A Markov Decision Process (MDP) is a mathematical framework used for modeling decision-making situations where outcomes are partly random and partly under the control of a decision-maker. An MDP provides a formalism for defining the environment in which an agent operates, including states, actions, transitions between states, and rewards. Each element plays a key role: the states represent the possible configurations the agent can find itself in, actions are the choices available to the agent at each state, and rewards give feedback on the desirability of outcomes.
In an MDP, the Markov property is crucial. It states that the future state of the process depends only on the current state and the action taken, not on the sequence of events that preceded it. This means that if you know the current state and the action taken, you can predict the next state without needing to know the history. This feature simplifies the modeling of decision-making problems, making it easier for developers to design algorithms that learn optimal policies—sets of actions that maximize expected rewards over time.
A practical example of MDP can be seen in robotics. Suppose you’re programming a robot to navigate a grid-like environment. The states could be the different grid positions, actions could include moving up, down, left, or right, and the rewards might be based on reaching goals or avoiding obstacles. By using MDPs, the robot can evaluate its actions based on the rewards and transition probabilities, enabling it to choose paths that maximize its overall success despite uncertainties in movement or changes in the environment. Overall, MDPs provide a structured way for developers to approach complex decision-making tasks in various fields.