Description: The Markov Decision Process (MDP) is a mathematical framework used to model decisions in situations where outcomes are partly random and partly under the control of the decision-maker. An MDP is formally defined by a set of states, a set of actions, a state transition function, and a reward function. In this context, a ‘state’ represents the current situation of the system, while an ‘action’ is a decision that can be made to influence the system’s state. The transition function describes how actions affect the probability of moving from one state to another, and the reward function assigns a value to each state or action, indicating the utility or benefit gained from taking an action in a given state. MDPs are fundamental in reinforcement learning as they provide a structure for agents to learn optimal decision-making through exploration and exploitation of their environment. This approach allows agents to maximize accumulated rewards over time, which is essential in applications ranging from robotics to gaming and optimization of complex systems.
History: The concept of Markov Decision Process was introduced in the 1950s by Richard Bellman, who developed dynamic programming. Bellman formulated the principle of optimality, which is fundamental for solving MDPs. Over the decades, the MDP framework has evolved and been integrated into various research areas, including artificial intelligence and game theory.
Uses: MDPs are used in a variety of fields, including robotics, where robots must make decisions in uncertain environments; in economics, to model decision-making under uncertainty in investment; and in artificial intelligence, especially in reinforcement learning, where agents learn to maximize rewards in complex environments.
Examples: A practical example of MDP is the use of reinforcement learning algorithms in video games, where an agent learns to play by optimizing its decisions based on the rewards obtained. Another example is route planning in logistics, where the goal is to minimize costs and delivery times in uncertain environments.
