Markov decision processes (MDPs) are a mathematical framework used to model decision-making in environments where outcomes are partially random and partially under the control of an agent. They relate directly to AI reasoning by providing a structured way to represent problems that involve sequential decisions, uncertainty, and optimization of long-term rewards. In AI systems, reasoning often requires balancing immediate actions with future consequences, and MDPs formalize this through states, actions, transition probabilities, and rewards. For example, a robot navigating a maze uses an MDP to decide which direction to move, weighing the chance of hitting a wall against the goal of reaching the exit efficiently.
At its core, an MDP breaks down a problem into states (the current situation), actions (possible choices), and transitions (how actions change states probabilistically). The agent’s goal is to learn a policy—a rule that maps states to actions—to maximize cumulative rewards. This aligns with AI reasoning because it forces the system to account for uncertainty (e.g., sensor noise in a self-driving car) and plan steps ahead. Algorithms like value iteration or Q-learning solve MDPs by iteratively estimating the value of each state, which represents the expected long-term reward. For instance, in a recommendation system, an MDP could model user interactions, where recommending a movie now affects future engagement, and the AI must balance exploration (trying new genres) against exploitation (sticking to known preferences).
Developers use MDPs in reinforcement learning (RL), a subset of AI where agents learn by interacting with an environment. Real-world applications include game AI (e.g., teaching a character to navigate a dynamic game world), resource management (e.g., optimizing server allocation in cloud computing), or healthcare (e.g., treatment planning with uncertain patient responses). However, MDPs assume the environment is fully observable, which isn’t always true. Extensions like partially observable MDPs (POMDPs) address this but add complexity. Understanding MDPs helps developers design systems that reason under uncertainty, prioritize goals, and adapt policies as data accumulates. For example, a delivery drone using an MDP might adjust its route in real-time based on weather changes while ensuring timely deliveries and battery efficiency.