Example
In MDP, a Bellman equation refers to a recursion for expected rewards. For example, the expected reward for being in a particular state s and following some fixed policy has the Bellman equation:
This equation describes the expected reward for taking the action prescribed by some policy .
The equation for the optimal policy is referred to as the Bellman optimality equation:
It describes the reward for taking the action giving the highest expected return.
Read more about this topic: Bellman Equation
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