-

 

 

 




Optimization Online





 

Admissibility of solution estimators for stochastic optimization

Amitabh Basu(basu.amitabh***at***jhu.edu)
Tu Nguyen(tnguy177***at***jhu.edu)
Ao Sun(asun17***at***jhu.edu)

Abstract: We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic optimization problem (which is also known as the empirical risk minimization (ERM) rule in learning literature). It is well known that for some simple stochastic optimization problems, the sample average estimator may not be admissible. This is known as Stein's paradox in the statistics literature. We show in this paper that for optimizing stochastic linear functions over compact sets, the sample average estimator *is* admissible. Moreover, we study problems with convex quadratic objectives subject to box constraints. Stein's paradox holds when there are no constraints and the dimension of the problem is at least three. We show that in the presence of box constraints, admissibility is recovered for dimensions 3 and 4.

Keywords: stochastic optimization, admissibility, Stein's paradox, statistical decision theory

Category 1: Stochastic Programming

Citation:

Download: [PDF]

Entry Submitted: 10/05/2019
Entry Accepted: 10/06/2019
Entry Last Modified: 10/05/2019

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society