---
title: "The MDP2 package"
author: "Lars Relund <lars@relund.dk>"
date: "`r Sys.Date()`"
bibliography: litt.bib
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{MDP2}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options: 
  chunk_output_type: console
---

<style> 
p {text-align: justify;} 
//.sourceCode {background-color: white;}
pre {
  // border-style: solid;
  // border-width: 1px;
  // border-color: grey;
  //background-color: grey !important;
}
img {
   //width: 100%;
   border: 0;
}
</style>

<!-- scale math down -->
<script type="text/x-mathjax-config"> 
    MathJax.Hub.Config({ 
        "HTML-CSS": { scale: 80 }
        });
</script>

```{r setup, include=FALSE}
library(knitr)
options(rmarkdown.html_vignette.check_title = FALSE,
        # formatR.arrow = TRUE, 
        # scipen=999, 
        # digits=5,
        width=90) 
#thm <- knit_theme$get("edit-kwrite")   # whitengrey, bright, print, edit-flashdevelop, edit-kwrite
#knit_theme$set(thm)
knitr::opts_chunk$set(
   # collapse = TRUE,
   comment = "#>",
   fig.align = 'center',
   fig.width = 9,
   fig.height = 5,
   fig.show = 'hold',
   out.extra = 'style="max-width:100%;"',
   # tidy = TRUE,
   # prompt=T,
   # comment=NA,
   cache = F
   # background = "red"
)
library(magrittr)
library(dplyr)
```


The `MDP2` package in R is a package for solving Markov decision processes (MDPs) with discrete 
time-steps, states and actions. Both traditional MDPs [@Puterman94], semi-Markov decision processes
(semi-MDPs) [@Tijms03] and hierarchical-MDPs (HMDPs) [@Kristensen00] can be solved under a finite
and infinite time-horizon.

Building and solving an MDP is done in two steps. First, the MDP is built and saved in a set 
of binary files. Next, you load the MDP into memory from the binary files and apply various
algorithms to the model.

The package implement well-known algorithms such as policy iteration and value iteration
under different criteria e.g. average reward per time unit and expected total discounted reward. The
model is stored using an underlying data structure based on the *state-expanded directed hypergraph*
of the MDP (@Relund06) implemented in `C++` for fast running times. <!-- Under development is also
support for MLHMP which is a Java implementation of algorithms for solving MDPs (@Kristensen03). 
-->

To illustrate the package capabilities have a look at the vignettes:

   * Building MDP models `vignette("building")`.
   * Solving an infinite-horizon MDP (semi-MDP) `vignette("infinite-mdp")`.
   * Solving a finite-horizon MDP (semi-MDP) `vignette("finite-mdp")`.
   * Solving an infinite-horizon HMDP `vignette("infinite-hmdp")`.


## References