IEDA Seminar - Learning Mixed Multinomial Logits with Provable Guarantees and its Applications in Multi-product Pricing
A mixture of multinomial logits (MMNL) generalizes the multinomial logit model, which is commonly used in modeling market demand to capture consumer heterogeneity. While 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 component-specific 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 multi-product pricing problems. We propose a piece-wise linear approximation (PLA) pricing policy based on the estimated MMNL and establish the bound of the optimality gap for the obtained pricing solution. Numerical studies are conducted to evaluate the performance of the proposed algorithms.
Dr. Zhenzhen Yan is an assistant professor at School of Physical and Mathematical Sciences, Nanyang Technological University. She joined SPMS since 2018. Before that, she received her PhD in Management Science from the National University of Singapore, and her BSc and MSc in Management Science, Operations Research from the National University of Defense and Technology in China. Her research interests mainly focus on the interplay between optimization and data analytics. Her first line of research is to solve various operations management problems and engineering problems from the distrbibutionally robust perspective, including supply chain design and operations, and healthcare operations. The second line is to develop data-driven optimization approaches with applications to e-commerce operations and resource allocation. Her work has been published in leading operations management journals including Management Science, Operations Research, MSOM and POMS, and top AI conferences including Neurips, UAI and AAAI. Her work has received media coverage in various outlets including the Straits Times and ScienceDaily etc. She currently serves as an Associate Editor of Decision Sciences.