Mode Connectivity in Auction Design

TL;DR

This paper proves that neural networks used for auction design, specifically RochetNet, exhibit mode connectivity, meaning locally optimal solutions are connected by a path of near-optimal solutions, providing theoretical insight into their empirical success.

Contribution

It provides the first theoretical analysis of mode connectivity in neural networks applied to differentiable economics and auction design.

Findings

Neural networks for auction design satisfy mode connectivity.

Locally optimal solutions are connected by a near-optimal path.

First theoretical justification of mode connectivity in this context.

Abstract

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.