---
title: "Sampling Multiple Parameter Sets at Once"
author: "Samuel Wilson"
date: "February 9, 2020"
output: html_document
vignette: >
  %\VignetteIndexEntry{Sampling Multiple Parameter Sets at Once}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
backup_options <- options()
options(width = 1000)
set.seed(1991)
```

### Sampling Local Optimums

Sometimes we may want to sample multiple promising parameter sets at the same time. This is especially effective if the process is being run in parallel. The ```bayesOpt``` function always samples the global optimum of the acquisition function, however it is also possible to tell it to sample local optimums of the acquisition function at the same time.
  
Using the ```acqThresh``` parameter, you can specify the minimum percentage utility of the global optimum required for a different local optimum to be considered. As an example, let's say we are optimizing 1 hyperparameter ```min_child_weight```, which is bounded between [0,5]. Our acquisition function may look like the following:

```{r, eval = TRUE, echo=FALSE, out.width = "600px", fig.align = "center"}
knitr::include_graphics("UCB.png")
```

In this case, there are 3 promising candidate parameters. We may want to run our scoring function on all 3. If ```acqThresh``` is set to be below ~0.95, and ```iters.k``` is set to at least 3, the process would use all 3 of the local maximums as candidate parameter sets in the next round of scoring function runs.

### Adding Noise  
If there are only 2 local optimums, and ```iters.k``` is 3, we still need to obtain another parameter set to run. We could choose a random parameter set within the bounds, however it is usually more worthwhile to decrease uncertainty around the promising points. Therefore, ```bayesOpt``` will randomly select points around our local optimums to sample if there aren't enough local optimums to satisfy ```iters.k```.

```{r revert_options, include=FALSE}
options(backup_options)
```