  Many important resource allocation problems involve the combinatorial
assignment of items, e.g., auctions or course allocation. Because the bundle
space grows exponentially in the number of items, preference elicitation is a
key challenge in these domains. Recently, researchers have proposed ML-based
mechanisms that outperform traditional mechanisms while reducing preference
elicitation costs for agents. However, one major shortcoming of the ML
algorithms that were used is their disregard of important prior knowledge about
agents' preferences. To address this, we introduce monotone-value neural
networks (MVNNs), which are designed to capture combinatorial valuations, while
enforcing monotonicity and normality. On a technical level, we prove that our
MVNNs are universal in the class of monotone and normalized value functions,
and we provide a mixed-integer linear program (MILP) formulation to make
solving MVNN-based winner determination problems (WDPs) practically feasible.
We evaluate our MVNNs experimentally in spectrum auction domains. Our results
show that MVNNs improve the prediction performance, they yield state-of-the-art
allocative efficiency in the auction, and they also reduce the run-time of the
WDPs. Our code is available on GitHub:
https://github.com/marketdesignresearch/MVNN.
