Mode Connectivity in Auction Design
This provides theoretical support for using neural networks in differentiable economics, addressing a fundamental challenge in algorithmic game theory, though it is incremental as it extends known concepts to a new context.
The paper tackles the problem of theoretically justifying the empirical success of neural networks in learning optimal auction mechanisms by proving that RochetNet and its generalization satisfy mode connectivity, meaning locally optimal solutions are connected by a path with minimal loss in performance.
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.