Asymptotic analysis of stochastic programs
Annals of Operations Research
A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
On the Rate of Convergence of Optimal Solutions of Monte Carlo Approximations of Stochastic Programs
SIAM Journal on Optimization
A robust minimax approach to classification
The Journal of Machine Learning Research
Operations Research
Adjustable robust solutions of uncertain linear programs
Mathematical Programming: Series A and B
Worst-case distribution analysis of stochastic programs
Mathematical Programming: Series A and B
Robust Mean-Covariance Solutions for Stochastic Optimization
Operations Research
Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach
Manufacturing & Service Operations Management
Digital Circuit Optimization via Geometric Programming
Operations Research
Second Order Cone Programming Approaches for Handling Missing and Uncertain Data
The Journal of Machine Learning Research
Primal-dual subgradient methods for convex problems
Mathematical Programming: Series A and B - Series B - Special Issue: Nonsmooth Optimization and Applications
Percentile Optimization for Markov Decision Processes with Parameter Uncertainty
Operations Research
Robustness and Regularization of Support Vector Machines
The Journal of Machine Learning Research
Neural Network Learning: Theoretical Foundations
Neural Network Learning: Theoretical Foundations
IEEE Transactions on Information Theory
Distributionally Robust Optimization and Its Tractable Approximations
Operations Research
Theory and Applications of Robust Optimization
SIAM Review
Consistency of support vector machines and other regularized kernel classifiers
IEEE Transactions on Information Theory
Robust solutions of uncertain linear programs
Operations Research Letters
Hi-index | 0.00 |
Motivated by data-driven decision making and sampling problems, we investigate probabilistic interpretations of robust optimization (RO). We establish a connection between RO and distributionally robust stochastic programming (DRSP), showing that the solution to any RO problem is also a solution to a DRSP problem. Specifically, we consider the case where multiple uncertain parameters belong to the same fixed dimensional space and find the set of distributions of the equivalent DRSP problem. The equivalence we derive enables us to construct RO formulations for sampled problems (as in stochastic programming and machine learning) that are statistically consistent, even when the original sampled problem is not. In the process, this provides a systematic approach for tuning the uncertainty set. The equivalence further provides a probabilistic explanation for the common shrinkage heuristic, where the uncertainty set used in an RO problem is a shrunken version of the original uncertainty set.