We address Stackelberg models of combinatorial congestion games (CCGs); we aim to optimize the parameters of CCGs so that the selfish behavior of non-atomic players attains desirable equilibria. This model is essential for designing such social infrastructures as traffic and communication networks. Nevertheless, computational approaches to the model have not been thoroughly studied due to two difficulties: (I) bilevel-programming structures and (II) the combinatorial nature of CCGs. We tackle them by carefully combining (I) the idea of \textit{differentiable} optimization and (II) data structures called \textit{zero-suppressed binary decision diagrams} (ZDDs), which can compactly represent sets of combinatorial strategies. Our algorithm numerically approximates the equilibria of CCGs, which we can differentiate with respect to parameters of CCGs by automatic differentiation. With the resulting derivatives, we can apply gradient-based methods to Stackelberg models of CCGs. Our method is tailored to induce Nesterov's acceleration and can fully utilize the empirical compactness of ZDDs. These technical advantages enable us to deal with CCGs with a vast number of combinatorial strategies. Experiments on real-world network design instances demonstrate the practicality of our method.

翻译：我们处理Stackelberg 组合式拥堵游戏模式(CCGs);我们的目标是优化 CCCG的参数,使非原子玩家的自私行为达到理想的平衡。这个模型对于设计交通和通信网络等社会基础设施至关重要。然而,由于两个困难,尚未彻底研究模型的计算方法:(一) 双级程序结构,和(二) 组合式热门游戏的组合性质。我们通过仔细结合(一)\textit{可区别}优化和(二) 数据结构,称为\textit{零压压二进制决定图表}(ZDDs),可以紧紧地代表组合式战略。我们的算法在数字上接近了CCGs的平衡性,我们可以通过自动区分CCGs的参数。我们用衍生物,可以将基于梯度的方法应用于Stackelberg的CCGs模型。我们的方法是用来引导Nesterov的加速度,并且能够充分利用CCDD的庞大的实验性网络设计方法。这些方法可以使我们在实际的网络上展示实际的C-BRADDDs的优势。