An Asymptotically Optimal Coordinate Descent Algorithm for Learning Bayesian Networks from Gaussian Models

  • Tong Xu
  • Simge Küçükyavuz
  • Ali Shojaie
    • Categories (Mixed) Integer Nonlinear Programming

    This paper studies the problem of learning Bayesian networks from continuous observational data, generated according to a linear Gaussian structural equation model. We consider an \(\ell_0\)-penalized maximum likelihood estimator for this problem which is known to have favorable statistical properties but is computationally challenging to solve, especially for medium-sized Bayesian networks. We propose a new … Read more

    A Markovian Model for Learning-to-Optimize

  • Michael Sucker
  • Peter Ochs
    • Categories Optimization in Data Science, Stochastic Approaches, Stochastic Programming Tags , , , ,

    We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory of the learned algorithm, for example, the expected (non-asymptotic) convergence rate and the expected time to reach the stopping criterion. … Read more

    Probing-Enhanced Stochastic Programming

  • Zhichao Ma
  • Youngdae Kim
  • Jeff Linderoth
  • James R. Luedtke
  • Logan Matthews
    • Categories Stochastic Programming Tags , , ,

    We consider a two-stage stochastic decision problem where the decision-maker has the opportunity to obtain information about the distribution of the random variables $\xi$ that appear in the problem through a set of discrete actions that we refer to as probing. Probing components of a random vector $\eta$ that is jointly-distributed with $\xi$ allows the … Read more

    Double-proximal augmented Lagrangian methods with improved convergence condition

  • Jianchao Bai
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Global Optimization Tags , , , ,

    In this paper, we propose a novel double-proximal augmented Lagrangian method(DP-ALM) for solving a family of linearly constrained convex minimization problems whose objective function is not necessarily smooth. This DP-ALM not only enjoys a flexible dual stepsize, but also contains a proximal subproblem with relatively smaller proximal parameter. By a new prediction-correction reformulation for this … Read more

    Analytic Formulas for Alternating Projection Sequences for the Positive Semidefinite Cone and an Application to Convergence Analysis

  • Hiroyuki Ochiai
  • Yoshiyuki Sekiguchi
  • Hayato Waki
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , , ,

    We derive analytic formulas for the alternating projection method applied to the cone \(S^n_+\) of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a sequence constructed by the alternating projection method. By applying these formulas, we analyze the alternating projection method in detail and show that the … Read more

    Machine Learning for Optimization-Based Separation: the Case of Mixed-Integer Rounding Cuts

  • Oscar Guaje
  • Aleksandr M. Kazachkov
  • Elias B. Khalil
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches

    Mixed-Integer Rounding (MIR) cuts are effective at improving the dual bound in Mixed-Integer Linear Programming (MIP). However, in practice, MIR cuts are separated heuristically rather than using optimization as the latter is prohibitively expensive. We present a hybrid cut generation framework in which we train a Machine Learning (ML) model to inform cut generation for … Read more

    The Blessing of Strategic Customers in Personalized Pricing

  • Zhi Chen
  • Bradley Sturt
  • Weijun Xie
    • Categories Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming

    We consider a feature-based personalized pricing problem in which the buyer is strategic: given the seller’s pricing policy, the buyer can augment the features that they reveal to the seller to obtain a low price for the product. We model the seller’s pricing problem as a stochastic program over an infinite-dimensional space of pricing policies … Read more

    Optimizing the lead time of operational flexibility trading from distributed industrial energy systems in future energy and flexibility markets

  • Daniel Bull
    • Categories (Mixed) Integer Linear Programming, Control Applications, Energy Tags , , , ,

    To meet the challenges of increasing volatile and distributed renewable energy generation in the electric grid, local flexibility and energy markets are currently investigated. These markets aim to encourage prosumers to trade their available flexible power locally, to be used if a grid congestion is being predicted. The markets are emerging, but the characterizing parameter … Read more

    Global Optimization of Non-Linear Systems of Equations by Simulating the Flight of a Projectile in the Conformational Space

  • Nick Harkiolakis
    • Categories Applications - Science and Engineering, Global Optimization, Nonlinear Optimization Tags , , , ,

    A new heuristic optimization algorithm is presented based on an analogy with the physical phenomenon of a projectile launched in a conformational space under the influence of a gravitational force. Its implementation simplicity and the option to enhance it with local search methods make it ideal for the optimization of non-linear systems of equations. The … Read more

    The Overflowing Bin Packing Problem: Theoretical Results and a New Flow Formulation

  • John Martinovic
  • Nico Strasdat
    • Categories (Mixed) Integer Linear Programming Tags , , , ,

    We consider a recently proposed one-dimensional packing problem, called the overflowing bin packing problem (OBPP). In this scenario, we are given a set of items (of known sizes) and a set of bins (of known capacities). Roughly speaking, the task is to assign the items to the bins in such a way that the total … Read more