Optimal Auctions through Deep Learning

Designing an auction that maximizes expected revenue is an intricate task. Indeed, as of today--despite major efforts and impressive progress over the past few years--only the single-item case is fully understood. In this work, we initiate the exploration of the use of tools from deep learning on this topic. The design objective is revenue optimal, dominant-strategy incentive compatible auctions. We show that multi-layer neural networks can learn almost-optimal auctions for settings for which there are analytical solutions, such as Myerson's auction for a single item, Manelli and Vincent's mechanism for a single bidder with additive preferences over two items, or Yao's auction for two additive bidders with binary support distributions and multiple items, even if no prior knowledge about the form of optimal auctions is encoded in the network and the only feedback during training is revenue and regret. We further show how characterization results, even rather implicit ones such as Rochet's characterization through induced utilities and their gradients, can be leveraged to obtain more precise fits to the optimal design. We conclude by demonstrating the potential of deep learning for deriving optimal auctions with high revenue for poorly understood problems.