What is a Markov Decision Process (MDP)?

A Markov Decision Process (MDP) is a mathematical framework used to model decision-making in situations where outcomes are partially random and partially under the control of a decision-maker. It consists of states, actions, transition probabilities, rewards, and a discount factor. States represent distinct scenarios the system can be in, actions are choices available to the decision-maker, transition probabilities define how actions move the system between states, and rewards quantify the immediate benefit of taking an action in a state. The discount factor balances immediate versus future rewards. MDPs are foundational in reinforcement learning and optimal control, as they formalize how an agent can achieve long-term goals through sequential decisions.

An MDP operates under the Markov property, meaning the next state and reward depend only on the current state and action, not on prior history. For example, consider a robot navigating a grid. Each grid cell is a state, and actions like “move north” or “grab object” transition the robot to adjacent cells with some probability (e.g., 80% success, 20% slip). Rewards might be +10 for reaching a goal, -1 for hitting a wall, and 0 otherwise. The agent’s goal is to learn a policy—a rule mapping states to actions—that maximizes cumulative rewards over time. Solving an MDP typically involves computing value functions (expected long-term reward from a state) or policies directly using algorithms like value iteration or policy iteration.

Developers use MDPs to model problems like game AI, resource allocation, or autonomous systems. For instance, in a recommendation system, states could represent user contexts (e.g., browsing history), actions are item recommendations, and rewards reflect user engagement. Transition probabilities model how recommendations affect user behavior. Algorithms like Q-learning, which approximates optimal policies without knowing the full MDP dynamics, are practical tools derived from this framework. Libraries such as OpenAI Gym provide environments to simulate MDP-based problems, enabling developers to test reinforcement learning agents. Understanding MDPs helps in designing systems that balance exploration (trying new actions) and exploitation (using known rewards), a core challenge in adaptive decision-making.