and comes with assumptions which are easy to check, roughly speaking: semialgebraicity and strong monotonicity. We illustrate the scope of our results by considering three fundamental composite problem settings: strongly convex problems, dual solutions to convex minimization problems and primal-dual solutions to min-max problems.
