Optimal auction design is a fundamental problem in algorithmic game theory.

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.

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981. Even after 30–40 years of intense research, the problem remains unsolved for settings with two or more items. We overview recent research results that show how tools from deep learning are shaping up to become a powerful tool for the automated design of near-optimal auctions auctions. In this approach, an auction is modeled as a multilayer neural network, with optimal auction design framed as a constrained learning problem that can be addressed with standard machine learning pipelines. Through this approach, it is possible to recover to a high degree of accuracy essentially all known analytically derived solutions for multi-item settings and obtain novel mechanisms for settings in which the optimal mechanism is unknown. Optimal auction design is one of the cornerstones of economic theory. It is of great practical importance, as auctions are used across industries and by the public sector to organize the sale of their products and services. Concrete examples are the US FCC Incentive Auction, the sponsored search auctions conducted by web search engines such as Google, and the auctions run on platforms such as eBay. In the standard independent private valuations model, each bidder has a valuation function over subsets of items, drawn independently from not necessarily identical distributions.