Will Ma

Strong mixed-integer programming formulations for trained neural networks

  • Ross Anderson
  • Joey Huchette
  • Juan Pablo Vielma
  • Will Ma
  • Christian Tjandraatmadja
    • Categories (Mixed) Integer Linear Programming, Statistics Tags , ,

    We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying that an image classification network is robust to adversarial inputs, or solving decision problems where the objective function is a machine learning model. … Read more

    Distributionally Robust Linear and Discrete Optimization with Marginals

  • Louis Chen
  • Karthik Natarajan
  • David Simchi-Levi
  • Will Ma
  • Zhenzhen Yan
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Polyhedra Tags , ,

    In this paper, we study the class of linear and discrete optimization problems in which the objective coefficients are chosen randomly from a distribution, and the goal is to evaluate robust bounds on the expected optimal value as well as the marginal distribution of the optimal solution. The set of joint distributions is assumed to … Read more