Markov Decision Processes

Definition

Markov Decision Processes (MDPs) are mathematical frameworks used to model decision-making in situations where outcomes are partly random and partly under the control of a decision maker. They consist of states, actions, transition probabilities, and rewards, allowing for the formulation of optimal policies that dictate the best action to take in each state to maximize cumulative rewards over time. MDPs are foundational in fields like reinforcement learning, where they help agents learn how to make decisions based on their environment.

5 Must Know Facts For Your Next Test

1. MDPs are defined by five components: a set of states, a set of actions, transition probabilities, reward functions, and discount factors.
2. The Bellman equation is crucial for solving MDPs as it relates the value of a state to the values of subsequent states following a given policy.
3. Optimal policies in MDPs can be found using dynamic programming methods such as value iteration and policy iteration.
4. MDPs assume the Markov property, which states that future states depend only on the current state and action, not on the history of past states.
5. Applications of MDPs extend beyond robotics and AI into economics, operations research, and any field requiring optimal decision-making under uncertainty.

Review Questions

• How do Markov Decision Processes model the relationship between states, actions, and rewards?
  • Markov Decision Processes model this relationship by defining a set of states where an agent can exist, a set of actions that the agent can take from each state, and a reward function that assigns values based on the actions taken. The transitions between states depend on both the current state and the chosen action, governed by transition probabilities. This framework enables the agent to evaluate which actions yield the highest expected cumulative reward over time.
• Discuss the significance of the Bellman equation in solving Markov Decision Processes.
  • The Bellman equation is significant because it provides a recursive relationship that helps compute the value of each state in an MDP based on immediate rewards and future expected values. By applying this equation iteratively, agents can evaluate and improve their policies, ensuring they choose actions that maximize long-term rewards. Solving MDPs using the Bellman equation is essential for developing effective strategies in reinforcement learning.
• Evaluate how the Markov property impacts decision-making strategies in reinforcement learning environments modeled as MDPs.
  • The Markov property simplifies decision-making strategies by asserting that future state transitions depend solely on the current state and action taken, without regard to past states. This characteristic allows reinforcement learning algorithms to efficiently learn optimal policies since they can rely on current observations rather than needing extensive historical data. As a result, agents can quickly adapt their strategies to dynamic environments, making MDPs a powerful tool for real-time decision-making.

Related terms

States: Distinct configurations or situations in which an agent can find itself while interacting with an environment.

Policies: A strategy or mapping from states to actions that dictates the behavior of an agent in an MDP.

Reinforcement Learning: A type of machine learning where agents learn to make decisions by receiving feedback from their actions in the form of rewards or penalties.