A Markov Decision Process (MDP) is a mathematical framework for modeling decision-making in situations where outcomes are partly random and partly under the control of a decision-maker. It’s a fundamental concept in reinforcement learning.
Components of an MDP
- States (S): A set of possible world states.
- Actions (A): A set of possible actions the agent can take.
- Transition probabilities (P): The probability of transitioning to a new state given the current state and action taken.
- Rewards (R): A function that maps state-action pairs to a scalar reward.
- Discount factor (γ): A value between 0 and 1 that determines the importance of future rewards.
The Markov Property
The core assumption of an MDP is the Markov property, which states that the future state depends only on the current state and the action taken, not on the entire history of the process.
Solving MDPs
The goal in an MDP is to find an optimal policy, which is a function that maps states to actions, maximizing the expected cumulative reward. Several algorithms can be used to solve MDPs, including:
- Value iteration: Iteratively updates the value function until convergence.
- Policy iteration: Alternates between policy evaluation and policy improvement.
- Dynamic programming: Exploits the underlying structure of the MDP to solve it efficiently.
Challenges in MDPs
- Large state and action spaces: Many real-world problems have extremely large state and action spaces, making exact solutions computationally intractable.
- Unknown dynamics: In many cases, the transition probabilities and rewards are unknown, requiring learning from experience.
- Partial observability: The agent may not have access to the complete state information.
Applications of MDPs
MDPs are applied in various fields, including:
- Robotics: Planning robot actions in uncertain environments.
- Finance: Portfolio optimization and risk management.
- Inventory management: Deciding optimal inventory levels.
- Healthcare: Treatment planning and patient management.
What is a transition probability in an MDP?
The transition probability specifies the likelihood of moving from one state to another given an action.
What is a reward in an MDP?
A reward is a scalar feedback signal indicating the goodness or badness of a state-action pair.
What is a discount factor in an MDP?
The discount factor determines the importance of future rewards.
What are the challenges in solving MDPs?
Large state and action spaces, unknown dynamics, and partial observability.
Where are MDPs used?
MDPs are applied in robotics, finance, inventory management, healthcare, and other fields.
What is the goal of an MDP?
The goal is to find an optimal policy that maximizes the expected cumulative reward.