3 présentations

• 
  16h45 - 17h07

  Nonlinear Decision Rules Made Scalable by Nonparametric Liftings

  • Eojin Han, prés., University of Notre Dame
  • Omid Nohadani, Benefits Science Technologies

  We consider a nonparametric lifting framework where the uncertainty space is lifted to higher dimensions to obtain nonlinear decision rules. Current lifting-based approaches require predetermined functions and are parametric. We propose two nonparametric liftings, which derive the nonlinear functions by leveraging the uncertainty set structure and problem coefficients. Both methods integrate the benefits from lifting and nonparametric approaches, and hence provide scalable decision rules with performance bounds. More specifically, the set-driven lifting is constructed by finding polyhedrons within uncertainty sets, inducing piecewise-linear decision rules with performance bounds. The dynamics-driven lifting, on the other hand, is constructed by extracting geometric information and accounting for problem coefficients. This is achieved by using linear decision rules, also enabling one to quantify lower bounds of objective improvements over linear decision rules. Numerical comparisons with competing methods demonstrate superior computational scalability and comparable performance in objectives, which are magnified in multistage problems.

• 
  17h07 - 17h29

  Relatively Robust Multicriteria Optimization

  • Thomas Weber, prés., EPFL

  For multicriteria optimization with linear scalarization and unknown weights, we propose relatively robust decisions that are Pareto-efficient and maximize a performance index. This index measures the worst-case ratio of the weighted objective to its maximum value over all weights. Key results include a boundary representation of the performance index as the minimum of criterion-specific performance ratios and a computationally simple method for determining relatively robust decisions with a specified performance tolerance by maximizing an epsilon-augmented performance index. The method only requires the continuity of criterion functions and the compactness of the feasible decision set, accommodating nonconvex sets and any finite action set. A notable feature is its endogenous derivation of tradeoffs between criteria, including a performance guarantee against decisions justified by any other weighting. Structural results, examples, and applications illustrate the method's potential.

• 
  17h29 - 17h51

  Robustness Path

  • Hao Hao, Carnegie Mellon University
  • Zhang Peter, prés., Carnegie Mellon University

  Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a robust solution (e.g., to implement an investment portfolio or perform robust machine learning inference), the user has to a priori decide the trade-off between efficiency (nominal performance) and robustness (worst-case performance) of the solution by choosing the uncertainty level hyperparameters. In many applications, this amounts to solving the problem many times and comparing their solutions. This makes robust optimization practically cumbersome or even intractable. We present a novel procedure based on the proximal point method (PPM) to approximate many Pareto-efficient robust solutions through a single PPM trajectory.