Computing simple mechanisms: Lift-and-round over marginal reduced forms

We study revenue maximization in multi-item multi-bidder auctions under the natural item-independence assumption – a classical problem in Multi-Dimensional Bayesian Mechanism Design. One of the biggest challenges in this area is developing algorithms to compute (approximately) optimal mechanisms that are not brute-force in the size of the bidder type space, which is usually exponential in the number of items in multi-item auctions. Unfortunately, such algorithms were only known for basic settings of our problem when bidders have unit-demand or additive valuations.