Stochastic Programming

Convergence of Trajectory Following Dynamic Programming algorithms for multistage stochastic problems without finite support assumptions

  • Maël Forcier
  • Vincent Leclère
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    We introduce a class of algorithms, called Trajectory Following Dynamic Programming (TFDP) algorithms, that iteratively refines approximation of cost-to-go functions of multistage stochastic problems with independent random variables. This framework encompasses most variants of the Stochastic Dual Dynamic Programming algorithm. Leveraging a Lipschitz assumption on the expected cost-to-go functions, we provide a new convergence and … Read more

    Dual solutions in convex stochastic optimization

  • Teemu Pennanen
  • Ari-Pekka Perkkiö
    • Categories Control Applications, Finance and Economics, Stochastic Programming Tags , , ,

    This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex space of random variables. It implies, in particular, the necessity of scenario-wise optimality conditions that are behind many fundamental … Read more

    Metrizing Fairness

  • Yves Rychener
  • Bahar Tașkesen
  • Daniel Kuhn
    • Categories Statistics, Stochastic Programming, Unconstrained Optimization Tags , , , , ,

    We study supervised learning problems for predicting properties of individuals who belong to one of two demographic groups, and we seek predictors that are fair according to statistical parity. This means that the distributions of the predictions within the two groups should be close with respect to the Kolmogorov distance, and fairness is achieved by … Read more

    Adjusted Distributionally Robust Bounds on Expected Loss Functions

  • Yasemin Merzifonluoğlu
  • Joseph Geunes
    • Categories Production and Logistics, Robust Optimization, Stochastic Programming Tags , , , ,

    Optimization problems in operations and finance often include a cost that is proportional to the expected amount by which a random variable exceeds some fixed quantity, known as the expected loss function. Representation of this function often leads to computational challenges, depending on the distribution of the random variable of interest. Moreover, in practice, a … Read more

    Neur2SP: Neural Two-stage Stochastic Programming

  • Justin Dumouchelle
  • Rahul Patel
  • Elias B. Khalil
  • Merve Bodur
    • Categories Stochastic Programming Tags , ,

    Stochastic programming is a powerful modeling framework for decision-making under uncertainty. In this work, we tackle two-stage stochastic programs (2SPs), the most widely applied and studied class of stochastic programming models. Solving 2SPs exactly requires evaluation of an expected value function that is computationally intractable. Additionally, having a mixed-integer linear program (MIP) or a nonlinear … Read more

    Conditional Distributionally Robust Functionals

  • Alexander Shapiro
  • Alois Pichler
    • Categories Stochastic Programming Tags , , , ,

    Risk measures incorporate a conservative or risk averse perspective in decisionmaking under uncertainty. Taking a variety of models for the potential outcomes into account, the distributionally robust decision is the most conservative decision among the decisions available. This paper investigates different versions of conditional risk measures and distributionally robust functionals in a multistage setting. The … Read more

    Monotonicity and Complexity of Multistage Stochastic Variational Inequalities

  • Jie Jiang
  • Hailin Sun
    • Categories Complementarity and Variational Inequalities, Stochastic Programming Tags , , ,

    In this paper, we consider multistage stochastic variational inequalities (MSVIs). First, we give multistage stochastic programs and multistage multi-player noncooperative game problems as source problems. After that, we derive the monotonicity properties of MSVIs under less restrictive conditions. Finally, the polynomial rate of convergence with respect to sample sizes between the original problem and its … Read more

    Robust Actionable Prescriptive Analytics

  • Li Chen
  • Melvyn Sim
  • Xun Zhang
  • Minglong Zhou
  • Long Zhao
    • Categories Linear Programming, Robust Optimization, Stochastic Programming Tags , , , , ,

    We propose a new robust actionable prescriptive analytics framework that leverages past data and side information to minimize a risk-based objective function under distributional ambiguity. Our framework aims to find a policy that directly transforms the side information into implementable decisions. Specifically, we focus on developing actionable response policies that offer the benefits of interpretability … Read more

    Online Non-parametric Estimation for Nonconvex Stochastic Programming

  • Shuotao Diao
  • Suvrajeet Sen
    • Categories Stochastic Programming Tags ,

    This paper presents a fusion of Stochastic Decomposition and the Majorization-Minimization algorithm (SD-MM) to solve a class of non-convex stochastic programs. The objective function is an expectation of a smooth concave function and a second-stage linear recourse function, which is common in stochastic programming (SP). This extension not only allows new stochastic difference-of-convex (dc) functions … Read more

    Capacity planning with uncertain endogenous technology learning

  • Tushar Rathi
  • Qi Zhang
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Optimal capacity expansion requires complex decision-making, often influenced by technology learning, which represents the reduction in expansion cost due to factors such as cumulative installed capacity. However, having perfect foresight over the technology cost reduction is highly unlikely. In this work, we develop a multistage stochastic programming framework to model capacity planning problems with endogenous … Read more