Stochastic Programming

Alternate Training of Shared and Task-Specific Parameters for Multi-Task Neural Networks

  • Stefania Bellavia
    • Categories Nonlinear Optimization, Stochastic Programming Tags , ,

    This paper introduces novel alternate training procedures for hard-parameter sharing Multi-Task Neural Networks (MTNNs). Traditional MTNN training faces challenges in managing conflicting loss gradients, often yielding sub-optimal performance. The proposed alternate training method updates shared and task-specific weights alternately, exploiting the multi-head architecture of the model. This approach reduces computational costs, enhances training regularization, and … Read more

    Adaptive Partitioning for Chance-Constrained Problems with Finite Support

  • Marius Roland
  • Alexandre Forel
  • Thibaut Vidal
    • Categories Integer Programming, Stochastic Programming

    This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem is constructed to yield a bound on the optimal value of the original problem. We show how to adapt the partitioning of the scenario set so … Read more

    Handling of long-term storage in multi-horizon stochastic programs

  • Michal Kaut
    • Categories Stochastic Programming Tags

    This paper shows how to implement long-term storage in the multi-horizon modelling paradigm, expanding the range of problems this approach is applicable to. The presented implementation is based on the HyOpt optimization model, but the ideas should be transferable also to other models implementing the multi-horizon approach. We illustrate the effects of several different formulations … Read more

    A two-stage stochastic programming approach incorporating spatially-explicit fire scenarios for optimal firebreak placement

  • Sebastián Dávila
  • Andres Weintraub
  • Franco Quezada
  • Jaime
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    Ensuring the effective placement of firebreaks across the landscape is a critical issue in wildfire prevention, as their success relies on their ability to block the spread of future fires. To address this challenge, it is essential to recognize the stochastic nature of fires, which are highly unpredictable from start to finish. The issue is … Read more

    Hardness of pricing routes for two-stage stochastic vehicle routing problems with scenarios

  • Matheus Jun Ota
  • Ricardo Fukasawa
    • Categories Combinatorial Optimization, Integer Programming, Stochastic Programming Tags , ,

    The vehicle routing problem with stochastic demands (VRPSD) generalizes the classic vehicle routing problem by considering customer demands as random variables. Similarly to other vehicle routing variants, state-of-the-art algorithms for the VRPSD are often based on set-partitioning formulations, which require efficient routines for the associated pricing problems. However, all these set-partitioning-based approaches have strong assumptions … Read more

    Zeroth-order Riemannian Averaging Stochastic Approximation Algorithms

  • Jiaxiang Li
  • Krishnakumar Balasubramanian
  • Shiqian Ma
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming

    We present Zeroth-order Riemannian Averaging Stochastic Approximation (\texttt{Zo-RASA}) algorithms for stochastic optimization on Riemannian manifolds. We show that \texttt{Zo-RASA} achieves optimal sample complexities for generating $\epsilon$-approximation first-order stationary solutions using only one-sample or constant-order batches in each iteration. Our approach employs Riemannian moving-average stochastic gradient estimators, and a novel Riemannian-Lyapunov analysis technique for convergence analysis. … Read more

    A Bilevel Optimization Approach for a Class of Combinatorial Problems with Disruptions and Probing

  • Leonardo Lozano
  • Juan Borrero
    • Categories Applications - OR and Management Sciences, Network Optimization, Stochastic Programming Tags , , ,

    We consider linear combinatorial optimization problems under uncertain disruptions that increase the cost coefficients of the objective function. A decision-maker, or planner, can invest resources to probe the components (i.e., the coefficients) in order to learn their disruption status. In the proposed probing optimization problem, the planner, knowing just the disruptions’ probabilities, selects which components … Read more

    Inexact Newton methods with matrix approximation by sampling for nonlinear least-squares and systems

  • Stefania Bellavia
  • Greta Malaspina
  • Benedetta Morini
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares, Stochastic Programming

    We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and inexact Newton methods for nonlinear systems of equations. Random models are formed using suitable sampling strategies for the matrices involved in the deterministic models. The analysis of the expected number of iterations needed in the worst case to achieve a desired level … Read more