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, dominant-strategy incentive compatibile, two-item auctions. In this work, we model a mechanism as a neural network, and use machine learning for the automated design of optimal auctions. We extend the \em RegretNet framework~\citedeep-auction to handle private budget constraints and Bayesian incentive compatibility. We discover new auctions with very close approximations to incentive-compatibility and high revenue for multi-unit auctions with private budgets, including problems with unit-demand bidders. For benchmarking purposes, we also illustrate that \em RegretNet can obtain essentially optimal designs for simpler settings where analytical solutions are available~\citeCHE2000,Malakhov2008,PAI2014.

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