Deep Learning for Revenue-Optimal Auctions with Budgets

The design of revenue-maximizing auctions for settings with private budgets is a hard task. Even the single-item case is not fully understood, and there are no analytical results for optimal, dominantstrategy incentive compatible, two-item auctions. In this work, we model the rules of an auction as a neural network, and use machine learning for the automated design of optimal auctions. We extend the RegretNet framework (Dütting et al. '17) to handle private budget constraints, as well as Bayesian incentive compatibility. We discover new auctions with high revenue for multi-unit auctions with private budgets, including problems with unit-demand bidders. For benchmarking purposes, we also demonstrate that RegretNet can obtain essentially optimal designs for simpler settings where analytical solutions are available [12, 24, 29].