Stochastic Programming

Stochastic Multi-level Composition Optimization Algorithms with Level-Independent Convergence Rates

  • Krishnakumar Balasubramanian
  • Saeed Ghadimi
  • Anthony Nguyen
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , ,

    In this paper, we study smooth stochastic multi-level composition optimization problems, where the objective function is a nested composition of $T$ functions. We assume access to noisy evaluations of the functions and their gradients, through a stochastic first-order oracle. For solving this class of problems, we propose two algorithms using moving-average stochastic estimates, and analyze … Read more

    An improved randomized algorithm with noise level tuning for large-scale noisy unconstrained DFO problems

  • Morteza Kimiaei
    • Categories Optimization Software Benchmark, Stochastic Programming, Unconstrained Optimization Tags , , , ,

    In this paper, a new randomized solver (called VRDFON) for noisy unconstrained derivative-free optimization (DFO) problems is discussed. Complexity result in the presence of noise for nonconvex functions is studied. Two effective ingredients of VRDFON are an improved derivative-free line search algorithm with many heuristic enhancements and quadratic models in adaptively determined subspaces. Numerical results … Read more

    On the Impact of Deep Learning-based Time-series Forecasts on Multistage Stochastic Programming Policies

  • Merve Bodur
  • Mucahit Cevik
  • Juyoung Wang
    • Categories Stochastic Programming Tags , , , ,

    Multistage stochastic programming provides a modeling framework for sequential decision-making problems that involve uncertainty. One typically overlooked aspect of this methodology is how uncertainty is incorporated into modeling. Traditionally, statistical forecasting techniques with simple forms, e.g., (first-order) autoregressive time-series models, are used to extract scenarios to be added to optimization models to represent the uncertain … Read more

    Multistage stochastic programs with the entropic risk measure

  • Oscar Dowson
  • David P. Morton
  • Bernardo K. Pagnoncelli
    • Categories Stochastic Programming

    Over the last two decades, coherent risk measures have been well studied as a principled, axiomatic way to measure the risk of a random variable. Because of this axiomatic approach, coherent risk measures have a number of attractive features for computation, and they have been integrated into a variety of stochastic programming algorithms, including stochastic … Read more

    Optimization for Supervised Machine Learning: Randomized Algorithms for Data and Parameters

  • Filip Hanzely
    • Categories Convex Optimization, Stochastic Programming Tags , , , , ,

    Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used to formulate these often ill-conditioned optimization tasks, there is a need for new efficient algorithms able to … Read more

    A Shared Mobility Based Framework for Evacuation Planning and Operations under Forecast Uncertainty

  • Huiwen Jia
  • Siqian Shen
  • Kati Moug
    • Categories Network Optimization, Stochastic Programming, Transportation

    To meet evacuation needs from carless populations who may require personalized assistance to evacuate safely, we propose a ridesharing-based evacuation program that recruits volunteer drivers before a disaster strikes, and then matches volunteers with evacuees who need assistance once demand is realized. We optimize resource planning and evacuation operations under uncertain spatiotemporal demand, and construct … Read more

    An Improved Analysis of Stochastic Gradient Descent with Momentum

  • Yuan Gao
  • Yanli Liu
  • Wotao Yin
    • Categories Stochastic Programming

    SGD with momentum (SGDM) has been widely applied in many machine learning tasks, and it is often applied with dynamic stepsizes and momentum weights tuned in a stagewise manner. Despite of its empirical advantage over SGD, the role of momentum is still unclear in general since previous analyses on SGDM either provide worse convergence bounds … Read more

    Large Deviation Bounds for Markov Chain Sample Average Approximation via Weak Convergence

  • Arnab Sur
    • Categories Stochastic Programming Tags , , , ,

    A common approach to solve stochastic optimization problems with expectations is to replace the expectations by its sample averages. Large sample asymptotic properties of this approximation are well studied when the sample is i.i.d. In many cases, however, i.i.d. samples are not readily available. On the contrary, one can generate a Harris recurrent Markov chain … Read more

    Accuracy and fairness trade-offs in machine learning: A stochastic multi-objective approach

  • Suyun Liu
  • Luis Nunes Vicente
    • Categories Data-Mining, Multi-Criteria Optimization, Stochastic Programming Tags , , , , , , , , ,

    In the application of machine learning to real life decision-making systems, e.g., credit scoring and criminal justice, the prediction outcomes might discriminate against people with sensitive attributes, leading to unfairness. The commonly used strategy in fair machine learning is to include fairness as a constraint or a penalization term in the minimization of the prediction … Read more

    Equilibrium Oil Market Share under the COVID-19 Pandemic

  • Xiaojun Chen
  • Yun Shi
  • Xiaozhou Wang
    • Categories Applications - OR and Management Sciences, Complementarity and Variational Inequalities, Stochastic Programming Tags , , ,

    Equilibrium models for energy markets under uncertain demand and supply have attracted considerable attentions. This paper focuses on modelling crude oil market share under the COVID-19 pandemic using two-stage stochastic equilibrium. We describe the uncertainties in the demand and supply by random variables and provide two types of production decisions (here-and-now and wait-and-see). The here-and-now … Read more