Edward Anderson

Sample Average Approximation and Model Predictive Control for Multistage Stochastic Optimization

  • Dominic S. T. Keehan
  • Andrew B. Philpott
  • Edward Anderson
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Sample average approximation-based stochastic dynamic programming and model predictive control are two different methods of approaching multistage stochastic optimization. Model predictive control—despite a lack of theoretical backing—is often used instead of stochastic dynamic programming due to computational necessity. For settings where the stage reward is a convex function of the random terms, the stage dynamics … Read more

    Sample average approximation and model predictive control for inventory optimization

  • Dominic S. T. Keehan
  • Andrew B. Philpott
  • Edward Anderson
    • Categories Dynamic Programming, Stochastic Programming Tags , , ,

    We study multistage stochastic optimization problems using sample average approximation (SAA) and model predictive control (MPC) as solution approaches. MPC is frequently employed when the size of the problem renders stochastic dynamic programming intractable, but it is unclear how this choice affects out-of-sample performance. To compare SAA and MPC out-of-sample, we formulate and solve an … Read more

    Improving sample average approximation using distributional robustness

  • Edward Anderson
  • Andrew B. Philpott
    • Categories Stochastic Programming Tags , ,

    We consider stochastic optimization problems in which we aim to minimize the expected value of an objective function with respect to an unknown distribution of random parameters. We analyse the out-of-sample performance of solutions obtained by solving a distributionally robust version of the sample average approximation problem for unconstrained quadratic problems, and derive conditions under … Read more

    Robust sample average approximation with small sample sizes

  • Edward Anderson
  • Andrew B. Philpott
    • Categories Robust Optimization, Stochastic Programming

    We consider solving stochastic optimization problems in which we seek to minimize the expected value of an objective function with respect to an unknown distribution of random parameters. Our focus is on models that use sample average approximation (SAA) with small sample sizes. We analyse the out-of-sample performance of solutions obtained by solving a robust … Read more

    Confidence Levels for CVaR Risk Measures and Minimax Limits

  • Edward Anderson
  • Huifu Xu
  • Dali Zhang
    • Categories Robust Optimization, Semi-infinite Programming, Stochastic Programming

    Conditional value at risk (CVaR) has been widely used as a risk measure in finance. When the confidence level of CVaR is set close to 1, the CVaR risk measure approximates the extreme (worst scenario) risk measure. In this paper, we present a quantitative analysis of the relationship between the two risk measures and its … Read more