Markov Decision Process

A Markov Decision Process (MDP) is a mathematical framework for modeling Decision-making under uncertainty, where outcomes depend only on the current state and chosen action—not on history. This memoryless property (the "Markov" assumption) makes MDPs tractable for computing optimal strategies.

An MDP consists of states, actions, transition probabilities, and rewards. At each step, an agent observes its state, selects an action, receives immediate reward, and transitions to a new state. The goal is to find a policy—a mapping from states to actions—that maximizes cumulative future reward over time.

MDPs power Reinforcement learning, where agents learn policies without explicit instructions. They appear everywhere: robot Reasoning, game AI, resource allocation, medical treatment planning in clinical contexts, and autonomous vehicles navigating uncertain environments.

The challenge lies in solving MDPs efficiently. Classical approaches like Dynamic programming work for small state spaces, but real-world problems often demand approximation. Modern techniques blend MDPs with neural networks to handle complexity.

Though rooted in control theory and operations research since the mid-20th century, MDPs remain foundational to AI because they elegantly balance tractability with expressiveness—capturing genuine uncertainty while staying computationally grounded.

Related

Reinforcement learning, Temporal Logic, Stochastic processes, Bellman equation, Policy gradient, Dynamic programming