MCMC with substitutions and multi-armed bandits with covariates : theory and applications
Abstract/Contents
- Abstract
- The first part introduces a new approach to nonparametric multi-armed bandit theory involving both the bandit and the covariate processes. The extension to bandit processes with a non-denumerable set of arms is also discussed. The approach developed herein can be readily extended to continuous-time processes by using arm elimination. It also carries out a stochastic search for a nearly optimal arm at covariate values in a given set before applying arm elimination. The procedure is shown to attain the asymptotically minimal rates for the regret over the given set. The second part discusses a new adaptive MCMC algorithm where acceptance rates are significantly improved. The basic idea is to approximate a target distribution by the empirical distribution of representative atoms, chosen sequentially by an MCMC scheme so that the distribution converges weakly to the target distribution as the number of iterations goes to infinity. We also establish the asymptotic normality of the Monte Carlo estimate of a functional of the target distribution and provide a consistent estimator of its standard error. The third part builds a data-driven methodology for the performance reliability and the improvement of sensor algorithms for automated driving perception tasks. The methodology takes as input three elements: one or various algorithms for object detection when the input is an image, a dataset of camera images that represents a sample from an environment, and a simple policy that serves as a proxy for a task such as driving assistance. We develop a statistical estimator, which combines these elements and a data augmentation technique, in order to rank the reliability of perception algorithms which is measured as the chance of collision given the speed of the ego vehicle and the distance to the closest object in range.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Xu, Huanzhong |
|---|---|
| Degree supervisor | Blanchet, Jose H |
| Thesis advisor | Blanchet, Jose H |
| Thesis advisor | Hong, Han |
| Thesis advisor | Lu, Ying, 1960- |
| Degree committee member | Hong, Han |
| Degree committee member | Lu, Ying, 1960- |
| Associated with | Stanford University, School of Engineering |
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Huanzhong Xu. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/xh086kx1071 |
Access conditions
- Copyright
- © 2023 by Huanzhong Xu
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