Robust Optimization

Integer Programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks

  • Yiling Zhang
    • Categories Integer Programming, Robust Optimization, Stochastic Programming

    We study distributionally robust chance-constrained programs (DRCCPs) with individual chance constraints under a Wasserstein ambiguity. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. The introduction of … Read more

    Distributionally and Adversarially Robust Logistic Regression via Intersecting Wasserstein Balls

  • Aras Selvi
    • Categories Data Science Theory, Robust Optimization

    Empirical risk minimization often fails to provide robustness against adversarial attacks in test data, causing poor out-of-sample performance. Adversarially robust optimization (ARO) has thus emerged as the de facto standard for obtaining models that hedge against such attacks. However, while these models are robust against adversarial attacks, they tend to suffer severely from overfitting. To … Read more

    Wasserstein Distributionally Robust Optimization with Heterogeneous Data Sources

  • Adrian Esteban Perez
  • Yves Rychener
  • Daniel Kuhn
  • Juan M. Morales
    • Categories Robust Optimization Tags , ,

    We study decision problems under uncertainty, where the decision-maker has access to K data sources that carry biased information about the underlying risk factors. The biases are measured by the mismatch between the risk factor distribution and the K data-generating distributions with respect to an optimal transport (OT) distance. In this situation the decision-maker can … Read more

    A Toll-Setting Problem with Robust Wardrop Equilibrium Conditions Under Budgeted Uncertainty

  • Yasmine Beck
  • Martine Labbé
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Transportation Tags , , , ,

    We consider the problem of determining optimal tolls in a traffic network in which a toll-setting authority aims to maximize revenues and the users of the network act in the sense of Wardrop’s user equilibrium. The setting is modeled as a mathematical problem with equilibrium constraints and a mixed-integer, nonlinear, and nonconvex reformulation is presented … Read more

    Stackelberg Games with k-Submodular Function under Distributional Risk-Receptiveness and Robustness

  • Seonghun Park
  • Manish Bansal
    • Categories Game Theory, Robust Optimization, Stochastic Programming

    \(\) We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg games between an attacker (or interdictor) and a defender where the attacker aims to minimize the defender’s objective of maximizing a k-submodular function. We allow uncertainties arising … Read more

    Robustness Analysis for Adaptive Optimization With Application to Industrial Decarbonization in the Netherlands

  • Justin Starreveld
  • Dick den Hertog
  • Jaron Davelaar
    • Categories Applications - OR and Management Sciences, Energy, Robust Optimization Tags , , ,

    Robustness analysis assesses the performance of a particular solution under variation in the input data. This is distinct from sensitivity analysis, which assesses how variation in the input data changes a model’s optimal solution. For risk assessment purposes, robustness analysis has more practical value than sensitivity analysis. This is because sensitivity analysis, when applied to … Read more

    Robust System Identification: Finite-sample Guarantees and Connection to Regularization

  • Hyuk Park
    • Categories Control Applications, Robust Optimization, Semi-definite Programming Tags , ,

    We address the problem of identifying a stable linear time-invariant system from a single sample trajectory. The least squares estimate (LSE) is a commonly used algorithm for this purpose. However, LSE may exhibit poor identification errors when the number of samples is small. To mitigate the issue, we introduce the robust LSE, which integrates robust … Read more

    A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

  • Man-Chung Yue
  • Yves Rychener
  • Daniel Kuhn
  • Viet Anh Nguyen
    • Categories Robust Optimization, Stochastic Programming

    The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either chosen heuristically – without compelling theoretical justification – or optimally in view of restrictive distributional assumptions. In this paper, we propose a principled approach to construct covariance … Read more

    A Clustering-based uncertainty set for Robust Optimization

  • Alireza Yazdani
  • Ahmadreza Marandi
  • Rob Basten
  • Lijia Tan
    • Categories (Mixed) Integer Nonlinear Programming, Cone Programming, Robust Optimization Tags , , , ,

    Robust Optimization (RO) is an approach to tackle uncertainties in the parameters of an optimization problem. Constructing an uncertainty set is crucial for RO, as it determines the quality and the conservativeness of the solutions. In this paper, we introduce an approach for constructing a data-driven uncertainty set through volume-based clustering, which we call Minimum-Volume … Read more

    Heuristic Methods for Mixed-Integer, Linear, and Γ-Robust Bilevel Problems

  • Yasmine Beck
  • Ivana Ljubić
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , ,

    Due to their nested structure, bilevel problems are intrinsically hard to solve–even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. To tackle the Γ-robust counterpart of the bilevel … Read more