Peyman Mohajerin Esfahani

From Infinite to Finite Programs: Explicit Error Bounds with Applications to Approximate Dynamic Programming

  • Daniel Kuhn
  • Tobias Sutter
  • John Lygeros
  • Peyman Mohajerin Esfahani
    • Categories Dynamic Programming, Infinite Dimensional Optimization, Stochastic Programming Tags , , , ,

    We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite convex programs in which the performance of the approximation is quantified explicitly. To this end, we adopt the recent developments in two areas of … Read more

    Data-Driven Inverse Optimization with Imperfect Information

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Soroosh Shafieezadeh-Abadeh
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming Tags , ,

    In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent’s objective function that best explains a historical sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect … Read more

    Distributionally Robust Logistic Regression

  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Soroosh Shafieezadeh-Abadeh
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high … Read more

    Data-Driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
    • Categories Robust Optimization, Stochastic Programming Tags ,

    We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of … Read more