Journal article
Comparison-Based Algorithms for One-Dimensional Stochastic Convex Optimization
INFORMS journal on optimization, Vol.2(1), pp.34-56
01/2020
DOI: 10.1287/ijoo.2019.0022
Abstract
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the newsvendor problem) or the objective values at the sampled points (e.g., the lost sales cost), which might not be available in practice. In this paper, we consider a new setup for stochastic optimization, in which the decision maker has access to only comparative information between a random sample and two chosen decision points in each iteration. We propose a comparison-based algorithm (CBA) to solve such problems in one dimension with convex objective functions. Particularly, the CBA properly chooses the two points in each iteration and constructs an unbiased gradient estimate for the original problem. We show that the CBA achieves the same convergence rate as the optimal stochastic gradient methods (with the samples observed). We also consider extensions of our approach to multidimensional quadratic problems as well as problems with nonconvex objective functions. Numerical experiments show that the CBA performs well in test problems.
Details
- Title: Subtitle
- Comparison-Based Algorithms for One-Dimensional Stochastic Convex Optimization
- Creators
- Xi Chen - New York UniversityQihang Lin - University of IowaZizhuo Wang - University of Minnesota
- Resource Type
- Journal article
- Publication Details
- INFORMS journal on optimization, Vol.2(1), pp.34-56
- DOI
- 10.1287/ijoo.2019.0022
- ISSN
- 2575-1484
- eISSN
- 2575-1492
- Language
- English
- Date published
- 01/2020
- Academic Unit
- Business Analytics
- Record Identifier
- 9984380593602771
Metrics
1 Record Views