  Optimal auctions maximize a seller's expected revenue subject to individual
rationality and strategyproofness for the buyers. Myerson's seminal work in
1981 settled the case of auctioning a single item; however, subsequent decades
of work have yielded little progress moving beyond a single item, leaving the
design of revenue-maximizing auctions as a central open problem in the field of
mechanism design. A recent thread of work in "differentiable economics" has
used tools from modern deep learning to instead learn good mechanisms. We focus
on the RegretNet architecture, which can represent auctions with arbitrary
numbers of items and participants; it is trained to be empirically
strategyproof, but the property is never exactly verified leaving potential
loopholes for market participants to exploit. We propose ways to explicitly
verify strategyproofness under a particular valuation profile using techniques
from the neural network verification literature. Doing so requires making
several modifications to the RegretNet architecture in order to represent it
exactly in an integer program. We train our network and produce certificates in
several settings, including settings for which the optimal strategyproof
mechanism is not known.
