Models of choice are a fundamental input to many now-canonical optimization problems in the field of Operations Management, including assortment, inventory, and price optimization. Naturally, accurate estimation of these models from data is a critical step in the application of these optimization problems in practice. Concurrently, recent advancements in deep learning have sparked interest in integrating these techniques into choice modeling. However, there is a noticeable research gap at the intersection of deep learning and choice modeling, particularly with both theoretical and empirical foundations. Thus motivated, we first propose a choice model that is the first to successfully (both theoretically and practically) leverage a modern neural network architectural concept (self-attention). Theoretically, we show that our attention-based choice model is a low-rank generalization of the Halo Multinomial Logit (Halo-MNL) model. We prove that whereas the Halo-MNL requires $\Omega(m^2)$ data samples to estimate, where $m$ is the number of products, our model supports a natural nonconvex estimator (in particular, that which a standard neural network implementation would apply) which admits a near-optimal stationary point with $O(m)$ samples. Additionally, we establish the first realistic-scale benchmark for choice model estimation on real data, conducting the most extensive evaluation of existing models to date, thereby highlighting our model's superior performance.

翻译：选择模型是运营管理领域中许多经典优化问题（包括品类规划、库存管理和价格优化）的基础输入。自然，从数据中准确估计这些模型是实践中应用这些优化问题的关键步骤。与此同时，深度学习的最新进展激发了将这些技术整合到选择建模中的兴趣。然而，在深度学习与选择建模的交叉领域存在显著的研究空白，尤其是在理论和实证基础方面。基于此，我们首先提出一种选择模型，该模型是首个成功（在理论和实践上）利用现代神经网络架构概念（自注意力）的模型。理论上，我们证明了基于注意力的选择模型是光环多项Logit（Halo-MNL）模型的低秩泛化。我们证明，Halo-MNL需要Ω(m²)个数据样本来估计（其中m为产品数量），而我们的模型支持一种自然的非凸估计器（即标准神经网络实现将采用的类型），该估计器在O(m)个样本下即可达到近最优的驻点。此外，我们建立了首个基于真实数据的选择模型估计的实际规模基准，对现有模型进行了迄今为止最广泛的评估，从而凸显了我们模型的卓越性能。