Stochastic Programming

Accelerated Stochastic Peaceman-Rachford Method for Empirical Risk Minimization

  • Jianchao Bai
  • Fengmiao Bian
  • Xiaokai Chang
  • Lin Du
    • Categories Convex Optimization, Stochastic Programming Tags , , , ,

    This work is devoted to studying an Accelerated Stochastic Peaceman-Rachford Splitting Method (AS-PRSM) for solving a family of structural empirical risk minimization problems. The objective function to be optimized is the sum of a possibly nonsmooth convex function and a finite-sum of smooth convex component functions. The smooth subproblem in AS-PRSM is solved by a stochastic gradient method using variance reduction … Read more

    The Sharpe predictor for fairness in machine learning

  • Suyun Liu
  • Luis Nunes Vicente
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization, Stochastic Programming Tags , , , ,

    In machine learning (ML) applications, unfair predictions may discriminate against a minority group. Most existing approaches for fair machine learning (FML) treat fairness as a constraint or a penalization term in the optimization of a ML model, which does not lead to the discovery of the complete landscape of the trade-offs among learning accuracy and … Read more

    Increasing Driver Flexibility through Personalized Menus and Incentives in Ridesharing and Crowdsourced Delivery Platforms

  • Hannah Horner
  • John E. Mitchell
  • Jennifer Pazour
    • Categories Applications - OR and Management Sciences, Stochastic Programming, Transportation Tags , , , , , ,

    Allowing drivers to choose which requests to fulfill provides drivers with much-needed autonomy in ridesharing and crowdsourced delivery platforms. While stochastic, a driver’s acceptance of requests in their menu is influenced by the platform’s offered compensation. Therefore, in this work, we create and solve an optimization model to determine personalized menus and incentives to offer … Read more

    Confidence Region for Distributed Stochastic Optimization Problem via Stochastic Gradient Tracking Method

  • Yongchao Liu
  • Shengchao Zhao
    • Categories Stochastic Programming Tags , , , ,

    Since stochastic approximation (SA) based algorithms are easy to implement and need less memory, they are very popular in distributed stochastic optimization problems. Many works have focused on the consistency of the objective values and the iterates returned by the SA based algorithms. It is of fundamental interest to know how to quantify the uncertainty … Read more

    A solution algorithm for chance-constrained problems with integer second-stage recourse decisions

  • Andrea Lodi
  • Enrico Malaguti
  • Michele Monaci
  • Giacomo Nannicini
  • Paolo Paronuzzi
    • Categories (Mixed) Integer Nonlinear Programming, Stochastic Programming

    We study a class of chance-constrained two-stage stochastic optimization problems where the second-stage recourse decisions belong to mixed-integer convex sets. Due to the nonconvexity of the second-stage feasible sets, standard decomposition approaches cannot be applied. We develop a provably convergent branch-and-cut scheme that iteratively generates valid inequalities for the convex hull of the second-stage feasible … Read more

    Dual SDDP for risk-averse multistage stochastic programs

  • Bernardo Freitas Paulo da Costa
  • Vincent Leclère
    • Categories Dynamic Programming, Stochastic Programming Tags , , , ,

    Risk-averse multistage stochastic programs appear in multiple areas and are challenging to solve. Stochastic Dual Dynamic Programming (SDDP) is a well-known tool to address such problems under time-independence assumptions. We show how to derive a dual formulation for these problems and apply an SDDP algorithm, leading to converging and deterministic upper bounds for risk-averse problems. … Read more

    Nash Bargaining Partitioning in Decentralized Portfolio Management

  • Francisco Benita
  • Stefano Nasini
  • Rabia Nessah
    • Categories Finance and Economics, Game Theory, Stochastic Programming Tags , , , ,

    In the context of decentralized portfolio management, understanding how to distribute a fixed budget among decentralized intermediaries is a relevant question for financial investors. We consider the Nash bargaining partitioning for a class of decentralized investment problems, where intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. … Read more

    Inexact Sequential Quadratic Optimization for Minimizing a Stochastic Objective Function Subject to Deterministic Nonlinear Equality Constraints

  • Frank E. Curtis
  • Daniel P. Robinson
  • Baoyu Zhou
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , ,

    An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is assumed that constraint function and derivative values can be computed, but that only stochastic approximations are available for the objective function and its … Read more

    Solving the Home Service Assignment, Routing, and Appointment Scheduling (H-SARA) problem with Uncertainties

  • Syu-Ning Johnn
  • Yiran Zhu
  • Andrés Miniguano-Trujillo
  • Akshay Gupte
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming, Transportation Tags , , , ,

    The Home Service Assignment, Routing, and Appointment scheduling (H-SARA) problem integrates the strategical fleet-sizing, tactical assignment, operational vehicle routing and scheduling subproblems at different decision levels, with a single period planning horizon and uncertainty (stochasticity) from the service duration, travel time, and customer cancellation rate. We propose a two-stage stochastic mixed-integer linear programming model for … Read more

    Practicable Robust Stochastic Optimization under Divergence Measures

  • Douglas Alem
  • Aakil Caunhye
    • Categories Robust Optimization, Stochastic Programming Tags , , , , ,

    We seek to provide practicable approximations of the two-stage robust stochastic optimization (RSO) model when its ambiguity set is constructed with an f-divergence radius. These models are known to be numerically challenging to various degrees, depending on the choice of the f-divergence function. The numerical challenges are even more pronounced under mixed-integer rst-stage decisions. In … Read more