A Markov Decision Process (MDP) is a mathematical framework used to model decision-making situations where outcomes are partly random and partly under the control of a decision-maker. The key components of an MDP include a set of states, a set of actions, a transition function, a reward function, and a discount factor. Together, these components work to define how an agent interacts with its environment to optimize its decision-making over time.
First, the set of states represents all possible situations the agent can encounter. Each state contains the information needed to make decisions. For instance, in a simple grid world, states can be represented by the positions of the agent within the grid. The set of actions encompasses all the possible moves or choices the agent can make from any given state. For example, in the same grid world, actions might include moving up, down, left, or right. The interaction between states and actions forms the basis of how the agent navigates through its environment.
Next, we have the transition function, which describes the probability of moving from one state to another after taking a specific action. This function accounts for the inherent randomness in the process. For instance, if an agent attempts to move right, there might be a probability that it slips and ends up in the left state instead. The reward function assigns a numerical value to each state or state-action pair, representing the immediate benefit the agent receives. Finally, the discount factor determines the importance of future rewards compared to immediate rewards. For example, a discount factor close to 1 values long-term rewards almost as highly as short-term rewards, whereas a factor close to 0 prioritizes immediate rewards. Together, these components structure the decision-making process in an MDP, allowing agents to find optimal strategies in uncertain environments.