强化学习 之 Actor Critic

参考

1、【强化学习】Actor-Critic公式推导分析（整体理解，包含AC、A3C））
2、Actor Critic（公式计算变形）
3、【强化学习】Actor-Critic算法详解（Actor-Critic with Eligibility Traces）
3.5、资格痕迹(Eligibility Traces)
4、简单认识Adam优化器
5、一文读懂 深度强化学习算法 A3C（损失函数中3个部分的各自意义）
5.5、交叉熵定义与运用
6、强化学习(十四) Actor-Critic（算法流程）
7、简单介绍AC 、A2C、A3C

简介

Actor Critic是一种结合体算法：
（1）Actor 的前生是 Policy Gradients，这能让它毫不费力地在连续动作中选取合适的动作，而 Q-learning 做这件事会瘫痪；
（2）Critic 的前生是 Q-learning 或者其他的 以值为基础的学习法，能进行单步更新，而传统的 Policy Gradients 则是回合更新，这降低了学习效率。

算法思想

Actor 基于概率选行为，Critic 基于 Actor 的行为 评判行为的得分，Actor 根据 Critic 的评分修改选行为的概率.

Actor网络

Actor 想要最大化期望的 reward, 在 Actor Critic 算法中, 我们用 “比平时好多少” (TD error) 来当做 reward。

1. 初始化参数

        self.sess = sess
        self.s = tf.placeholder(tf.float32, [1, n_features], "state")
        self.a = tf.placeholder(tf.int32, None, "act")
        self.td_error = tf.placeholder(tf.float32, None, "td_error")  # TD_error

2. 各层网络

        with tf.variable_scope('Actor'):
            l1 = tf.layers.dense(
                inputs=self.s,
                units=20,    # number of hidden units
                activation=tf.nn.relu,
                kernel_initializer=tf.random_normal_initializer(0., .1),    # weights
                bias_initializer=tf.constant_initializer(0.1),  # biases
                name='l1'
            )
            
            self.acts_prob = tf.layers.dense(		# 输出动作的概率
                inputs=l1,
                units=n_actions,    # output units
                activation=tf.nn.softmax,   # get action probabilities
                kernel_initializer=tf.random_normal_initializer(0., .1),  # weights
                bias_initializer=tf.constant_initializer(0.1),  # biases
                name='acts_prob'
            )

3. 学习更新

        with tf.variable_scope('exp_v'):
            log_prob = tf.log(self.acts_prob[0, self.a])     # log 动作概率
            self.exp_v = tf.reduce_mean(log_prob * self.td_error)   # log 概率 * TD 方向

        with tf.variable_scope('train'):
            self.train_op = tf.train.AdamOptimizer(lr).minimize(-self.exp_v)  # minimize(-exp_v) = maximize(exp_v)

    def learn(self, s, a, td):
        s = s[np.newaxis, :]
        feed_dict = {self.s: s, self.a: a, self.td_error: td}
        _, exp_v = self.sess.run([self.train_op, self.exp_v], feed_dict)
        return exp_v

s, a 用于产生 Gradient ascent 的方向，
td 则来自 Critic，用于告诉 Actor 这方向对不对。

4. 基于分析出的概率来选动作

	# 与Policy Gradient步骤相同
    def choose_action(self, s):
        s = s[np.newaxis, :]
        probs = self.sess.run(self.acts_prob, {self.s: s})   # get probabilities for all actions
        return np.random.choice(np.arange(probs.shape[1]), p=probs.ravel())   # return a int

Critic网络

1. 初始化参数

        self.sess = sess
        self.s = tf.placeholder(tf.float32, [1, n_features], "state")
        self.v_ = tf.placeholder(tf.float32, [1, 1], "v_next")
        self.r = tf.placeholder(tf.float32, None, 'r')

2. 各层网络

        with tf.variable_scope('Critic'):
            l1 = tf.layers.dense(
                inputs=self.s,
                units=20,  # 隐藏层单元数量
                activation=tf.nn.relu,  
                # have to be linear to make sure the convergence of actor.
                # But linear approximator seems hardly learns the correct Q.
                kernel_initializer=tf.random_normal_initializer(0., .1),  # weights
                bias_initializer=tf.constant_initializer(0.1),  # biases
                name='l1'
            )
            
			# 预测状态state的价值 v
            self.v = tf.layers.dense(
                inputs=l1,
                units=1,  # output units
                activation=None,
                kernel_initializer=tf.random_normal_initializer(0., .1),  # weights
                bias_initializer=tf.constant_initializer(0.1),  # biases
                name='V'
            )

3. 学习更新
Critic 的更新很简单，就是像 Q learning 那样更新现实和估计的误差 (TD error) 就好了。

        with tf.variable_scope('squared_TD_error'):
            self.td_error = self.r + (GAMMA * self.v_) - self.v
            self.loss = tf.square(self.td_error)    # TD_error = (r+gamma*V_next) - V_eval

        with tf.variable_scope('train'):
            self.train_op = tf.train.AdamOptimizer(lr).minimize(self.loss)

    def learn(self, s, r, s_):
        s, s_ = s[np.newaxis, :], s_[np.newaxis, :]
		# 计算下一个状态s_的价值v_
        v_ = self.sess.run(self.v, {self.s: s_})	
        td_error, _ = self.sess.run([self.td_error, self.train_op],
                                      {self.s: s, self.v_: v_, self.r: r})
        return td_error

此处学习的是 状态的价值 (state value)，不是行为的价值 (action value)
通过计算 TD_error = (r + v_) - v，用 TD_error 评判这一步的行为有没有带来比平时更好的结果

程序主体部分

参数设置

OUTPUT_GRAPH = False
MAX_EPISODE = 3000
DISPLAY_REWARD_THRESHOLD = 200  # renders environment if total episode reward is greater then this threshold
MAX_EP_STEPS = 1000   # maximum time step in one episode
RENDER = False  # rendering wastes time
GAMMA = 0.9     # reward discount in TD error
LR_A = 0.001    # learning rate for actor
LR_C = 0.01     # learning rate for critic

建立网络

sess = tf.Session()

actor = Actor(sess, n_features=N_F, n_actions=N_A, lr=LR_A)
# critic需要比actor学习的快
critic = Critic(sess, n_features=N_F, lr=LR_C)    

sess.run(tf.global_variables_initializer())

循环训练

for i_episode in range(MAX_EPISODE):
    s = env.reset()
    t = 0
    track_r = []     # 每个episode的所有奖励
    while True:
        if RENDER: 
        	env.render()

        a = actor.choose_action(s)

        s_, r, done, info = env.step(a)

        if done: 
        	r = -20    # 回合结束的惩罚

        track_r.append(r)

        # Critic学习， gradient = grad[r + gamma * V(s_) - V(s)]
        td_error = critic.learn(s, r, s_) 
        # Actor学习，true_gradient = grad[logPi(s,a) * td_error]
        actor.learn(s, a, td_error)     

        s = s_
        t += 1

        if done or t >= MAX_EP_STEPS:
            ep_rs_sum = sum(track_r)

            if 'running_reward' not in globals():
                running_reward = ep_rs_sum
            else:
                running_reward = running_reward * 0.95 + ep_rs_sum * 0.05
            if running_reward > DISPLAY_REWARD_THRESHOLD: 
            	RENDER = True  # rendering
            print("episode:", i_episode, "  reward:", int(running_reward))
            break

A3C

A3C是在AC的基础上，在多个线程异步执行AC算法，得到网络参数的增量后，异步地更新到全局模型中。在下一次迭代时，使用当前模型的最新参数作为新一次训练的基础参数。算法如下：