  A recent approach to automated mechanism design, differentiable economics,
represents auctions by rich function approximators and optimizes their
performance by gradient descent. The ideal auction architecture for
differentiable economics would be perfectly strategyproof, support multiple
bidders and items, and be rich enough to represent the optimal (i.e.
revenue-maximizing) mechanism. So far, such an architecture does not exist.
There are single-bidder approaches (MenuNet, RochetNet) which are always
strategyproof and can represent optimal mechanisms. RegretNet is multi-bidder
and can approximate any mechanism, but is only approximately strategyproof. We
present an architecture that supports multiple bidders and is perfectly
strategyproof, but cannot necessarily represent the optimal mechanism. This
architecture is the classic affine maximizer auction (AMA), modified to offer
lotteries. By using the gradient-based optimization tools of differentiable
economics, we can now train lottery AMAs, competing with or outperforming prior
approaches in revenue.
