Understanding Markov Decision Processes (MDPs)

Before diving into the value iteration algorithm, it’s essential to understand the basics of Markov Decision Processes. An MDP is defined by:

• States (S): A finite set of states that represent all possible situations in the environment.
• Actions (A): A finite set of actions available to the agent.
• Transition Model (P): The probability P(s′∣s, a)P(s′∣s, a) of transitioning from state ss to state s′s′ after taking action aa.
• Reward Function (R): The immediate reward received after transitioning from state ss to state s′s′ due to action aa.
• Discount Factor (γγ): A factor between 0 and 1 that represents the present value of future rewards.

The objective of an MDP is to find an optimal policy ππ that maximizes the expected cumulative reward for the agent over time.

Value iteration is a fundamental algorithm in the field of reinforcement learning and dynamic programming. It is used to compute the optimal policy and value function for a Markov Decision Process (MDP). This article explores the value iteration algorithm, its key concepts, and its applications.