提出可统一逼近广义凸函数及其梯度的可微层，简化优化问题求解。
Universal Representation of Generalized Convex Functions and their Gradients
- 设计具有凸参数空间的可微层，实现对广义凸函数的通用逼近。
- 理论证明该层及其梯度能逼近任意广义凸函数及其梯度。
- 应用于最优传输与多商品拍卖，将复杂双层问题转为高效单层优化。
大量优化问题可表述为广义凸函数（GCFs）形式。当此类结构存在时，可将某些嵌套的双层目标转化为适合标准一阶优化方法的单层问题。本文提出一种具有凸参数空间的新可微层，并证明（定理5.1和5.2）该层及其梯度是广义凸函数及其梯度的通用逼近器。我们展示了该参数化在实际中的应用：(i) 使用一般代价函数学习最优传输映射；(ii) 学习多商品最优拍卖。在这两种情形中，均表明该层可将原有的双层或极小极大公式转化为可通过一阶方法高效求解的单层问题。
原文摘要 · Abstract (English)
A wide range of optimization problems can often be written in terms of generalized convex functions (GCFs). When this structure is present, it can convert certain nested bilevel objectives into single-level problems amenable to standard first-order optimization methods. We provide a new differentiable layer with a convex parameter space and show (Theorems 5.1 and 5.2) that it and its gradient are universal approximators for GCFs and their gradients. We demonstrate how this parameterization can be leveraged in practice by (i) learning optimal transport maps with general cost functions and (ii) learning optimal auctions of multiple goods. In both these cases, we show how our layer can be used to convert the existing bilevel or min-max formulations into single-level problems that can be solved efficiently with first-order methods.
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