Markov Decision Process (MDP)

A Markov Decision Process (MDP) is a mathematical framework for modeling decision-making in situations where outcomes are partly random and partly under the control of a decision-maker. It is a foundational concept in Reinforcement Learning (RL), providing a formal way to describe an environment. An agent interacts with this environment by observing its state and choosing an action, with the goal of maximizing a cumulative reward signal over time. The core idea is based on the Markov property, which assumes that the future is independent of the past given the present; in other words, the current state provides all the necessary information to make an optimal decision.

How Markov Decision Processes Work

An MDP is defined by several key components that describe the interaction between an agent and its environment:

• States (S): A set of all possible situations or configurations the agent can be in. For example, the location of a robot in a room or the inventory level of a product.
• Actions (A): A set of all possible moves the agent can take in each state. For a robot, this could be moving forward, left, or right.
• Transition Probability: The probability of moving from a current state to a new state after taking a specific action. This captures the uncertainty in the environment, such as a robot's wheels slipping.
• Reward Function: A signal that indicates the immediate value of transitioning to a new state. Rewards can be positive or negative and guide the agent toward desirable outcomes.
• Policy (π): The strategy the agent uses to select actions in each state. The ultimate goal of solving an MDP is to find an optimal policy—one that maximizes the total expected reward over the long run.

The process is cyclical: the agent observes the current state, selects an action based on its policy, receives a reward, and moves to a new state. This loop continues, allowing the agent to learn from its experiences.

Real-World Applications

MDPs are used to model a wide range of sequential decision-making problems.

1. Robotics and Autonomous Navigation: In robotics, an MDP can model how a robot navigates a complex space. The states could be the robot's coordinates and orientation, while actions are its movements (e.g., forward, turn). The rewards can be positive for reaching a destination and negative for colliding with obstacles or using excess energy. Perception systems, often using computer vision (CV) for object detection, provide the state information required for the MDP. This is fundamental to applications like autonomous vehicles, which must constantly make decisions based on sensory input.
2. Inventory and Supply Chain Management: Businesses can use MDPs to optimize inventory control. The state is the current stock level, actions are how much product to reorder, and the reward function balances the profit from sales against the costs of holding inventory and stockouts. This helps in making optimal ordering decisions under uncertain demand, a key challenge in AI for retail. Leading organizations like the Association for Supply Chain Management explore such advanced optimization methods.

Relationship to Other Concepts

It is useful to distinguish MDPs from related concepts in machine learning (ML):

• Reinforcement Learning (RL): RL is the field of AI concerned with training agents to make optimal decisions. MDPs provide the mathematical framework that formally defines the problem RL algorithms are designed to solve. When the environment's transition and reward models are unknown, RL techniques are used to learn the optimal policy through trial and error. Deep Reinforcement Learning extends this by using deep learning models to handle complex, high-dimensional state spaces, as covered in foundational texts like Sutton and Barto's book.
• Hidden Markov Models (HMM): Unlike MDPs where the state is fully observable, Hidden Markov Models (HMMs) are used when the state is not directly visible but must be inferred from a sequence of observations. HMMs are for analysis and inference, not decision-making, as they do not include actions or rewards.
• Dynamic Programming: When a complete and accurate model of the MDP (i.e., known transition probabilities and rewards) is available, it can be solved using Dynamic Programming methods like value iteration and policy iteration to find the optimal policy.

Developing solutions for MDPs often involves using RL libraries such as Gymnasium and ML frameworks like PyTorch or TensorFlow. The perception component of these systems, which identifies the current state, can be built using models like Ultralytics YOLO11. The entire workflow, from managing training data to model deployment, can be streamlined using platforms like Ultralytics HUB and managed with robust MLOps practices.