Learning Mixed Multinomial Logits with Provable Guarantees and Its Applications in Multiproduct Pricing

• 成果类型: Article; Early Access
• 署名作者: Hu, Yiqun; Liu, Limeng; Simchi-Levi, David; Yan, Zhenzhen
• 署名单位: Nanyang Technological University; Massachusetts Institute of Technology (MIT)
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2022.03792
• 发表日期: 2025
• 关键词: estimation of MMNL; provable convergence guarantees; sample complexity analysis; pricing with MMNL

摘要

A mixture of multinomial logits (mixed multinomial logit (MMNL)) generalizes the multinomial logit model, which is commonly used in modeling market demand to capture consumer heterogeneity. Although extensive algorithms have been developed in the literature to learn MMNL models, theoretical results are limited. Built on the Frank-Wolfe (FW) method, we propose a new algorithm that learns both mixture weights and componentspecific logit parameters with provable convergence guarantees for an arbitrary number of mixtures. Our algorithm utilizes historical choice data to generate a set of candidate choice probability vectors, each being close to the ground truth with a high probability. We further provide a sample complexity analysis to show that only a polynomial number of samples is required to secure the performance guarantee of our algorithm. Finally, we apply the learned MMNL to data-driven multiproduct pricing problems and quantify how the estimation errors affect the pricing optimality under our proposed data-driven pricing framework Numerical studies are conducted to evaluate the performance of the proposed algorithms.