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.

翻译：许多重要的资源分配问题涉及物品的组合分配，例如拍卖或课程分配。由于组合空间随物品数量呈指数增长，偏好 elicitation 是这些领域的关键挑战。近期，研究人员提出了基于机器学习的机制，这些机制在降低代理偏好 elicitation 成本的同时，优于传统机制。然而，所用机器学习算法的一个主要缺点是忽略了关于代理偏好的重要先验知识。为解决此问题，我们引入了单调值神经网络（MVNNs），其设计目标是在捕获组合估值的同时，强制满足单调性和正则性。在技术层面，我们证明了MVNNs在单调且归一化的值函数类中具有普适性，并提出了一种混合整数线性规划（MILP）公式，使基于MVNN的胜者决定问题（WDPs）在实践上可解。我们在频谱拍卖领域通过实验评估了MVNNs。结果表明，MVNNs提升了预测性能，在拍卖中实现了最先进的配置效率，并减少了WDPs的运行时间。我们的代码可在GitHub获取：https://github.com/marketdesignresearch/MVNN。