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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 REINFORCE in TensorFlow
Just like we did before for q-learning, this time we'll design a neural network to learn CartPole-v0 via policy gradient (REINFORCE).
Step1:  Building the policy network
For REINFORCE algorithm, we'll need a model that predicts action probabilities given states.
For numerical stability, please do not include the softmax layer into your network architecture. 
We'll use softmax or log-softmax where appropriate.
Step2:  Loss function and updates
We now need to define objective and update over policy gradient.
Our objective function is
$$ J \approx  { 1 \over N } \sum  {s_i,a_i} \pi\theta (a_i | s_i) \cdot G(s_i,a_i) $$
Following the REINFORCE algorithm, we can define our objective as follows
Step5:  Computing cumulative rewards
Step7:  Playing the game
Step9:  Results & video
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Python Code:
# This code creates a virtual display to draw game images on. 
# If you are running locally, just ignore it
import os
if type(os.environ.get("DISPLAY")) is not str or len(os.environ.get("DISPLAY")) == 0:
    !bash ../xvfb start
    os.environ['DISPLAY'] = ':1'
import gym
import numpy as np, pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
env = gym.make("CartPole-v0")
# gym compatibility: unwrap TimeLimit
if hasattr(env,'env'):
    env=env.env
env.reset()
n_actions = env.action_space.n
state_dim = env.observation_space.shape
plt.imshow(env.render("rgb_array"))
Explanation: REINFORCE in TensorFlow
Just like we did before for q-learning, this time we'll design a neural network to learn CartPole-v0 via policy gradient (REINFORCE).
End of explanation
import tensorflow as tf
tf.reset_default_graph()
# create input variables. We only need <s,a,R> for REINFORCE
states = tf.placeholder('float32', (None,)+state_dim, name="states")
actions = tf.placeholder('int32', name="action_ids")
cumulative_rewards = tf.placeholder('float32', name="cumulative_returns")
import keras
import keras.layers as L
#sess = tf.InteractiveSession()
#keras.backend.set_session(sess)
#<define network graph using raw tf or any deep learning library>
#network = keras.models.Sequential()
#network.add(L.InputLayer(state_dim))
#network.add(L.Dense(200, activation='relu'))
#network.add(L.Dense(200, activation='relu'))
#network.add(L.Dense(n_actions, activation='linear'))
network = keras.models.Sequential()
network.add(L.Dense(256, activation="relu", input_shape=state_dim, name="layer_1"))
network.add(L.Dense(n_actions, activation="linear", name="layer_2"))
print(network.summary())
#question: counting from the beginning of the model, the logits are in layer #9: model.layers[9].output
    
#logits = network.layers[2].output #<linear outputs (symbolic) of your network>
logits = network(states)
policy = tf.nn.softmax(logits)
log_policy = tf.nn.log_softmax(logits)
# utility function to pick action in one given state
def get_action_proba(s): 
    return policy.eval({states: [s]})[0]
Explanation: Building the policy network
For REINFORCE algorithm, we'll need a model that predicts action probabilities given states.
For numerical stability, please do not include the softmax layer into your network architecture. 
We'll use softmax or log-softmax where appropriate.
End of explanation
# select log-probabilities for chosen actions, log pi(a_i|s_i)
indices = tf.stack([tf.range(tf.shape(log_policy)[0]), actions], axis=-1)
log_policy_for_actions = tf.gather_nd(log_policy, indices)
# REINFORCE objective function
# hint: you need to use log_policy_for_actions to get log probabilities for actions taken
J =  tf.reduce_mean((log_policy_for_actions * cumulative_rewards), axis=-1)# <policy objective as in the last formula. Please use mean, not sum.>
# regularize with entropy
entropy =  tf.reduce_mean(policy*log_policy) # <compute entropy. Don't forget the sign!>
# all network weights
all_weights =  tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES) #<a list of all trainable weights in your network>
# weight updates. maximizing J is same as minimizing -J. Adding negative entropy.
loss = -J - 0.1*entropy
update = tf.train.AdamOptimizer().minimize(loss, var_list=all_weights)
Explanation: Loss function and updates
We now need to define objective and update over policy gradient.
Our objective function is
$$ J \approx  { 1 \over N } \sum  {s_i,a_i} \pi\theta (a_i | s_i) \cdot G(s_i,a_i) $$
Following the REINFORCE algorithm, we can define our objective as follows: 
$$ \hat J \approx { 1 \over N } \sum  {s_i,a_i} log \pi\theta (a_i | s_i) \cdot G(s_i,a_i) $$
When you compute gradient of that function over network weights $ \theta $, it will become exactly the policy gradient.
End of explanation
def get_cumulative_rewards(rewards,    # rewards at each step
                           gamma=0.99  # discount for reward
                           ):
    
    take a list of immediate rewards r(s,a) for the whole session 
    compute cumulative rewards R(s,a) (a.k.a. G(s,a) in Sutton '16)
    R_t = r_t + gamma*r_{t+1} + gamma^2*r_{t+2} + ...
    The simple way to compute cumulative rewards is to iterate from last to first time tick
    and compute R_t = r_t + gamma*R_{t+1} recurrently
    You must return an array/list of cumulative rewards with as many elements as in the initial rewards.
    
    #<your code here>
    cumulative_rewards = np.zeros((len(rewards)))
    cumulative_rewards[-1] = rewards[-1]
    for t in range(len(rewards)-2, -1, -1):
        cumulative_rewards[t] = rewards[t] + gamma * cumulative_rewards[t + 1]
    return cumulative_rewards #< array of cumulative rewards>
assert len(get_cumulative_rewards(range(100))) == 100
assert np.allclose(get_cumulative_rewards([0, 0, 1, 0, 0, 1, 0], gamma=0.9),
                   [1.40049, 1.5561, 1.729, 0.81, 0.9, 1.0, 0.0])
assert np.allclose(get_cumulative_rewards([0, 0, 1, -2, 3, -4, 0], gamma=0.5),
                   [0.0625, 0.125, 0.25, -1.5, 1.0, -4.0, 0.0])
assert np.allclose(get_cumulative_rewards([0, 0, 1, 2, 3, 4, 0], gamma=0),
                   [0, 0, 1, 2, 3, 4, 0])
print("looks good!")
def train_step(_states, _actions, _rewards):
    given full session, trains agent with policy gradient
    _cumulative_rewards = get_cumulative_rewards(_rewards)
    update.run({states: _states, actions: _actions,
                cumulative_rewards: _cumulative_rewards})
Explanation: Computing cumulative rewards
End of explanation
def generate_session(t_max=1000):
    play env with REINFORCE agent and train at the session end
    # arrays to record session
    states, actions, rewards = [], [], []
    s = env.reset()
    for t in range(t_max):
        # action probabilities array aka pi(a|s)
        action_probas = get_action_proba(s)
        a = np.random.choice(a=len(action_probas), p=action_probas) #<pick random action using action_probas>
        new_s, r, done, info = env.step(a)
        # record session history to train later
        states.append(s)
        actions.append(a)
        rewards.append(r)
        s = new_s
        if done:
            break
    train_step(states, actions, rewards)
    # technical: return session rewards to print them later
    return sum(rewards)
s = tf.InteractiveSession()
s.run(tf.global_variables_initializer())
for i in range(100):
    rewards = [generate_session() for _ in range(100)]  # generate new sessions
    print("mean reward:%.3f" % (np.mean(rewards)))
    if np.mean(rewards) > 300:
        print("You Win!") # but you can train even further
        break
Explanation: Playing the game
End of explanation
# record sessions
import gym.wrappers
env = gym.wrappers.Monitor(gym.make("CartPole-v0"),
                           directory="videos", force=True)
sessions = [generate_session() for _ in range(100)]
env.close()
# show video
from IPython.display import HTML
import os
video_names = list(
    filter(lambda s: s.endswith(".mp4"), os.listdir("./videos/")))
HTML(
<video width="640" height="480" controls>
  <source src="{}" type="video/mp4">
</video>
.format("./videos/"+video_names[-1]))  # this may or may not be _last_ video. Try other indices
from submit import submit_cartpole
submit_cartpole(generate_session, "tonatiuh_rangel@hotmail.com", "Cecc5rcVxaVUYtsQ")
# That's all, thank you for your attention!
# Not having enough? There's an actor-critic waiting for you in the honor section.
# But make sure you've seen the videos first.
Explanation: Results & video
End of explanation
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