Sample Average Approximation For Functional Decisions Under Shape Constraints
- Resource Type
- Conference
- Authors
- Singham, Dashi I.; Lam, Henry
- Source
- 2020 Winter Simulation Conference (WSC) Winter Simulation Conference (WSC), 2020. :2791-2799 Dec, 2020
- Subject
- Computing and Processing
General Topics for Engineers
Uncertainty
Estimation
Approximation algorithms
Random variables
Numerical models
Optimization
Convergence
- Language
- ISSN
- 1558-4305
Sample average approximation methods are most often applied when the set of decision variables is finite. This research develops a method of finding optimal solutions to infinite-dimensional simulation optimization problems when the decision variable is a monotone function on a random variable used to model the uncertainty itself. This problem is motivated from approximately solving the principal-agent problem in economics, but also has close connections to nonparametric statistical estimation. We demonstrate how to approximate the infinite-dimensional problem with a discrete formulation that allows the use of standard sample average approximation methods. We also demonstrate how to utilize related bounding techniques on the optimal value, and show convergence results for the estimated optimal values and solutions.