discrete choice models

Mitigating Choice Model Ambiguity: A General Framework and its Application to Assortment Optimization

  • Oyku Naz Attila
  • Sanjay Dominik Jena
  • Walter Rei
    • Categories Optimization in Data Science, Robust Optimization, Stochastic Programming Tags , , ,

    In several application domains, discrete choice models have become a popular tool to accurately predict complex choice behavior within the classical predict-then-optimize paradigm. Due to a variety of possible error sources, however, estimated choice models may be subject to ambiguity, which may induce different optimal decisions of highly varying quality. While previous studies focused on … Read more

    Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution

  • Bahar TaČ™kesen
  • Soroosh Shafieezadeh-Abadeh
  • Daniel Kuhn
    • Categories Convex and Nonsmooth Optimization, Robust Optimization, Stochastic Programming Tags , , , , , ,

    Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, machine learning and computer vision, however, this perception has not yet received a theoretical justification. To fill this gap, we prove that … Read more

    Assortment Optimization under Heteroscedastic Data

  • Selin Damla Ahipasaoglu
  • Zeyu Sun
    • Categories Applications - OR and Management Sciences Tags , , , ,

    We study assortment problems under the Marginal Exponential Model (MEM) with deterministic demand. We show that optimal solutions to such assortment problems can be efficiently determined under some mild conditions, and provide a simple approach that finds near optimal solutions when these conditions fail. Furthermore, we improve the existing MEM parameter estimation method given by … Read more

    A Persistency Model and Its Applications in Choice Modeling

  • Song Miao
  • Karthik Natarajan
  • Chung-Piaw Teo
    • Categories (Mixed) Integer Linear Programming Tags ,

    Given a discrete optimization problem $Z(\mb{\tilde{c}})=\max\{\mb{\tilde{c}}’\mb{x}:\mb{x}\in \mathcal{X}\}$, with objective coefficients $\mb{\tilde{c}}$ chosen randomly from a distribution ${\mathcal{\theta}}$, we would like to evaluate the expected value $E_\theta(Z(\mb{\tilde{c}}))$ and the probability $P_{\mathcal{\theta}}(x^*_i(\mb{\tilde{c}})=k)$ where $x^*(\mb{\tilde{c}})$ is an optimal solution to $Z(\mb{\tilde{c}})$. We call this the persistency problem for a discrete optimization problem under uncertain objective, and $P_{\mathcal{\theta}}(x^*_i(\mb{\tilde{c}})=k)$, the … Read more