Stochastic Programming

Multistage Conditional Compositional Optimization

  • Buse Şen
  • Yifan Hu
  • Daniel Kuhn
    • Categories Stochastic Programming

    We introduce Multistage Conditional Compositional Optimization (MCCO) as a new paradigm for decision-making under uncertainty that combines aspects of multistage stochastic programming and conditional stochastic optimization. MCCO minimizes a nest of conditional expectations and nonlinear cost functions. It has numerous applications and arises, for example, in optimal stopping, linear-quadratic regulator problems, distributionally robust contextual bandits, … Read more

    A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muon

  • Serge Gratton
  • Philippe L. Toint
    • Categories Data Science Algorithms, Stochastic Programming, Unconstrained Optimization Tags , , ,

    A unified framework for first-order optimization algorithms for nonconvex unconstrained optimization is proposed that uses adaptively preconditioned gradients and includes popular methods such as full and diagonal AdaGrad, AdaNorm, as well as adpative variants of Shampoo and Muon. This framework also allows combining heterogeneous geometries across different groups of variables while preserving a unified convergence … Read more

    Complexity of an inexact stochastic SQP algorithm for equality constrained optimization

  • Michael J. O'Neill
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , ,

    In this paper, we consider nonlinear optimization problems with a stochastic objective function and deterministic equality constraints. We propose an inexact two-stepsize stochastic sequential quadratic programming (SQP) algorithm and analyze its worst-case complexity under mild assumptions. The method utilizes a step decomposition strategy and handles stochastic gradient estimates by assigning different stepsizes to different components … Read more

    Variational Consistency of Robust Integral Functionals Induced by Empirical Measures

  • Qiao Yi Wang
    • Categories Robust Optimization, Stochastic Programming

    We study the variational convergence of robust integral functionals induced by empirical probability measures. We establish a generalized consistency framework where the ambiguity set is constructed using a probability metric. By replacing traditional uniform equicontinuity assumptions with inherent convexity and general probability metric domination, we prove the almost sure pointwise and uniform convergence of the … Read more

    Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers

  • I. Esra Buyuktahtakin Toy
    • Categories Data Science Algorithms, Optimization in Data Science, Stochastic Programming Tags , , , , , , , , , , ,

    Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management sciences (OR/MS), which have long offered conceptual and methodological foundations for sequential decision-making under uncertainty. At the same time, recent advances in deep learning, including feedforward neural … Read more

    An Inexact Trust-Region Method for Structured Nonsmooth Optimization with Application to Risk-Averse Stochastic Programming

  • Drew P. Kouri
    • Categories Nonsmooth Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming Tags , , , , ,

    We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure arise in numerous applications including risk-averse stochastic programming and subproblems for nonsmooth penalty nonlinear programming methods. Our method permits the … Read more

    On vehicle routing problems with stochastic demands — Scenario-optimal recourse policies

  • Matheus Jun Ota
  • Ricardo Fukasawa
    • Categories Branch and Cut Algorithms, Stochastic Programming, Transportation Tags , ,

    Two-Stage Vehicle Routing Problems with Stochastic Demands (VRPSDs) form a class of stochastic combinatorial optimization problems where routes are planned in advance, demands are revealed upon vehicle arrival, and recourse actions are triggered whenever capacity is exceeded. Following recent works, we consider VRPSDs where demands are given by an empirical probability distribution of scenarios. Existing … Read more

    An objective-function-free algorithm for nonconvex stochastic optimization with deterministic equality and inequality constraints

  • Serge Gratton
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    An algorithm is proposed for solving optimization problems with stochastic objective and deterministic equality and inequality constraints. This algorithm is objective-function-free in the sense that it only uses the objective’s gradient and never evaluates the function value. It is based on an adaptive selection of function-decreasing and constraint-improving iterations, the first ones using an Adagrad-type … Read more

    Globalized Adversarial Regret Optimization: Robust Decisions with Uncalibrated Predictions

  • Jannis Kurtz
  • Bart Paul Gerard van Parys
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds in simple settings. However, when predictions lack rigorous error bounds (as is typical of modern machine learning methods) classical robust models often … Read more