Mode Connectivity in Auction Design

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; that is, 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 nonconvex optimization problems. Funding: All three authors gratefully acknowledge support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program [Grant ScaleOpt–757481 (all three authors); Grant ForEFront–615640 (C. Hertrich)]. Y. Tao is partially supported by the National Key R&D Program of China [Grant 2023YFA1009500].