discrete choice models

Optimism in the Face of Ambiguity Principle for Multi-Armed Bandits

  • Mengmeng Li
  • Daniel Kuhn
  • Bahar TaČ™kesen
    • Categories Convex Optimization, Data Science Algorithms, Data Science Applications Tags , ,

    \(\) Follow-The-Regularized-Leader (FTRL) algorithms often enjoy optimal regret for adversarial as well as stochastic bandit problems and allow for a streamlined analysis. However, FTRL algorithms require the solution of an optimization problem in every iteration and are thus computationally challenging. In contrast, Follow-The-Perturbed-Leader (FTPL) algorithms achieve computational efficiency by perturbing the estimates of the rewards … 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

    A Unified Analysis for Assortment Planning with Marginal Distributions

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

    In this paper, we study assortment planning under the marginal distribution model (MDM), a semiparametric choice model that only requires information about the marginal noise in the utilities of alternatives and does not assume independence of the noise terms. It is already known in the literature that the multinomial logit (MNL) model belongs to the … 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