深度强化学习(DRL 3) - 从Q-learning到Deep Q Network(DQN)

迷南。 2024-02-23 07:55 73阅读 0赞

#### 目录 ####

*   *  [一、Q-learning][Q-learning]
     *  [二、Deep Q Network][Deep Q Network]
     *  [三、Double DQN][Double DQN]

### 一、Q-learning ###

关于Q-learning，网上的资料很多。

![在这里插入图片描述][c5705e826399f26d93116999db2254cf.png]

Q-learning最核心的是有一个Q表，它记录了在环境中的 **所有状态(s)** 以及每个状态可以进行的 **所有行为(a)** 的Q值，初值设为0。

Q值的更新公式如下：

Q ( s , a ) ← Q ( s , a ) + α \[ r + γ m a x a ′ Q ( s ′ , a ′ ) − Q ( s , a ) \] Q(s,a)←Q(s,a)+α\[r+\\gamma max\_\{a'\}Q(s^′,a^′)−Q(s,a)\] Q(s,a)←Q(s,a)+α\[r+γmaxa′Q(s′,a′)−Q(s,a)\]

*  其中 α α α表示学习速率，取值小于1
 *  r r r是设置的奖励
 *  智能体在状态s经过行为a转移到状态s’， m a x a ′ Q ( s ′ , a ′ ) max\_\{a'\}Q(s^′,a^′) maxa′Q(s′,a′) 是状态 s ′ s' s′ 那一行最大Q值
 *  γ \\gamma γ则是衰减速率，取值在0到1之间， γ \\gamma γ越大，智能体就会越注重长期利益， γ \\gamma γ越小，智能体越短视。

每改变一次状态就会更新一次Q值

Q-learning 是一个 off-policy 的算法，它可以离线学习。它可以随机进行若干次游戏，将游戏过程保存起来，学习的时候就可以避免陷入局部最优。

Q-learning 的代码实现：

# -*- coding: UTF-8 -*-
    import numpy as np
    import pandas as pd
    
    
    class QLearningTable:
        def __init__(self, actions, learning_rate=0.01, reward_decay=0.9, e_greedy=0.9):
            self.actions = actions  # a list
            self.lr = learning_rate
            self.gamma = reward_decay
            self.epsilon = e_greedy
            self.q_table = pd.DataFrame(columns=self.actions, dtype=np.float64)
    
        def choose_action(self, observation):
            self.check_state_exist(observation)
            # action selection
            if np.random.uniform() < self.epsilon:
                # choose best action
                state_action = self.q_table.loc[observation, :]
                state_action = state_action.reindex(np.random.permutation(state_action.index))     # some actions have same value
                action = state_action.idxmax()
            else:
                # choose random action
                action = np.random.choice(self.actions)
            return action
    
        def learn(self, s, a, r, s_):
            self.check_state_exist(s_)
            q_predict = self.q_table.loc[s, a]
            if s_ != 'terminal':
                q_target = r + self.gamma * self.q_table.loc[s_, :].max()  # next state is not terminal
            else:
                q_target = r  # next state is terminal
            self.q_table.loc[s, a] += self.lr * (q_target - q_predict)  # update
    
        def check_state_exist(self, state):
            if state not in self.q_table.index:
                # append new state to q table
                self.q_table = self.q_table.append(
                    pd.Series(
                        [0]*len(self.actions),
                        index=self.q_table.columns,
                        name=state,
                    )
                )

### 二、Deep Q Network ###

如果想用Q-learning玩之前的CartPole-v0游戏，会发现CartPole-v0的状态值太多了，它的observation有 **车的位置，车的速度，杆子的角度，杆子顶端的速度** 四个值，并且是连续的数值，四个值再进行量化，Q表实在是太大了。用Q-learning玩游戏和随机玩游戏没区别，学习不到东西。可能Q-learning只适用于走迷宫类的游戏，每一步的状态都可以很简单的描述出来，4\*4的迷宫只需要用16个状态就可以全部囊括。

我们用Deep Q Network来解决这个问题， Deep Q Network融合了神经网络和 Q learning。

*  我们可以将状态和动作当成神经网络的输入, 然后经过神经网络分析后得到动作的 Q 值, 这样我们就没必要在表格中记录 Q 值, 而是直接使用神经网络生成 Q 值.
 *  或者只输入状态值, 输出所有的动作值, 然后按照 Q learning 的原则, 直接选择拥有最大值的动作当做下一步要做的动作.
    
    ![在这里插入图片描述][330df2fc33d1748d0c1aa38330815e6b.jpeg]

需要搭建两个神经网络，**target\_net 和 eval\_net ，**  
target\_net 用于预测 q\_target 值, 他不会及时更新参数.  
target\_net 用于预测 q\_eval, 这个神经网络拥有最新的神经网络参数.

两个神经网络结构是完全一样的, 只是里面的参数不一样. target\_net 是 eval\_net 的一个历史版本, 拥有 eval\_net 很久之前的一组参数, 而且这组参数被固定一段时间, 然后再被 eval\_net 的新参数所替换. 而 eval\_net 是不断在被提升的。这样做是为了打乱数据间的相关性，避免陷入局部最优。

神经网络的输入数据是\[s,a,r,s’\],输出数据是状态s下所有行为a的Q值。  
target\_net 只会输出Q值（q\_target ），不会进行训练，而eval\_net 输出Q值（q\_eval）之后会根据q\_target和q\_eval进行反向传播训练，更新eval\_net 的参数。

Deep Q Network整个算法的运作：

1.  初始化target\_net 和 target\_net。
2.  观察游戏状态observation，选择合适的observation作为输入，一般情况会对observation做数据处理，使其更容易训练，这里不用。
3.  设置合适的奖励reward。
4.  先进行若干次游戏，将游戏数据存储到memory中。
5.  从memory中随机选取训练数据batch\_memory用于批量训练。
6.  训练eval\_net 一段时间后，将eval\_net 的参数复制给target\_net 。
7.  训练过程中产生的新的游戏数据会替代memory中的旧数据。

回到游戏CartPole-v0

DQN.py：

import numpy as np
    import tensorflow as tf
    
    np.random.seed(1)
    tf.set_random_seed(1)
    
    
    # Deep Q Network off-policy
    class DeepQNetwork:
        def __init__(
                self,
                n_actions,
                n_features,
                learning_rate=0.01,
                reward_decay=0.9,
                e_greedy=0.9,
                replace_target_iter=300,
                memory_size=500,
                batch_size=32,
                e_greedy_increment=None,
                output_graph=True,
        ):
            self.n_actions = n_actions
            self.n_features = n_features
            self.lr = learning_rate
            self.gamma = reward_decay
            self.epsilon_max = e_greedy
            self.replace_target_iter = replace_target_iter
            self.memory_size = memory_size
            self.batch_size = batch_size
            self.epsilon_increment = e_greedy_increment
            self.epsilon = 0 if e_greedy_increment is not None else self.epsilon_max
    
            # total learning step
            self.learn_step_counter = 0
    
            # initialize zero memory [s, a, r, s_]
            # [4, 1, 1, 4]
            self.memory = np.zeros((self.memory_size, n_features * 2 + 2))
    
            # consist of [target_net, evaluate_net]
            self._build_net()
    
            t_params = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES, scope='target_net')
            e_params = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES, scope='eval_net')
    
            with tf.variable_scope('hard_replacement'):
                self.target_replace_op = [tf.assign(t, e) for t, e in zip(t_params, e_params)]
    
            self.sess = tf.Session()
    
            if output_graph:
                # $ tensorboard --logdir=logs
                tf.summary.FileWriter("logs/", self.sess.graph)
    
            self.sess.run(tf.global_variables_initializer())
            self.cost_his = []
    
        def _build_net(self):
            # ------------------ all inputs ------------------------
            self.s = tf.placeholder(tf.float32, [None, self.n_features], name='s')  # input State
            self.s_ = tf.placeholder(tf.float32, [None, self.n_features], name='s_')  # input Next State
            self.r = tf.placeholder(tf.float32, [None, ], name='r')  # input Reward
            self.a = tf.placeholder(tf.int32, [None, ], name='a')  # input Action
    
            w_initializer, b_initializer = tf.random_normal_initializer(0., 0.3), tf.constant_initializer(0.1)
    
            # ------------------ build evaluate_net ------------------
            with tf.variable_scope('eval_net'):
                e1 = tf.layers.dense(self.s, 20, tf.nn.relu, kernel_initializer=w_initializer,
                                     bias_initializer=b_initializer, name='e1')
                self.q_eval = tf.layers.dense(e1, self.n_actions, kernel_initializer=w_initializer,
                                              bias_initializer=b_initializer, name='q')
    
            # ------------------ build target_net ------------------
            with tf.variable_scope('target_net'):
                t1 = tf.layers.dense(self.s_, 20, tf.nn.relu, kernel_initializer=w_initializer,
                                     bias_initializer=b_initializer, name='t1')
                self.q_next = tf.layers.dense(t1, self.n_actions, kernel_initializer=w_initializer,
                                              bias_initializer=b_initializer, name='t2')
    
            with tf.variable_scope('q_target'):
                q_target = self.r + self.gamma * tf.reduce_max(self.q_next, axis=1, name='Qmax_s_')  # shape=(None, )
                self.q_target = tf.stop_gradient(q_target)
            with tf.variable_scope('q_eval'):
                a_indices = tf.stack([tf.range(tf.shape(self.a)[0], dtype=tf.int32), self.a], axis=1)
                self.q_eval_wrt_a = tf.gather_nd(params=self.q_eval, indices=a_indices)  # shape=(None, )
            with tf.variable_scope('loss'):
                self.loss = tf.reduce_mean(tf.squared_difference(self.q_target, self.q_eval_wrt_a, name='TD_error'))
            with tf.variable_scope('train'):
                self._train_op = tf.train.RMSPropOptimizer(self.lr).minimize(self.loss)
    
        def store_transition(self, s, a, r, s_):
            if not hasattr(self, 'memory_counter'):
                self.memory_counter = 0
            transition = np.hstack((s, [a, r], s_))
            # replace the old memory with new memory
            index = self.memory_counter % self.memory_size
            self.memory[index, :] = transition
            self.memory_counter += 1
    
        def choose_action(self, observation):
            # to have batch dimension when feed into tf placeholder
            observation = observation[np.newaxis, :]
    
            if np.random.uniform() < self.epsilon:
                # forward feed the observation and get q value for every actions
                actions_value = self.sess.run(self.q_eval, feed_dict={ 
       self.s: observation})
                action = np.argmax(actions_value)
            else:
                action = np.random.randint(0, self.n_actions)
            return action
    
        def learn(self):
            # check to replace target parameters
            if self.learn_step_counter % self.replace_target_iter == 0:
                self.sess.run(self.target_replace_op)
                print('\ntarget_params_replaced\n')
    
            # sample batch memory from all memory
            if self.memory_counter > self.memory_size:
                sample_index = np.random.choice(self.memory_size, size=self.batch_size)
            else:
                sample_index = np.random.choice(self.memory_counter, size=self.batch_size)
            batch_memory = self.memory[sample_index, :]
    
            _, cost = self.sess.run(
                [self._train_op, self.loss],
                feed_dict={ 
       
                    self.s: batch_memory[:, :self.n_features],
                    self.a: batch_memory[:, self.n_features],
                    self.r: batch_memory[:, self.n_features + 1],
                    self.s_: batch_memory[:, -self.n_features:],
                })
    
            self.cost_his.append(cost)
    
            # increasing epsilon
            self.epsilon = self.epsilon + self.epsilon_increment if self.epsilon < self.epsilon_max else self.epsilon_max
            self.learn_step_counter += 1
    
        def plot_cost(self):
            import matplotlib.pyplot as plt
            plt.plot(np.arange(len(self.cost_his)), self.cost_his)
            plt.ylabel('Cost')
            plt.xlabel('training steps')
            plt.show()
    
    
    if __name__ == '__main__':
        DQN = DeepQNetwork(3, 4, output_graph=True)

DQN\_CarPole.py:

import gym
    from DQN import DeepQNetwork
    
    env = gym.make('CartPole-v0')
    env = env.unwrapped
    RL = DeepQNetwork(n_actions=env.action_space.n,
                      n_features=env.observation_space.shape[0],
                      learning_rate=0.01, e_greedy=0.9,
                      replace_target_iter=100, memory_size=2000,
                      e_greedy_increment=0.0008, )
    total_steps = 0  # 记录步数
    
    for i_episode in range(100):
    
        # 获取回合 i_episode 第一个 observation
        observation = env.reset()
        ep_r = 0
        while True:
            env.render()  # 刷新环境
    
            action = RL.choose_action(observation)  # 选行为
    
            observation_, reward, done, info = env.step(action)  # 获取下一个 state
    
            x, x_dot, theta, theta_dot = observation_  # 细分开, 为了修改原配的 reward
    
            # x 是车的水平位移, 所以 r1 是车越偏离中心, 分越少
            # theta 是棒子离垂直的角度, 角度越大, 越不垂直. 所以 r2 是棒越垂直, 分越高
            r1 = (env.x_threshold - abs(x)) / env.x_threshold - 0.8
            r2 = (env.theta_threshold_radians - abs(theta)) / env.theta_threshold_radians - 0.5
            reward = r1 + r2  # 总 reward 是 r1 和 r2 的结合, 既考虑位置, 也考虑角度, 这样 DQN 学习更有效率
    
            # 保存这一组记忆
            RL.store_transition(observation, action, reward, observation_)
    
            if total_steps > 1000:
                RL.learn()  # 学习
    
            ep_r += reward
            if done:
                print('episode: ', i_episode,
                      'ep_r: ', round(ep_r, 2),
                      ' epsilon: ', round(RL.epsilon, 2))
                break
    
            observation = observation_
            total_steps += 1
    # 最后输出 cost 曲线
    RL.plot_cost()
    env.close()

运行DQN\_CarPole.py  
发现小车确实变得越来越稳定。

最后输出的损失函数曲线

![在这里插入图片描述][26b660e036613197980b6b4393edec7d.png]

### 三、Double DQN ###

无论是Q-learning还是DQN，更新Q值的的时候都会用到 m a x Q maxQ maxQ。

Q-learning:  
Q ( s , a ) ← Q ( s , a ) + α \[ r + γ m a x a ′ Q ( s ′ , a ′ ) − Q ( s , a ) \] Q(s,a)←Q(s,a)+α\[r+\\gamma max\_\{a'\}Q(s^′,a^′)−Q(s,a)\] Q(s,a)←Q(s,a)+α\[r+γmaxa′Q(s′,a′)−Q(s,a)\]

DQN:

![在这里插入图片描述][36021b45708602a49701aff146150b4e.png]

使用max虽然可以快速让Q值向可能的优化目标靠拢，但是很容易过犹不及，导致过度估计(Over Estimation)，所谓过度估计就是最终我们得到的算法模型有很大的偏差(bias)，可能就会发现Q值都超级大。

DDQN通过解耦目标Q值动作的选择和目标Q值的计算这两步，来达到消除过度估计的问题。

![在这里插入图片描述][f9bbefbc481fb3dbde12e0d203cde9e4.png]

DDQN更新：

![在这里插入图片描述][4398476c6bb14145aaa90491d33ca52c.png]

在DDQN这里，不再是直接在目标Q网络里面找各个动作中最大Q值，而是先在当前Q网络中先找出最大Q值对应的动作。然后利用这个选择出来的动作在目标Q网络里面去计算目标Q值。

DoubleDQN.py

import numpy as np
    import tensorflow as tf
    
    np.random.seed(1)
    tf.set_random_seed(1)
    
    
    class DoubleDQN:
        def __init__(
                self,
                n_actions,
                n_features,
                learning_rate=0.005,
                reward_decay=0.9,
                e_greedy=0.9,
                replace_target_iter=200,
                memory_size=3000,
                batch_size=32,
                e_greedy_increment=None,
                output_graph=False,
        ):
            self.n_actions = n_actions
            self.n_features = n_features
            self.lr = learning_rate
            self.gamma = reward_decay
            self.epsilon_max = e_greedy
            self.replace_target_iter = replace_target_iter
            self.memory_size = memory_size
            self.batch_size = batch_size
            self.epsilon_increment = e_greedy_increment
            self.epsilon = 0 if e_greedy_increment is not None else self.epsilon_max
            self.learn_step_counter = 0
            self.memory = np.zeros((self.memory_size, n_features * 2 + 2))
            self._build_net()
            t_params = tf.get_collection('target_net_params')
            e_params = tf.get_collection('eval_net_params')
            self.replace_target_op = [tf.assign(t, e) for t, e in zip(t_params, e_params)]
    
            self.sess = tf.Session()
    
            if output_graph:
                tf.summary.FileWriter("logs/", self.sess.graph)
    
            self.sess.run(tf.global_variables_initializer())
            self.cost_his = []
    
        def _build_net(self):
            def build_layers(s, c_names, n_l1, w_initializer, b_initializer):
                with tf.variable_scope('l1'):
                    w1 = tf.get_variable('w1', [self.n_features, n_l1], initializer=w_initializer, collections=c_names)
                    b1 = tf.get_variable('b1', [1, n_l1], initializer=b_initializer, collections=c_names)
                    l1 = tf.nn.relu(tf.matmul(s, w1) + b1)
    
                with tf.variable_scope('l2'):
                    w2 = tf.get_variable('w2', [n_l1, self.n_actions], initializer=w_initializer, collections=c_names)
                    b2 = tf.get_variable('b2', [1, self.n_actions], initializer=b_initializer, collections=c_names)
                    out = tf.matmul(l1, w2) + b2
                return out
    
            # ------------------ build evaluate_net ------------------
            self.s = tf.placeholder(tf.float32, [None, self.n_features], name='s')  # input
            self.q_target = tf.placeholder(tf.float32, [None, self.n_actions], name='Q_target')  # for calculating loss
    
            with tf.variable_scope('eval_net'):
                c_names, n_l1, w_initializer, b_initializer = \
                    ['eval_net_params', tf.GraphKeys.GLOBAL_VARIABLES], 20, \
                    tf.random_normal_initializer(0., 0.3), tf.constant_initializer(0.1)  # config of layers
    
                self.q_eval = build_layers(self.s, c_names, n_l1, w_initializer, b_initializer)
    
            with tf.variable_scope('loss'):
                self.loss = tf.reduce_mean(tf.squared_difference(self.q_target, self.q_eval))
            with tf.variable_scope('train'):
                self._train_op = tf.train.RMSPropOptimizer(self.lr).minimize(self.loss)
    
            # ------------------ build target_net ------------------
            self.s_ = tf.placeholder(tf.float32, [None, self.n_features], name='s_')  # input
            with tf.variable_scope('target_net'):
                c_names = ['target_net_params', tf.GraphKeys.GLOBAL_VARIABLES]
    
                self.q_next = build_layers(self.s_, c_names, n_l1, w_initializer, b_initializer)
    
        def store_transition(self, s, a, r, s_):
            if not hasattr(self, 'memory_counter'):
                self.memory_counter = 0
            transition = np.hstack((s, [a, r], s_))
            index = self.memory_counter % self.memory_size
            self.memory[index, :] = transition
            self.memory_counter += 1
    
        def choose_action(self, observation):
            observation = observation[np.newaxis, :]
            actions_value = self.sess.run(self.q_eval, feed_dict={ 
       self.s: observation})
            action = np.argmax(actions_value)
    
            if not hasattr(self, 'q'):  # record action value it gets
                self.q = []
                self.running_q = 0
            self.running_q = self.running_q * 0.99 + 0.01 * np.max(actions_value)
            self.q.append(self.running_q)
    
            if np.random.uniform() > self.epsilon:  # choosing action
                action = np.random.randint(0, self.n_actions)
            return action
    
        def learn(self):
            if self.learn_step_counter % self.replace_target_iter == 0:
                self.sess.run(self.replace_target_op)
                print('\ntarget_params_replaced\n')
    
            if self.memory_counter > self.memory_size:
                sample_index = np.random.choice(self.memory_size, size=self.batch_size)
            else:
                sample_index = np.random.choice(self.memory_counter, size=self.batch_size)
            batch_memory = self.memory[sample_index, :]
    
            q_next, q_eval4next = self.sess.run(
                [self.q_next, self.q_eval],
                feed_dict={ 
       self.s_: batch_memory[:, -self.n_features:],  # next observation
                           self.s: batch_memory[:, -self.n_features:]})  # next observation
            q_eval = self.sess.run(self.q_eval, { 
       self.s: batch_memory[:, :self.n_features]})
    
            q_target = q_eval.copy()
    
            batch_index = np.arange(self.batch_size, dtype=np.int32)
            eval_act_index = batch_memory[:, self.n_features].astype(int)
            reward = batch_memory[:, self.n_features + 1]
    
            max_act4next = np.argmax(q_eval4next,
                                     axis=1)  # the action that brings the highest value is evaluated by q_eval
            selected_q_next = q_next[batch_index, max_act4next]  # Double DQN, select q_next depending on above actions
    
            q_target[batch_index, eval_act_index] = reward + self.gamma * selected_q_next
    
            _, self.cost = self.sess.run([self._train_op, self.loss],
                                         feed_dict={ 
       self.s: batch_memory[:, :self.n_features],
                                                    self.q_target: q_target})
            self.cost_his.append(self.cost)
    
            self.epsilon = self.epsilon + self.epsilon_increment if self.epsilon < self.epsilon_max else self.epsilon_max
            self.learn_step_counter += 1
    
        def plot_cost(self):
            import matplotlib.pyplot as plt
            plt.plot(np.arange(len(self.cost_his)), self.cost_his)
            plt.ylabel('Cost')
            plt.xlabel('training steps')
            plt.show()

DoubleDQN\_CarPole.py

import tensorflow as tf
    import gym
    from DoubleDQN import DoubleDQN
    
    env = gym.make('CartPole-v0')
    env = env.unwrapped
    
    double_DQN = DoubleDQN(n_actions=env.action_space.n,
                           n_features=env.observation_space.shape[0],
                           memory_size=2000,
                           e_greedy_increment=0.001,
                           output_graph=True)
    total_steps = 0  # 记录步数
    
    for i_episode in range(100):
    
        # 获取回合 i_episode 第一个 observation
        observation = env.reset()
        ep_r = 0
        while True:
            env.render()  # 刷新环境
    
            action = double_DQN.choose_action(observation)  # 选行为
    
            observation_, reward, done, info = env.step(action)  # 获取下一个 state
    
            x, x_dot, theta, theta_dot = observation_  # 细分开, 为了修改原配的 reward
    
            # x 是车的水平位移, 所以 r1 是车越偏离中心, 分越少
            # theta 是棒子离垂直的角度, 角度越大, 越不垂直. 所以 r2 是棒越垂直, 分越高
            r1 = (env.x_threshold - abs(x)) / env.x_threshold - 0.8
            r2 = (env.theta_threshold_radians - abs(theta)) / env.theta_threshold_radians - 0.5
            reward = r1 + r2  # 总 reward 是 r1 和 r2 的结合, 既考虑位置, 也考虑角度, 这样 DQN 学习更有效率
    
            # 保存这一组记忆
            double_DQN.store_transition(observation, action, reward, observation_)
    
            if total_steps > 1000:
                double_DQN.learn()  # 学习
    
            ep_r += reward
            if done:
                print('episode: ', i_episode,
                      'ep_r: ', round(ep_r, 2),
                      ' epsilon: ', round(double_DQN.epsilon, 2))
                break
    
            observation = observation_
            total_steps += 1
    # 最后输出 cost 曲线
    double_DQN.plot_cost()
    env.close()

输出损失函数结果

![在这里插入图片描述][07d55096ce9287792de2aabed262b98a.png]

对比DQN，可以发现DoubleDQN效果明显好很多。

[Q-learning]: http://www.voidme.com/content/zvfbadnche#Qlearning_2
[Deep Q Network]: http://www.voidme.com/content/zvfbadnche#Deep_Q_Network_82
[Double DQN]: http://www.voidme.com/content/zvfbadnche#Double_DQN_329
[c5705e826399f26d93116999db2254cf.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/23/51ff3a70ce054ea19d6145f3eec4c393.png
[330df2fc33d1748d0c1aa38330815e6b.jpeg]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/23/b261c437babf4a9f8eef1f2df9061c6d.png
[26b660e036613197980b6b4393edec7d.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/23/6c7fd2dc89dd468f900058c75126a272.png
[36021b45708602a49701aff146150b4e.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/23/543cd4693a27476c9f49e14ded6cc26d.png
[f9bbefbc481fb3dbde12e0d203cde9e4.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/23/0d6337e566d14dfd8263f115821d8de9.png
[4398476c6bb14145aaa90491d33ca52c.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/23/6be34feeea2a4ffda90f509f74284553.png
[07d55096ce9287792de2aabed262b98a.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/02/23/f9e2d40a4c094c7795a175dbbaa570e6.png