Monotone-Value Neural Networks: Exploiting Preference Monotonicity in Combinatorial Assignment

Abstract

Many important resource allocation problems involve the combinatorial assignment of items (e.g., combinatorial auctions, combinatorial exchanges, and combinatorial course allocation). Because the bundle space grows exponentially in the number of items, preference elicitation is a key challenge in these domains, in particular because agents may view items as substitutes or complements. Recently, researchers have proposed machine learning (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 that they ignore important prior knowledge about agents' preferences. To address this, we introduce monotone-value neural networks (MVNNs), which are carefully designed to capture combinatorial valuations, while enforcing monotonicity (i.e., adding an item to a bundle weakly increases its value) and normality (i.e., the empty bundle has zero value). On a technical level, we make two main contributions. First, we prove that our MVNNs are universal in the class of monotone and normalized value functions; second, we provide a mixed-integer program (MIP) formulation to make solving MVNN-based winner determination problems practically feasible. We evaluate our MVNNs experimentally in spectrum auction domains. Our results show that MVNNs improve the prediction performance when learning agents' value functions, they improve the allocative efficiency of the auction, and they also reduce the run-time of the winner determination problem.