Optimal auction design is a fundamental problem in algorithmic game theory. This problem is notoriously difficult already in very simple settings. Recent work in differentiable economics showed that neural networks can efficiently learn known optimal auction mechanisms and discover interesting new ones. In an attempt to theoretically justify their empirical success, we focus on one of the first such networks, RochetNet, and a generalized version for affine maximizer auctions. We prove that they satisfy mode connectivity, i.e., locally optimal solutions are connected by a simple, piecewise linear path such that every solution on the path is almost as good as one of the two local optima. Mode connectivity has been recently investigated as an intriguing empirical and theoretically justifiable property of neural networks used for prediction problems. Our results give the first such analysis in the context of differentiable economics, where neural networks are used directly for solving non-convex optimization problems.

翻译：最优拍卖设计是算法博弈论中的基本问题。即使在非常简单的情景中，这一问题也因难以处理而著称。差异经济学的最新研究表明，神经网络可以高效学习已知的最优拍卖机制，并发现有趣的新机制。为了从理论上解释其经验成功，我们聚焦于最早出现的此类网络之一——RochetNet，以及针对仿射最大化者拍卖的通用版本。我们证明它们满足模态连通性，即局部最优解由一条简单的分段线性路径连接，使得路径上的每个解的性能几乎与两个局部最优解之一相当。模态连通性近年来已被研究为预测问题中神经网络的一种引人入胜的经验和理论可证性质。我们的结果首次在差异经济学背景下开展此类分析，其中神经网络被直接用于解决非凸优化问题。