bilevel optimization

Bilevel stochastic methods for optimization and machine learning: Bilevel stochastic descent and DARTS

  • Tommaso Giovannelli
  • Griffin D. Kent
  • Luís Nunes Vicente
    • Categories Data-Mining, Nonlinear Optimization, Stochastic Programming Tags , , ,

    Two-level stochastic optimization formulations have become instrumental in a number of machine learning contexts such as neural architecture search, continual learning, adversarial learning, and hyperparameter tuning. Practical stochastic bilevel optimization problems become challenging in optimization or learning scenarios where the number of variables is high or there are constraints. The goal of this paper is … Read more

    A New Bilevel Optimization Approach for Computing Ramsey Numbers

  • Fabio Furini
  • Pablo San Segundo
    • Categories 0-1 Programming, Graphs and Matroids, Network Optimization Tags , , , ,

    In this article we address the problem of finding lower bounds for small Ramsey numbers $R(m,n)$ using circulant graphs. Our constructive approach is based on finding feasible colorings of circulant graphs using Integer Programming (IP) techniques. First we show how to model the problem as a Stackelberg game and, using the tools of bilevel optimization, … Read more

    Linearizing Bilinear Products of Shadow Prices and Dispatch Variables in Bilevel Problems for Optimal Power System Planning

  • Grani A. Hanasusanto
  • Nicholas Laws
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Smart Grids Tags , , , ,

    This work presents a general method for linearizing bilinear terms in the upper level of bilevel optimization problems when the bilinear terms are products of the primal and dual variables of the lower level. Bilinear terms of this form often appear in energy market optimization models where the dual variable represents the market price of … Read more

    A novel approach for bilevel programs based on Wolfe duality

  • Yuwei Li
  • Guihua Lin
  • Jin Zhang
  • Xide Zhu
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be transformed into a … 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

    A Gentle and Incomplete Introduction to Bilevel Optimization

  • Yasmine Beck
  • Martin Schmidt
    • Categories Other Topics Tags ,

    These are lecture notes on bilevel optimization. The class of bilevel optimization problems is formally introduced and motivated using examples from different fields. Afterward, the main focus is on how to solve linear and mixed-integer linear bilevel optimization problems. To this end, we first consider various single-level reformulations of bilevel optimization problems with linear or … Read more

    Design of Poisoning Attacks on Linear Regression Using Bilevel Optimization

  • Miguel F. Anjos
  • Luce Brotcorne
  • Diego Cattaruzza
  • Zeynep Suvak
    • Categories Complementarity and Variational Inequalities Tags , , ,

    Poisoning attack is one of the attack types commonly studied in the field of adversarial machine learning. The adversary generating poison attacks is assumed to have access to the training process of a machine learning algorithm and aims to prevent the algorithm from functioning properly by injecting manipulative data while the algorithm is being trained. … Read more

    On Convex Lower-Level Black-Box Constraints in Bilevel Optimization with an Application to Gas Market Models with Chance Constraints

  • Holger Heitsch
  • René Henrion
  • Thomas Kleinert
  • Martin Schmidt
    • Categories Applications - OR and Management Sciences, Cutting Plane Approaches, Stochastic Programming Tags , , , ,

    Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this … Read more

    Application-Driven Learning via Joint Prediction and Optimization of Demand and Reserves Requirement

  • Joaquim Dias Garcia
  • Tito Homem-de-Mello
  • Francisco D. Muñoz
  • Alexandre Street
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Optimization of Simulated Systems Tags , , , , ,

    Forecasting and decision-making are generally modeled as two sequential steps with no feedback, following an open-loop approach. In power systems, operators first forecast loads trying to minimize errors with respect to historical data. They also size reserve requirements based on error estimates. Next, energy and reserves are scheduled and the system is operated following the … Read more

    A Bilevel Optimization Approach to Decide the Feasibility of Bookings in the European Gas Market

  • Martine Labbé
  • Martin Schmidt
  • Johannes Thürauf
  • Fränk Plein
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    The European gas market is organized as a so-called entry-exit system with the main goal to decouple transport and trading. To this end, gas traders and the transmission system operator (TSO) sign so-called booking contracts that grant capacity rights to traders to inject or withdraw gas at certain nodes up to this capacity. On a … Read more