  Iterative combinatorial auctions (CAs) are often used in multi-billion dollar
domains like spectrum auctions, and speed of convergence is one of the crucial
factors behind the choice of a specific design for practical applications. To
achieve fast convergence, current CAs require careful tuning of the price
update rule to balance convergence speed and allocative efficiency. Brero and
Lahaie (2018) recently introduced a Bayesian iterative auction design for
settings with single-minded bidders. The Bayesian approach allowed them to
incorporate prior knowledge into the price update algorithm, reducing the
number of rounds to convergence with minimal parameter tuning. In this paper,
we generalize their work to settings with no restrictions on bidder valuations.
We introduce a new Bayesian CA design for this general setting which uses Monte
Carlo Expectation Maximization to update prices at each round of the auction.
We evaluate our approach via simulations on CATS instances. Our results show
that our Bayesian CA outperforms even a highly optimized benchmark in terms of
clearing percentage and convergence speed.
