Markov Decision Process

A Markov Decision Process (MDP) is a mathematical framework used to model decision-making problems in a stochastic environment. It consists of a set of states, a set of actions, a transition function, reward function, and a discount factor.

The states represent the possible situations or conditions of the system, while actions represent the available choices that can be made at each state. The transition function specifies the probability of moving from one state to another after taking a particular action. The reward function determines the immediate reward received for each transition, while the discount factor is used to give preference to immediate rewards over future rewards.

The objective of an MDP is to find a policy that maximizes the expected cumulative reward over time. A policy is a rule that specifies the action to take at each state. The optimal policy is the one that leads to the highest expected cumulative reward.

The MDP framework is widely used in various fields, including robotics, finance, healthcare, and transportation, to name a few. It is a powerful tool for modeling decision-making problems in uncertain environments and has led to significant advances in artificial intelligence and machine learning.