Paper Info
Title
Models and algorithms for distributionally robust least squares problems
Abstract
We present three different robust frameworks using probabilistic ambiguity descriptions of the data in least squares problems. These probability ambiguity descriptions are given by: (1) confidence region over the first two moments; (2) bounds on the probability measure with moments constraints; (3) the Kantorovich probability distance from a given measure. For the first case, we give an equivalent formulation and show that the optimization problem can be solved using a semidefinite optimization reformulation or polynomial time algorithms. For the second case, we derive the equivalent Lagrangian problem and show that it is a convex stochastic programming problem. We further analyze three special subcases: (i) finite support; (ii) measure bounds by a reference probability measure; (iii) measure bounds by two reference probability measures with known density functions. We show that case (i) has an equivalent semidefinite programming reformulation and the sample average approximations of case (ii) and (iii) have equivalent semidefinite programming reformulations. For ambiguity description (3), we show that the finite support case can be solved by using an equivalent second order cone programming reformulation.
Year
DOI
Venue
2014
10.1007/s10107-013-0681-9
Mathematical Programming: Series A and B
Keywords
Field
DocType
93b35 sensitivity,90c22 semidefinite programming,62j07 ridge regression; shrinkage estimators,90c15 stochastic programming,62g35 robustness,62j05 linear regression,93e24 least squares and related methods
Least squares,Confidence region,Second-order cone programming,Discrete mathematics,Mathematical optimization,Probability measure,Algorithm,Time complexity,Stochastic programming,Optimization problem,Semidefinite programming,Mathematics
Journal
Volume
Issue
ISSN
146
1-2
1436-4646
Citations 
PageRank 
References 
11
0.75
9
Authors
2
Name
Order
Citations
PageRank
Sanjay Mehrotra152177.18
He Zhang2111.43