What is a Markov decision process (MDP) algorithm in C and how is it implemented?

Table of Contents

• Introduction
• Components of a Markov Decision Process
• Implementation in C
  • Example: Simple MDP Implementation
    • Example Code for MDP in C:
  • Explanation of the Code
• Conclusion

Introduction

A Markov Decision Process (MDP) is a mathematical framework used for modeling decision-making in situations where outcomes are partly random and partly under the control of a decision-maker. MDPs are widely applicable in various fields, including robotics, economics, and artificial intelligence, particularly in reinforcement learning scenarios. This framework allows agents to make optimal decisions based on the states, actions, rewards, and transitions in their environment.

Components of a Markov Decision Process

An MDP consists of the following components:

1. States (S): A finite set of states representing the possible situations an agent can be in.
2. Actions (A): A finite set of actions available to the agent in each state.
3. Transition Function (P): A probability function that describes the likelihood of moving from one state to another given a specific action.
4. Reward Function (R): A function that assigns a numerical reward for each state-action pair.
5. Discount Factor (γ): A value between 0 and 1 that indicates the importance of future rewards compared to immediate rewards.

Implementation in C

Example: Simple MDP Implementation

Below is a basic implementation of a Markov Decision Process in C. This example models a simple 2x2 grid environment where an agent can move and receives rewards for certain actions.

Example Code for MDP in C:

Explanation of the Code

• Constants: Defines the number of rows and columns in the grid, along with the discount factor (GAMMA) and convergence threshold (THETA).
• Value Iteration Function: The valueIteration function computes the value function using the Bellman equation until convergence. It updates the value based on possible actions (up, down, left, right).
• Reward Structure: The reward matrix defines rewards for each state, with a specific reward for reaching the goal state.
• Main Function: Initializes the reward matrix, calls the value iteration function, and displays the resulting value function.

Conclusion

The Markov Decision Process (MDP) is a crucial framework for modeling decision-making under uncertainty in environments. The C implementation provided demonstrates how to use value iteration to compute the value function based on state transitions and rewards. MDPs serve as the foundation for many reinforcement learning algorithms and applications, offering a structured approach to complex decision-making problems.