What is the Bellman equation used for in reinforcement learning?

The Bellman equation is a fundamental equation in reinforcement learning that is used to express the relationship between the value of a state and the values of its successor states. It provides a recursive definition of the optimal value function, which represents the maximum expected cumulative reward that an agent can achieve starting from a given state. There are two main forms of the Bellman equation: the Bellman equation for value functions and the Bellman equation for Q-functions. The Bellman equation for value functions expresses the value of a state 's' as the immediate reward received plus the discounted value of the....