Policy gradient theorem
As discussed in Chapter 9, Deep Reinforcement Learning, in Reinforcement Learning the agent is situated in an environment that is in state st', an element of state space 
. The state space may be discrete or continuous. The agent takes an action at from the action space 
by obeying the policy, 
. may be discrete or continuous. Because of executing the action at, the agent receives a reward r
t+1 and the environment transitions to a new state s
t+1. The new state is dependent only on the current state and action. The goal of the agent is to learn an optimal policy 
that maximizes the return from all the states:
(Equation 9.1.1)
The return, 
, is defined as the discounted cumulative reward from time t until the end of the episode or when the terminal state is reached:
(Equation 9.1.2)
From Equation 9.1.2, the return can also be interpreted as a value of a given state by following the policy 
. It can be observed from Equation 9.1.1 that future...
