Policy Gradient綜述：

  　Policy Gradient，通過學習當前環境，直接給出要輸出的動作的概率值。

　  Policy Gradient  不是單步更新，只能等玩完一個epoch，再更新引數，所以是一個off-policy

數學推導

最大化R,,用梯度下降，需要求R的梯度。

 vt的計算

Policy Gradient  不是單步更新，只能等玩完一個epoch，得到每個epoch的observation_list \ action\_list reward_list

學習的時候，根據這三個list更新引數，其中下圖公式中的vt 根據reward_list算出來。

 vt的計算

Policy Gradient  不是單步更新，只能等玩完一個epoch，得到每個epoch的observation_list \ action\_list reward_list

學習的時候，根據這三個list更新引數，其中下圖公式中的vt 根據reward_list算出來。

實現方式

神經網路分類模型，但是在算loss 的時候，logloss需要乘一個係數vt,這個係數與獎勵Reward相關，如果採用當前動作，

在接下來的遊戲中獲得的Reward越大，那麼在更新梯度的時候加大當前梯度下降的速度。

演算法步驟

 vt的計算

Policy Gradient  不是單步更新，只能等玩完一個epoch，得到每個epoch的observation_list \ action\_list reward_list

學習的時候，根據這三個list更新引數，其中下圖公式中的vt 根據reward_list算出來。

程式碼

  1 """
  2 This part of code is the reinforcement learning brain, which is a brain of the agent.
 
  3 All decisions are made in here.
  4 
  5 Policy Gradient, Reinforcement Learning.
  6 
  7 View more on my tutorial page: https://morvanzhou.github.io/tutorials/
  8 
  9 Using:
 10 Tensorflow: 1.0
 11 gym: 0.8.0
 12 """
 13 
 14 import numpy as np
 15 import tensorflow as tf
 16 
 17 # reproducible
 18 np.random.seed(1)
 19 tf.set_random_seed(1)
 20 
 21 
 22 class PolicyGradient:
 23     def __init__(
 24             self,
 25             n_actions,
 26             n_features,
 27             learning_rate=0.01,
 28             reward_decay=0.95,
 29             output_graph=False,
 30     ):
 31         self.n_actions = n_actions
 32         self.n_features = n_features
 33         self.lr = learning_rate
 34         self.gamma = reward_decay
 35         
 36 
 37         #每個epoch的observation \ action\ reward
 38         self.ep_obs, self.ep_as, self.ep_rs = [], [], []
 39 
 40         self._build_net()
 41 
 42         self.sess = tf.Session()
 43 
 44         if output_graph:
 45             # $ tensorboard --logdir=logs
 46             # http://0.0.0.0:6006/
 47             # tf.train.SummaryWriter soon be deprecated, use following
 48             tf.summary.FileWriter("logs/", self.sess.graph)
 49 
 50         self.sess.run(tf.global_variables_initializer())
 51 
 52     def _build_net(self):
 53         with tf.name_scope('inputs'):
 54             self.tf_obs = tf.placeholder(tf.float32, [None, self.n_features], name="observations")
 55             self.tf_acts = tf.placeholder(tf.int32, [None, ], name="actions_num")
 56             self.tf_vt = tf.placeholder(tf.float32, [None, ], name="actions_value")
 57         # fc1
 58         layer = tf.layers.dense(
 59             inputs=self.tf_obs,
 60             units=10,
 61             activation=tf.nn.tanh,  # tanh activation
 62             kernel_initializer=tf.random_normal_initializer(mean=0, stddev=0.3),
 63             bias_initializer=tf.constant_initializer(0.1),
 64             name='fc1'
 65         )
 66         # fc2
 67         all_act = tf.layers.dense(
 68             inputs=layer,
 69             units=self.n_actions,
 70             activation=None,
 71             kernel_initializer=tf.random_normal_initializer(mean=0, stddev=0.3),
 72             bias_initializer=tf.constant_initializer(0.1),
 73             name='fc2'
 74         )
 75 
 76         self.all_act_prob = tf.nn.softmax(all_act, name='act_prob')  # use softmax to convert to probability
 77 
 78         with tf.name_scope('loss'):
 79             # to maximize total reward (log_p * R) is to minimize -(log_p * R), and the tf only have minimize(loss)
 80             neg_log_prob = tf.nn.sparse_softmax_cross_entropy_with_logits(logits=all_act, labels=self.tf_acts)   # this is negative log of chosen action
 81             # or in this way:
 82             # neg_log_prob = tf.reduce_sum(-tf.log(self.all_act_prob)*tf.one_hot(self.tf_acts, self.n_actions), axis=1)
 83             loss = tf.reduce_mean(neg_log_prob * self.tf_vt)  # reward guided loss
 84 
 85         with tf.name_scope('train'):
 86             self.train_op = tf.train.AdamOptimizer(self.lr).minimize(loss)
 87 
 88     def choose_action(self, observation):
 89         prob_weights = self.sess.run(self.all_act_prob, feed_dict={self.tf_obs: observation[np.newaxis, :]})
 90         action = np.random.choice(range(prob_weights.shape[1]), p=prob_weights.ravel())  # select action w.r.t the actions prob
 91         return action
 92 
 93     def store_transition(self, s, a, r):
 94         self.ep_obs.append(s)
 95         self.ep_as.append(a)
 96         self.ep_rs.append(r)
 97 
 98     def learn(self):
 99         # discount and normalize episode reward
100         discounted_ep_rs_norm = self._discount_and_norm_rewards()
101 
102         # train on episode
103         self.sess.run(self.train_op, feed_dict={
104              self.tf_obs: np.vstack(self.ep_obs),  # shape=[None, n_obs]
105              self.tf_acts: np.array(self.ep_as),  # shape=[None, ]
106              self.tf_vt: discounted_ep_rs_norm,  # shape=[None, ]
107         })
108 
109         self.ep_obs, self.ep_as, self.ep_rs = [], [], []    # empty episode data
110         return discounted_ep_rs_norm
111 
112     def _discount_and_norm_rewards(self):
113         # discount episode rewards
114         discounted_ep_rs = np.zeros_like(self.ep_rs)
115         running_add = 0
116         for t in reversed(range(0, len(self.ep_rs))):
117             running_add = running_add * self.gamma + self.ep_rs[t]
118             discounted_ep_rs[t] = running_add
119 
120         # normalize episode rewards
121         discounted_ep_rs -= np.mean(discounted_ep_rs)
122         discounted_ep_rs /= np.std(discounted_ep_rs)
123         return discounted_ep_rs