What are the four key components of a Markov Decision Process (MDP)?

The four key components of a Markov Decision Process (MDP) are states, actions, transition probabilities, and rewards. States represent the different situations or configurations the agent can be in. The set of all possible states is often denoted by 'S'. For example, in a game of chess, a state would represent the current arrangement of pieces on the board. Actions are the choices the agent can make in each state. The set of all possible actions is often denoted by 'A'. For example, in chess, an action would be a legal move of a piece. Transition probabilities define the probability of transitioning from one state to another after taking a specific action. They are often denoted by 'P(s' | s, a)', representing the probability of ending up in state 's'' after taking action 'a' in state 's'. For example, in a simplified environment, taking a 'move forward' action might have a 80% chance of actually moving forward and a 20% chance of staying in the same place due to unforeseen circumstances. Rewards are numerical values that the agent receives after transitioning to a new state. They quantify the desirability of being in that state. Rewards are often denoted by 'R(s, a, s')', representing the reward received after taking action 'a' in state 's' and transitioning to state 's''. For example, in a game, reaching a winning state might give a large positive reward, while losing might give a negative reward. These four components define the environment in which the agent operates and provide the basis for learning an optimal policy, which is a strategy for choosing actions that maximize the cumulative reward over time.