Stochastic Programming

A Unifying Framework for the Capacitated Vehicle Routing Problem under Risk and Ambiguity

  • Shubhechyya Ghosal
  • Chin Pang Ho
  • Wolfram Wiesemann
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , ,

    We propose a generic model for the capacitated vehicle routing problem (CVRP) under demand uncertainty. By combining risk measures, satisficing measures or disutility functions with complete or partial characterizations of the probability distribution governing the demands, our formulation bridges the popular but often independently studied paradigms of stochastic programming and distributionally robust optimization. We characterize … Read more

    Statistical Inference of Contextual Stochastic Optimization with Endogenous Uncertainty

  • Junyu Cao
  • Rui Gao
    • Categories Robust Optimization, Statistics, Stochastic Programming Tags

    This paper considers contextual stochastic optimization with endogenous uncertainty, where random outcomes depend on both contextual information and decisions. We analyze the statistical properties of solutions from two prominent approaches: predict-then-optimize (PTO), which first predicts a model between outcomes, contexts, and decisions, and then optimizes the downstream objective; and estimate- then-optimize (ETO), which directly estimates … Read more

    Robust CARA Optimization

  • Li Chen
  • Melvyn Sim
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , ,

    We propose robust optimization models and their tractable approximations that cater for ambiguity-averse decision makers whose underlying risk preferences are consistent with constant absolute risk aversion (CARA). Specifically, we focus on maximizing the worst-case expected exponential utility where the underlying uncertainty is generated from a set of stochastically independent factors with ambiguous marginals. To obtain … Read more

    Inexact bilevel stochastic gradient methods for constrained and unconstrained lower-level problems

  • Tommaso Giovannelli
  • Griffin D. Kent
  • Luis Nunes Vicente
    • Categories Data-Mining, Nonlinear Optimization, Stochastic Programming Tags , , ,

    Two-level stochastic optimization formulations have become instrumental in a number ofmachine learning contexts such as continual learning, neural architecture search, adversariallearning, and hyperparameter tuning. Practical stochastic bilevel optimization problemsbecome challenging in optimization or learning scenarios where the number of variables ishigh or there are constraints. In this paper, we introduce a bilevel stochastic gradient method … Read more

    Confidence Interval Software for Multi-stage Stochastic Programs

  • Xiaotie Chen
  • Sylvain Cazaux
  • Brian Knight
  • David L. Woodruff
    • Categories Stochastic Programming Tags , ,

    When the uncertainty is explicitly modeled in an optimization problem, it is often necessary to use samples to compute a solution, which gives rise to a need to compute confidence intervals around the objective function value that is obtained. In this paper we describe software that implements well-known methods for two stage problems and we … Read more

    Adaptive Sampling Quasi-Newton Methods for Zeroth-Order Stochastic Optimization

  • Raghu Bollapragada
  • Stefan M. Wild
    • Categories Convex Optimization, Nonlinear Optimization, Stochastic Programming Tags , ,

    We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic function using finite differences within a common random number framework. We develop modified versions of a norm … Read more

    Sinkhorn Distributionally Robust Optimization

  • Jie Wang
  • Rui Gao
  • Yao Xie
    • Categories Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming

    We study distributionally robust optimization (DRO) with Sinkhorn distance—a variant of Wasserstein distance based on entropic regularization. We derive convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. Compared with Wasserstein DRO, our proposed approach offers enhanced computational tractability for a broader class of loss functions, and the worst-case distribution exhibits … Read more

    Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance

  • Hamed Rahimian
  • Güzin Bayraksan
  • Tito Homem-de-Mello
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    We study multistage distributionally robust optimization (DRO) to hedge against ambiguity in quantifying the underlying uncertainty of a problem. Recognizing that not all the realizations and scenario paths might have an “effect” on the optimal value, we investigate the question of how to define and identify critical scenarios for nested multistage DRO problems. Our analysis … Read more

    Stochastic Scheduling of Chemotherapy Appointments Considering Patient Acuity Levels

  • Melih Celik
  • Serhat Gul
  • Sirma Karakaya
    • Categories Applications - OR and Management Sciences, Scheduling, Stochastic Programming Tags , ,

    The uncertainty in infusion durations and non-homogeneous care level needs of patients are the critical factors that lead to difficulties in chemotherapy scheduling. We study the problem of scheduling patient appointments and assigning patients to nurses under uncertainty in infusion durations for a given day. We consider instantaneous nurse workload, represented in terms of total … Read more

    Data-Driven Distributionally Preference Robust Optimization Models Based on Random Utility Representation in Multi-Attribute Decision Making

  • Jian Hu
  • Huifu Xu
  • Dali Zhang
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Preference robust optimization (PRO) has recently been studied to deal with utility based decision making problems under ambiguity in the characterization of the decision maker’s (DM) preference. In this paper, we propose a novel PRO modeling paradigm which combines the stochastic utility theory with distributionally robust optimization technique. Based on the stochastic utility theory, our … Read more