stochastic optimization

On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems

  • Welington de Oliveira
  • Yongjia Song
  • Wim van Ackooij
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , , ,

    We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing iterates during the solution process. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. Numerical experiments on a hydrothermal scheduling … Read more

    Statistical inference and hypotheses testing of risk averse stochastic programs

  • Vincent Guigues
  • Alexander Shapiro
  • Volker Krätschmer
    • Categories Stochastic Programming Tags , , , , ,

    We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value when the stochastic program is expressed in terms of a law invariant coherent risk measure having a discrete Kusuoka representation. The obtained results … Read more

    Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization

  • Donald Goldfarb
  • Wei Liu
  • Shiqian Ma
  • Xiao Wang
    • Categories Nonlinear Optimization Tags , , , , ,

    In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle ($\SFO$). We propose a general framework for such methods, for which we prove almost sure convergence to stationary points and analyze its worst-case … Read more

    Algorithms for stochastic optimization with expectation constraints

  • Guanghui Lan
  • Zhiqiang Zhou
    • Categories Bound-constrained Optimization, Convex and Nonsmooth Optimization, Stochastic Programming Tags , , , ,

    This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with an expectation constraint on either decision variables or problem parameters. We first present a new stochastic approximation (SA) type algorithm, namely the cooperative SA (CSA), to handle problems with the expectation constraint on devision variables. We show that … Read more

    Statistical inference and hypotheses testing of risk averse stochastic programs

  • Vincent Guigues
  • Alexander Shapiro
  • Volker Krätschmer
    • Categories Statistics, Stochastic Programming Tags , , , , ,

    We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions when the stochastic program is expressed in terms of a law invariant coherent risk measure. The obtained results are applied … Read more

    An empirical analysis of scenario generation methods for stochastic optimization

  • Nils Löhndorf
    • Categories Stochastic Programming Tags , , , , , , ,

    This work presents an empirical analysis of popular scenario generation methods for stochastic optimization, including quasi-Monte Carlo, moment matching, and methods based on probability metrics, as well as a new method referred to as Voronoi cell sampling. Solution quality is assessed by measuring the error that arises from using scenarios to solve a multi-dimensional newsvendor … Read more

    Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

  • Vincent Guigues
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , ,

    We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic … Read more

    Nonstationary Direct Policy Search for Risk-Averse Stochastic Optimization

  • Belgacem Bouzaiene-Ayari
  • Somayeh Moazeni
  • Boris Defourny
  • Warren B. Powell
    • Categories Dynamic Programming, Parallel Algorithms, Stochastic Programming Tags , ,

    This paper presents an approach to non-stationary policy search for finite-horizon, discrete-time Markovian decision problems with large state spaces, constrained action sets, and a risk-sensitive optimality criterion. The methodology relies on modeling time variant policy parameters by a non-parametric response surface model for an indirect parametrized policy motivated by the Bellman equation. Through the interpolating … Read more

    The Value of Stochastic Programming in Day-Ahead and Intraday Generation Unit Commitment

  • Kenneth McKinnon
  • Tim Schulze
    • Categories Scheduling, Stochastic Programming Tags , , ,

    The recent expansion of renewable energy supplies has prompted the development of a variety of efficient stochastic optimization models and solution techniques for hydro-thermal scheduling. However, little has been published about the added value of stochastic models over deterministic ones. In the context of day-ahead and intraday unit commitment under wind uncertainty, we compare two-stage … Read more

    An Asynchronous Mini-Batch Algorithm for Regularized Stochastic Optimization

  • Arda Aytekin
  • Hamid Reza Feyzmahdavian
  • Mikael Johansson
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

    Mini-batch optimization has proven to be a powerful paradigm for large-scale learning. However, the state of the art parallel mini-batch algorithms assume synchronous operation or cyclic update orders. When worker nodes are heterogeneous (due to different computational capabilities or different communication delays), synchronous and cyclic operations are inefficient since they will leave workers idle waiting … Read more