Robust Optimization

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

    A Max-Min-Max Algorithm for Large-Scale Robust Optimization

  • Kai Tu
  • Zhi Chen
  • Man-Chung Yue
    • Categories Robust Optimization Tags , , ,

    Robust optimization (RO) is a powerful paradigm for decision making under uncertainty. Existing algorithms for solving RO, including the reformulation approach and the cutting-plane method, do not scale well, hindering the application of RO to large-scale decision problems. In this paper, we devise a first-order algorithm for solving RO based on a novel max-min-max perspective. … Read more

    An MILP-Based Solution Scheme for Factored and Robust Factored Markov Decision Processes

  • Huikang Liu
  • Wolfram Wiesemann
  • Man-Chung Yue
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags ,

    Factored Markov decision processes (MDPs) are a prominent paradigm within the artificial intelligence community for modeling and solving large-scale MDPs whose rewards and dynamics decompose into smaller, loosely interacting components. Through the use of dynamic Bayesian networks and context-specific independence, factored MDPs can achieve an exponential reduction in the state space of an MDP and … Read more

    Robust Drone Delivery with Weather Information

  • Chun Cheng
  • Yossiri Adulyasak
  • Louis-Martin Rousseau
    • Categories Robust Optimization, Transportation Tags , , , ,

    Problem definition: Drone delivery has recently garnered significant attention due to its potential for faster delivery at a lower cost than other delivery options. When scheduling drones from a depot for delivery to various destinations, the dispatcher must take into account the uncertain wind conditions, which affect the delivery times of drones to their destinations, … Read more

    Distributionally Robust Optimization with Decision-Dependent Information Discovery

  • Qing Jin
  • Angelos Georghiou
  • Phebe Vayanos
  • Grani A. Hanasusanto
    • Categories Robust Optimization Tags , , , , ,

    We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the first stage. This class of problems finds many important applications in selection problems (e.g., in hiring, project portfolio optimization, or optimal sensor location). … Read more