Title: Credible, Sealed-bid, Optimal Repeated Auctions With Differentiable Economics. Abstract: Online advertisement auctions happen billions of times per day.  Bidders in auctions strategize to improve their own utility, subject to published auctions' rules.  Yet, bidders may not know that an auction has been run as promised.  A credible auction is one in which bidders can trust the auctioneer to run its allocation and pricing mechanisms as promised.  It is known that, assuming no communication between bidders, no credible, sealed-bid, and incentive compatible (aka ``truth-telling'' or otherwise truthful-participation-incentivizing) mechanism can exist. In reality, bidders can certainly communicate, so what happens if we relax this (typically unrealistic) constraint? 

In this work, we propose a framework incorporating cryptography to allow computationally-efficient, credible, revenue-maximizing (aka ``optimal'') auctions in a repeated auction setting. Our contribution is two-fold: first, we introduce a protocol for running repeated auctions with a verification scheme, and we show such a protocol can eliminate the auctioneer's incentive to deviate while costing negligible additional computation. Secondly, we provide a method for training optimal auctions under uncertain bidder participation profiles, which generalizes our protocol to a much wider class of auctions in the online ad market. Our empirical results show strong support for both the theory and competency of the proposed method. 