Convex optimization for Monte Carlo : stochastic optimization for importance sampling
Abstract/Contents
- Abstract
- In Monte Carlo simulations it is often essential that a method is accompanied by an appropriate variance reduction method. Reducing the variance of a Monte Carlo method is, at least conceptually, an optimization problem, and mathematical optimization has indeed been used as a theoretical and conceptual tool in this pursuit. However, traditional Monte Carlo methods have only used numerical optimization sparingly, and convex optimization even less. Numerical optimization is study of algorithms for finding a solution to an optimization problem, as opposed to the study of analytical solutions of an optimization problem. Convex optimization is the study of convex optimization problems, a subclass of optimization problems for which efficient algorithms for finding the global optimum exists. In this work we present a framework for using convex optimization for Monte Carlo. More specifically, we present a framework for using stochastic convex optimization for adaptive importance sampling, self-normalized importance sampling, and what-if simulations. The main idea is to perform importance sampling and numerical optimization simultaneously. In particular, the numerical optimization does not rely on blackbox optimization solvers, and this allows the computational cost of each iteration to remain cheap. Because the optimization is performed on a convex problem, we can establish convergence and optimality.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Ryu, Ernest K |
|---|---|
| Associated with | Stanford University, Department of Computational and Mathematical Engineering. |
| Primary advisor | Boyd, Stephen P |
| Thesis advisor | Boyd, Stephen P |
| Thesis advisor | Duchi, John |
| Thesis advisor | Owen, Art B |
| Advisor | Duchi, John |
| Advisor | Owen, Art B |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Ernest K. Ryu. |
|---|---|
| Note | Submitted to the Department of Computational and Mathematical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Ernest Kang Ryu
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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