# Optimal Policies for MDPs (Optimal Policies for MDPs)

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## Description

In an MDP, a policy is a choice of what action to choose at each state An Optimal Policy is a policy where you are always choosing the action that maximizes the “return”/”utility” of the current state. The problem here is to find such an optimal policy from a given MDP.

## Parameters

$n$: number of states

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Bellman Value Iteration (VI) | 1957 | $O({2}^n)$ | $O(n)$ | Exact | Deterministic | Time |

Howard Policy Iteration (PI) | 1960 | $O(n^{3})$ | $O(n)$ | Exact | Deterministic | Time |

Puterman Modified Policy Iteration (MPI) | 1974 | $O(n^{3})$ | $O(n)$ | Exact | Deterministic |

## Time Complexity Graph

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