data-driven optimization

PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming

  • Bo Tang
  • Elias B. Khalil
    • Categories Optimization Software and Modeling Systems Tags , ,

    In deterministic optimization, it is typically assumed that all parameters of the problem are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from historical data. A typical predict-then-optimize approach separates predictions and optimization into two stages. Recently, end-to-end predict-then-optimize has become an attractive alternative. In this … Read more

    Vessel Deployment with Limited Information: Distributionally Robust Chance Constrained Models

  • Yue Zhao
  • Zhi Chen
  • Andrew Lim
  • Zhenzhen Zhang
    • Categories Robust Optimization, Transportation Tags , , , , ,

    This paper studies the fundamental vessel deployment problem in the liner shipping industry, which decides the numbers of mixed-type ships and their sailing frequencies on fixed routes to provide sufficient vessel capacity for fulfilling stochastic shipping demands with high probability. In reality, it is usually difficult (if not impossible) to acquire a precise joint distribution … Read more

    On Linear Optimization over Wasserstein Balls

  • Daniel Kuhn
  • Wolfram Wiesemann
  • Man-Chung Yue
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under … Read more

    From Data to Decisions: Distributionally Robust Optimization is Optimal

  • Daniel Kuhn
  • Bart Paul Gerard Van Parys
  • Peyman Mohajerin Esfahani
    • Categories Robust Optimization, Second-Order Cone Programming, Stochastic Programming Tags , , , , ,

    We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a procedure that transforms the data to an estimate of the expected cost function under the unknown data-generating distribution, … Read more

    Data-Driven Optimization of Reward-Risk Ratio Measures

  • Ran Ji
  • Miguel A. Lejeune
    • Categories Finance and Economics, Stochastic Programming Tags , , , , ,

    We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a … Read more

    Data-Driven Optimization of Reward-Risk Ratio Measures

  • Ran Ji
    • Categories Finance and Economics, Stochastic Programming Tags , , , , ,

    We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a … Read more

    Phi-Divergence Constrained Ambiguous Stochastic Programs for Data-Driven Optimization

  • Güzin Bayraksan
  • David Love
    • Categories Stochastic Programming Tags , , ,

    This paper investigates the use of phi-divergences in ambiguous (or distributionally robust) two-stage stochastic programs. Classical stochastic programming assumes the distribution of uncertain parameters are known. However, the true distribution is unknown in many applications. Especially in cases where there is little data or not much trust in the data, an ambiguity set of distributions … 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

    Near-Optimal Ambiguity sets for Distributionally Robust Optimization

  • Vishal Gupta
    • Categories Robust Optimization, Statistics Tags , ,

    We propose a novel, Bayesian framework for assessing the relative strengths of data-driven ambiguity sets in distributionally robust optimization (DRO). The key idea is to measure the relative size between a candidate ambiguity set and an \emph{asymptotically optimal} set as the amount of data grows large. This asymptotically optimal set is provably the smallest convex … 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