  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.
