What are Markov Decision Processes (MDPs) in reinforcement learning?

What are Markov Decision Processes (MDPs) in reinforcement learning? Markov Decision Processes (MDPs) are mathematical frameworks used to model decision-making in situations where outcomes are partly random and partly under the control of a decision-maker (an agent). In reinforcement learning (RL), MDPs provide a structured way to represent an environment where an agent learns to take actions to maximize cumulative rewards. An MDP consists of states (possible configurations of the environment), actions (choices the agent can make), transition probabilities (likelihood of moving between states after an action), rewards (feedback for actions), and a discount factor (to prioritize immediate vs. future rewards). For example, in a robot navigation task, states could represent the robot’s location, actions could be movement directions, and rewards might be given for reaching a goal. The core idea is that the agent interacts with the environment by observing states, taking actions, and adapting based on rewards.

Key Components and the Markov Property The strength of MDPs lies in their components and the Markov property, which states that the future depends only on the current state and action, not on prior history. States encapsulate all necessary information to make decisions, simplifying the problem. For instance, consider a delivery drone deciding its path: the current battery level and location (state) determine possible actions (fly, recharge), transition probabilities (e.g., 90% chance of reaching the next waypoint), and rewards (penalties for delays, bonuses for on-time delivery). The transition probabilities and rewards are often represented as matrices or functions. A discount factor (e.g., 0.9) ensures the agent values near-term rewards more highly than distant ones, balancing immediate and long-term goals. This structure allows developers to model complex, stochastic environments systematically.

Solving MDPs and Applications Solving an MDP involves finding an optimal policy—a rule that tells the agent which action to take in each state to maximize total rewards. Algorithms like value iteration or policy iteration calculate the expected long-term reward (value) of states or actions, iteratively refining estimates until convergence. For example, a warehouse robot might use Q-learning (an RL algorithm based on MDPs) to learn the fastest routes by updating its action-value estimates based on trial and error. Practical challenges include handling large state spaces (e.g., video games with millions of pixels) and balancing exploration (trying new actions) with exploitation (using known good actions). MDPs are widely used in robotics, game AI, resource allocation, and healthcare—any domain requiring sequential decision-making under uncertainty. Their mathematical rigor makes them a foundational tool for RL, enabling developers to formalize problems and test solutions systematically.