Abstract
where the function f or its gradient rf are not directly accessible except through Monte Carlo estimates, we present three solution algorithms: fixed-step for infinite population sampling, fixed-step for finite population sampling, and line search for infinite population sampling. The salient feature of each of these algorithms is that the Monte Carlo sampling is adaptive to the algorithm trajectory, sampling little when the algorithm iterates are assessed to be far away from a first-order critical point and sampling more when the algorithm iterates are assessed to be close to a first-order critical point. We show that a specific form of such adaptive sampling that balances the squared bias and variance of gradient estimates achieves global convergence to a first-order critical point in addition to enjoying the fastest achievable convergence under Monte Carlo sampling. Our numerical experience on popular example problems shows promise.
Degree Type
Thesis
Degree Name
Master of Science in Industrial Engineering (MSIE)
Department
Industrial Engineering
Committee Chair
Raghu Pasupathy
Committee Co-Chair
Hong Wan
Date of Award
5-2018
Recommended Citation
Tan, Hui, "Adaptive Sampling Fixed-Step and Line Search Methods For Stochastic Optimization" (2018). Open Access Theses. 1463.
https://docs.lib.purdue.edu/open_access_theses/1463
Committee Member 1
Gesualdo Scutari