Markov Decision Process (MDP) is a mathematical framework for modeling decision-making problems in a stochastic environment. It is one of the essential tools in Reinforcement Learning (RL).
In MDP, an agent interacts with an environment based on the current state and the action taken by the agent. The environment responds with a reward and a new state. The system is modeled as a tuple (S, A, P, R, ), where:
- S: the set of possible states in the environment.
- A: the set of actions available to the agent.
- P: the probability distribution of transitioning from one state to another, given an action.
- R: the reward function that maps a state-action pair to a scalar reward value.
- : the discount factor that balances the importance of immediate rewards versus future rewards.
Reinforcement Learning, on the other hand, is a type of machine learning concerned with how agents learn to make decisions in an uncertain and dynamic environment. An RL agent learns from experience by interacting with the environment, observing the state and reward information, and adjusting its behavior to maximize the expected long-term reward. The MDP and RL are related because the former provides a formal framework for modeling decision-making problems, and the latter utilizes this framework to learn optimal policies for the agent.
For example, consider a game where an agent must navigate through a grid, collecting rewards and avoiding obstacles. In this game, the state can be the current position of the agent in the grid, the set of actions could be the directions (up, down, left, and right), and the reward could be the points received for collecting items. If the agent moves to a new position, transition probabilities from the current state to the new state could depend on the chosen action and the current environment conditions. The objective of the agent would be to maximize the total number of rewards collected while navigating, which could be achieved through RL algorithms that learn from the state and action information.