Fundamental of Artificial Intelligence - MDP Algorithm

This repository contains my MDP algorithm assignment for the Fundamental of Artificial Intelligence course at An-Najah National University (NNU).

Overview

This project implements the Value Iteration algorithm for Markov Decision Processes (MDP). The Value Iteration algorithm is used to determine the optimal policy and value function for a given set of states and transition probabilities.

Problem Description

In Artificial Intelligence, many real-world problems can be modeled as Markov Decision Processes (MDPs). An MDP is a mathematical framework used to model decision-making problems where outcomes are partially random and partially under the control of a decision-maker. The MDP algorithm is a solution method for determining the optimal policy, which defines the best action to take in each state to maximize long-term rewards.

Why MDP Algorithm?

The MDP algorithm is valuable because it provides a systematic approach to decision-making in uncertain environments. By modeling a problem as an MDP, we can find the optimal policy that maximizes expected rewards over time. This is particularly useful in various domains such as robotics, finance, healthcare, and more.

How MDP Works

MDP works by iteratively updating the value function for each state-action pair based on the expected future rewards. The algorithm calculates the value of being in a particular state and taking a particular action, considering the immediate reward and the expected future rewards discounted by a factor called the discount factor (gamma). By repeating this process, the algorithm converges to the optimal value function and policy.

Features

• Value Iteration: Computes the value function for each state-action pair and determines the optimal policy.
• Value History Display: Prints the value history in a tabular format using pandas.
• Optimal Policy Display: Prints the optimal policy for each state.

Getting Started

1. Clone this repository to your local machine:

git clone [email protected]:IsmaelMousa/mdp-value-iteration.git

2. Navigate to the mdp-value-iteration directory:

cd mdp-value-iteration

3. Setup virtual environment:

python3 -m venv .venv

4. Activate the virtual environment:

source .venv/bin/activate

5. Install the required dependencies:

make install

6. Run the program:

make run

Results

Without Discount Factor: 
i        0      1        2           3           4
S1 a1  0.0  100.0  100.100  100.101089  100.101190
S1 a2  0.0   90.0  101.089  101.189989  101.191178
S2 a3  0.0   11.0   11.100   11.101089   11.101190
S3     0.0    0.0    0.000    0.000000    0.000000

Optimal Policy: 
Optimal action for state S1: a2
Optimal action for state S2: a3

--------------------------------------------------

With Discount Factor = 0.9: 
i        0      1         2           3           4
S1 a1  0.0  100.0  100.0900  100.090081  100.090081
S1 a2  0.0   90.0   99.9801  100.061100  100.061173
S2 a3  0.0   11.0   11.0900   11.090081   11.090081
S3     0.0    0.0    0.0000    0.000000    0.000000

Optimal Policy: 
Optimal action for state S1: a1
Optimal action for state S2: a3

Conclusion

In conclusion, the MDP algorithm provides a powerful framework for modeling and solving decision-making problems in artificial intelligence. By understanding the problem description, the workings of MDP, and the output it generates, one can effectively apply this algorithm to a wide range of real-world scenarios.