2016-09-19 10:00:00 2016-09-19 11:00:00 America/Indiana/Indianapolis PhD Seminar - Sara Shashaani 'Adaptive Sampling Trust-Region Methods for Derivative-Based and Derivative-Free Simulation Optimization' GRIS 316
PhD Seminar - Sara Shashaani
Event Date: | September 19, 2016 |
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Hosted By: | Raghu Pasupathy and Susan Hunter |
Time: | 10:00-11:00 AM |
Location: | GRIS 316 |
Contact Name: | Cheryl Barnhart |
Contact Phone: | 765-494-5434 |
Contact Email: | cbarnhar@purdue.edu |
Open To: | all |
Priority: | No |
School or Program: | Industrial Engineering |
ABSTRACT
We consider unconstrained optimization problems where only ``stochastic" estimates of the objective function are available as replicates from a Monte Carlo oracle.
In the first study we assume that the function gradients are directly observable through the Monte Carlo simulation. We present ASTRO --- an adaptive sampling based trust-region optimization method where a stochastic local model is constructed, optimized, and updated iteratively. ASTRO is a derivative-based algorithm and provides almost sure convergence to a first-order critical point.
In the second study the Monte Carlo oracle is assumed to provide no direct observations of the function gradient. We present ASTRO-DF --- a class of derivative-free trust-region algorithms, where the stochastic local model is obtained through interpolation. We demonstrate the almost-sure convergence of ASTRO-DF's iterates to a first-order critical point. The question of using more complicated models, e.g., regression or stochastic kriging, in combination with adaptive sampling is worth further investigation and will benefit from the methods of proof presented in this study.
Function (and gradient) estimation and model construction within ASTRO and ASTRO-DF are adaptive in the sense that continuously monitoring and balancing metrics of sampling and structural errors determine the extent of Monte Carlo sampling. Such balancing of errors is designed to ensure that Monte Carlo effort within ASTRO and ASTRO-DF is sensitive to algorithm trajectory, meaning more sampling when an iterate is inferred to be close to a critical point and less sampling when far away. We investigate the implementation of ASTRO and propose heuristics that enhance the implementation of ASTRO-DF. Finite-time performance of these algorithms is reported on a series of low to moderate dimensional problems.