Robust Optimization

Adjustable Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

  • Haolin Ruan
  • Zhi Chen
  • Chin Pang Ho
    • Categories Robust Optimization Tags , , ,

    We study adjustable distributionally robust optimization problems where their ambiguity sets can potentially encompass an infinite number of expectation constraints. Although such an ambiguity set has great modeling flexibility in characterizing uncertain probability distributions, the corresponding adjustable problems remain computationally intractable and challenging. To overcome this issue, we propose a greedy improvement procedure that consists … 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

    Robust Epidemiological Prediction and Optimization

  • Chenyi Fu
  • Melvyn Sim
  • Minglong Zhou
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    The COVID-19 pandemic has brought many countries to their knees, and the urgency to return to normalcy has never been greater. Epidemiological models, such as the SEIR compartmental model, are indispensable tools for, among other things, predicting how pandemic may spread over time and how vaccinations and different public health interventions could affect the outcome. … Read more

    RSOME in Python: An Open-Source Package for Robust Stochastic Optimization Made Easy

  • Peng Xiong
  • Zhi Chen
    • Categories Modeling Languages and Systems, Robust Optimization Tags , , ,

    We develop a Python package called RSOME for modeling a wide spectrum of robust and distributionally robust optimization problems. RSOME serves as a modeling platform for formulating various optimization problems subject to distributional ambiguity in a highly readable and mathematically intuitive manner. Compared with the MATLAB version, RSOME in Python is more versatile and well … Read more

    Distributionally Robust Optimization with Markovian Data

  • Daniel Kuhn
  • Tobias Sutter
  • Mengmeng Li
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with d states. We propose a data-driven distributionally robust optimization model to estimate the problem’s objective function and optimal solution. By leveraging results from … Read more

    New complexity results and algorithms for min-max-min robust combinatorial optimization

  • Jannis Kurtz
    • Categories Combinatorial Optimization, Convex and Nonsmooth Optimization, Robust Optimization Tags , , ,

    In this work we investigate the min-max-min robust optimization problem applied to combinatorial problems with uncertain cost-vectors which are contained in a convex uncertainty set. The idea of the approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions would … Read more

    Robust Generalization despite Distribution Shift via Minimum Discriminating Information

  • Andreas Krause
  • Daniel Kuhn
  • Tobias Sutter
    • Categories Robust Optimization Tags , , , , ,

    Training models that perform well under distribution shifts is a central challenge in machine learning. In this paper, we introduce a modeling framework where, in addition to training data, we have partial structural knowledge of the shifted test distribution. We employ the principle of minimum discriminating information to embed the available prior knowledge, and use … Read more

    Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts

  • Jose Blanchet
  • Daniel Kuhn
  • Viet Anh Nguyen
  • Bahar TaČ™kesen
  • Man-Chung Yue
    • Categories Nonlinear Systems and Least-Squares, Robust Optimization, Stochastic Programming

    Least squares estimators, when trained on a few target domain samples, may predict poorly. Supervised domain adaptation aims to improve the predictive accuracy by exploiting additional labeled training samples from a source distribution that is close to the target distribution. Given available data, we investigate novel strategies to synthesize a family of least squares estimator … Read more

    A Generic Optimization Framework for Resilient Systems

  • Marc E. Pfetsch
  • Andreas Schmitt
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization Tags , , , ,

    This paper addresses the optimal design of resilient systems, in which components can fail. The system can react to failures and its behavior is described by general mixed integer nonlinear programs, which allows for applications to many (technical) systems. This then leads to a three-level optimization problem. The upper level designs the system minimizing a … Read more

    On the Optimality of Affine Decision Rules in Robust and Distributionally Robust Optimization

  • Angelos Georghiou
  • Angelos Tsoukalas
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags ,

    We propose tight conditions under which two-stage robust and distributionally robust optimization problems are optimally solved in affine decision rules. Contrary to previous work, our conditions do not impose any structure on the support of the uncertain problem parameters, and they ensure point-wise (as opposed to worst-case) optimality of affine decision rules. The absence of … Read more