七个流行的强化学习算法及代码实现

目前流行的强化学习算法包括 Q-learning、SARSA、DDPG、A2C、PPO、DQN 和 TRPO。 这些算法已被用于在游戏、机器人和决策制定等各种应用中，并且这些流行的算法还在不断发展和改进，本文我们将对其做一个简单的介绍。

1、Q-learning

Q-learning：Q-learning 是一种无模型、非策略的强化学习算法。 它使用 Bellman 方程估计最佳动作值函数，该方程迭代地更新给定状态动作对的估计值。 Q-learning 以其简单性和处理大型连续状态空间的能力而闻名。

下面是一个使用 Python 实现 Q-learning 的简单示例：

import numpy as np
 
 # Define the Q-table and the learning rate
 Q = np.zeros((state_space_size, action_space_size))
 alpha = 0.1
 
 # Define the exploration rate and discount factor
 epsilon = 0.1
 gamma = 0.99
 
 for episode in range(num_episodes):
     current_state = initial_state
     while not done:
         # Choose an action using an epsilon-greedy policy
         if np.random.uniform(0, 1) < epsilon:
             action = np.random.randint(0, action_space_size)
         else:
             action = np.argmax(Q[current_state])
 
         # Take the action and observe the next state and reward
         next_state, reward, done = take_action(current_state, action)
 
         # Update the Q-table using the Bellman equation
         Q[current_state, action] = Q[current_state, action] + alpha * (reward + gamma * np.max(Q[next_state]) - Q[current_state, action])
 
         current_state = next_state

上面的示例中，state_space_size 和 action_space_size 分别是环境中的状态数和动作数。 num_episodes 是要为运行算法的轮次数。 initial_state 是环境的起始状态。 take_action(current_state, action) 是一个函数，它将当前状态和一个动作作为输入，并返回下一个状态、奖励和一个指示轮次是否完成的布尔值。

在 while 循环中，使用 epsilon-greedy 策略根据当前状态选择一个动作。 使用概率 epsilon选择一个随机动作，使用概率 1-epsilon选择对当前状态具有最高 Q 值的动作。

采取行动后，观察下一个状态和奖励，使用Bellman方程更新q。 并将当前状态更新为下一个状态。这只是 Q-learning 的一个简单示例，并未考虑 Q-table 的初始化和要解决的问题的具体细节。

2、SARSA

SARSA：SARSA 是一种无模型、基于策略的强化学习算法。 它也使用Bellman方程来估计动作价值函数，但它是基于下一个动作的期望值，而不是像 Q-learning 中的最优动作。 SARSA 以其处理随机动力学问题的能力而闻名。

import numpy as np
 
 # Define the Q-table and the learning rate
 Q = np.zeros((state_space_size, action_space_size))
 alpha = 0.1
 
 # Define the exploration rate and discount factor
 epsilon = 0.1
 gamma = 0.99
 
 for episode in range(num_episodes):
     current_state = initial_state
     action = epsilon_greedy_policy(epsilon, Q, current_state)
     while not done:
         # Take the action and observe the next state and reward
         next_state, reward, done = take_action(current_state, action)
         # Choose next action using epsilon-greedy policy
         next_action = epsilon_greedy_policy(epsilon, Q, next_state)
         # Update the Q-table using the Bellman equation
         Q[current_state, action] = Q[current_state, action] + alpha * (reward + gamma * Q[next_state, next_action] - Q[current_state, action])
         current_state = next_state
         action = next_action

state_space_size和action_space_size分别是环境中的状态和操作的数量。num_episodes是您想要运行SARSA算法的轮次数。Initial_state是环境的初始状态。take_action(current_state, action)是一个将当前状态和作为操作输入的函数，并返回下一个状态、奖励和一个指示情节是否完成的布尔值。

在while循环中，使用在单独的函数epsilon_greedy_policy(epsilon, Q, current_state)中定义的epsilon-greedy策略来根据当前状态选择操作。使用概率 epsilon选择一个随机动作，使用概率 1-epsilon对当前状态具有最高 Q 值的动作。

上面与Q-learning相同，但是采取了一个行动后，在观察下一个状态和奖励时它然后使用贪心策略选择下一个行动。并使用Bellman方程更新q表。

3、DDPG

DDPG 是一种用于连续动作空间的无模型、非策略算法。 它是一种actor-critic算法，其中actor网络用于选择动作，而critic网络用于评估动作。 DDPG 对于机器人控制和其他连续控制任务特别有用。

import numpy as np
 from keras.models import Model, Sequential
 from keras.layers import Dense, Input
 from keras.optimizers import Adam
 
 # Define the actor and critic models
 actor = Sequential()
 actor.add(Dense(32, input_dim=state_space_size, activation='relu'))
 actor.add(Dense(32, activation='relu'))
 actor.add(Dense(action_space_size, activation='tanh'))
 actor.compile(loss='mse', optimizer=Adam(lr=0.001))
 
 critic = Sequential()
 critic.add(Dense(32, input_dim=state_space_size, activation='relu'))
 critic.add(Dense(32, activation='relu'))
 critic.add(Dense(1, activation='linear'))
 critic.compile(loss='mse', optimizer=Adam(lr=0.001))
 
 # Define the replay buffer
 replay_buffer = []
 
 # Define the exploration noise
 exploration_noise = OrnsteinUhlenbeckProcess(size=action_space_size, theta=0.15, mu=0, sigma=0.2)
 
 for episode in range(num_episodes):
     current_state = initial_state
     while not done:
         # Select an action using the actor model and add exploration noise
         action = actor.predict(current_state)[0] + exploration_noise.sample()
         action = np.clip(action, -1, 1)
 
         # Take the action and observe the next state and reward
         next_state, reward, done = take_action(current_state, action)
 
         # Add the experience to the replay buffer
         replay_buffer.append((current_state, action, reward, next_state, done))
 
         # Sample a batch of experiences from the replay buffer
         batch = sample(replay_buffer, batch_size)
 
         # Update the critic model
         states = np.array([x[0] for x in batch])
         actions = np.array([x[1] for x in batch])
         rewards = np.array([x[2] for x in batch])
         next_states = np.array([x[3] for x in batch])
 
         target_q_values = rewards + gamma * critic.predict(next_states)
         critic.train_on_batch(states, target_q_values)
 
         # Update the actor model
         action_gradients = np.array(critic.get_gradients(states, actions))
         actor.train_on_batch(states, action_gradients)
 
         current_state = next_state

在本例中，state_space_size和action_space_size分别是环境中的状态和操作的数量。num_episodes是轮次数。Initial_state是环境的初始状态。Take_action (current_state, action)是一个函数，它接受当前状态和操作作为输入，并返回下一个操作。

4、A2C

A2C（Advantage Actor-Critic）是一种有策略的actor-critic算法，它使用Advantage函数来更新策略。 该算法实现简单，可以处理离散和连续的动作空间。

import numpy as np
 from keras.models import Model, Sequential
 from keras.layers import Dense, Input
 from keras.optimizers import Adam
 from keras.utils import to_categorical
 
 # Define the actor and critic models
 state_input = Input(shape=(state_space_size,))
 actor = Dense(32, activation='relu')(state_input)
 actor = Dense(32, activation='relu')(actor)
 actor = Dense(action_space_size, activation='softmax')(actor)
 actor_model = Model(inputs=state_input, outputs=actor)
 actor_model.compile(loss='categorical_crossentropy', optimizer=Adam(lr=0.001))
 
 state_input = Input(shape=(state_space_size,))
 critic = Dense(32, activation='relu')(state_input)
 critic = Dense(32, activation='relu')(critic)
 critic = Dense(1, activation='linear')(critic)
 critic_model = Model(inputs=state_input, outputs=critic)
 critic_model.compile(loss='mse', optimizer=Adam(lr=0.001))
 
 for episode in range(num_episodes):
     current_state = initial_state
     done = False
     while not done:
         # Select an action using the actor model and add exploration noise
         action_probs = actor_model.predict(np.array([current_state]))[0]
         action = np.random.choice(range(action_space_size), p=action_probs)
 
         # Take the action and observe the next state and reward
         next_state, reward, done = take_action(current_state, action)
 
         # Calculate the advantage
         target_value = critic_model.predict(np.array([next_state]))[0][0]
         advantage = reward + gamma * target_value - critic_model.predict(np.array([current_state]))[0][0]
 
         # Update the actor model
         action_one_hot = to_categorical(action, action_space_size)
         actor_model.train_on_batch(np.array([current_state]), advantage * action_one_hot)
 
         # Update the critic model
         critic_model.train_on_batch(np.array([current_state]), reward + gamma * target_value)
 
         current_state = next_state

在这个例子中，actor模型是一个神经网络，它有2个隐藏层，每个隐藏层有32个神经元，具有relu激活函数，输出层具有softmax激活函数。critic模型也是一个神经网络，它有2个隐含层，每层32个神经元，具有relu激活函数，输出层具有线性激活函数。

使用分类交叉熵损失函数训练actor模型，使用均方误差损失函数训练critic模型。动作是根据actor模型预测选择的，并添加了用于探索的噪声。

5、PPO

PPO（Proximal Policy Optimization）是一种策略算法，它使用信任域优化的方法来更新策略。 它在具有高维观察和连续动作空间的环境中特别有用。 PPO 以其稳定性和高样品效率而著称。

import numpy as np
 from keras.models import Model, Sequential
 from keras.layers import Dense, Input
 from keras.optimizers import Adam
 
 # Define the policy model
 state_input = Input(shape=(state_space_size,))
 policy = Dense(32, activation='relu')(state_input)
 policy = Dense(32, activation='relu')(policy)
 policy = Dense(action_space_size, activation='softmax')(policy)
 policy_model = Model(inputs=state_input, outputs=policy)
 
 # Define the value model
 value_model = Model(inputs=state_input, outputs=Dense(1, activation='linear')(policy))
 
 # Define the optimizer
 optimizer = Adam(lr=0.001)
 
 for episode in range(num_episodes):
     current_state = initial_state
     while not done:
         # Select an action using the policy model
         action_probs = policy_model.predict(np.array([current_state]))[0]
         action = np.random.choice(range(action_space_size), p=action_probs)
 
         # Take the action and observe the next state and reward
         next_state, reward, done = take_action(current_state, action)
 
         # Calculate the advantage
         target_value = value_model.predict(np.array([next_state]))[0][0]
         advantage = reward + gamma * target_value - value_model.predict(np.array([current_state]))[0][0]
 
         # Calculate the old and new policy probabilities
         old_policy_prob = action_probs[action]
         new_policy_prob = policy_model.predict(np.array([next_state]))[0][action]
 
         # Calculate the ratio and the surrogate loss
         ratio = new_policy_prob / old_policy_prob
         surrogate_loss = np.minimum(ratio * advantage, np.clip(ratio, 1 - epsilon, 1 + epsilon) * advantage)
 
         # Update the policy and value models
         policy_model.trainable_weights = value_model.trainable_weights
         policy_model.compile(optimizer=optimizer, loss=-surrogate_loss)
         policy_model.train_on_batch(np.array([current_state]), np.array([action_one_hot]))
         value_model.train_on_batch(np.array([current_state]), reward + gamma * target_value)
 
         current_state = next_state

6、DQN

DQN（深度 Q 网络）是一种无模型、非策略算法，它使用神经网络来逼近 Q 函数。 DQN 特别适用于 Atari 游戏和其他类似问题，其中状态空间是高维的，并使用神经网络近似 Q 函数。

import numpy as np
 from keras.models import Sequential
 from keras.layers import Dense, Input
 from keras.optimizers import Adam
 from collections import deque
 
 # Define the Q-network model
 model = Sequential()
 model.add(Dense(32, input_dim=state_space_size, activation='relu'))
 model.add(Dense(32, activation='relu'))
 model.add(Dense(action_space_size, activation='linear'))
 model.compile(loss='mse', optimizer=Adam(lr=0.001))
 
 # Define the replay buffer
 replay_buffer = deque(maxlen=replay_buffer_size)
 
 for episode in range(num_episodes):
     current_state = initial_state
     while not done:
         # Select an action using an epsilon-greedy policy
         if np.random.rand() < epsilon:
             action = np.random.randint(0, action_space_size)
         else:
             action = np.argmax(model.predict(np.array([current_state]))[0])
 
         # Take the action and observe the next state and reward
         next_state, reward, done = take_action(current_state, action)
 
         # Add the experience to the replay buffer
         replay_buffer.append((current_state, action, reward, next_state, done))
 
         # Sample a batch of experiences from the replay buffer
         batch = random.sample(replay_buffer, batch_size)
 
         # Prepare the inputs and targets for the Q-network
         inputs = np.array([x[0] for x in batch])
         targets = model.predict(inputs)
         for i, (state, action, reward, next_state, done) in enumerate(batch):
             if done:
                 targets[i, action] = reward
             else:
                 targets[i, action] = reward + gamma * np.max(model.predict(np.array([next_state]))[0])
 
         # Update the Q-network
         model.train_on_batch(inputs, targets)
 
         current_state = next_state

上面的代码，Q-network有2个隐藏层，每个隐藏层有32个神经元，使用relu激活函数。该网络使用均方误差损失函数和Adam优化器进行训练。

7、TRPO

TRPO （Trust Region Policy Optimization）是一种无模型的策略算法，它使用信任域优化方法来更新策略。 它在具有高维观察和连续动作空间的环境中特别有用。

TRPO 是一个复杂的算法，需要多个步骤和组件来实现。TRPO不是用几行代码就能实现的简单算法。

所以我们这里使用实现了TRPO的现有库，例如OpenAI Baselines，它提供了包括TRPO在内的各种预先实现的强化学习算法，。

要在OpenAI Baselines中使用TRPO，我们需要安装:

pip install baselines

然后可以使用baselines库中的trpo_mpi模块在你的环境中训练TRPO代理，这里有一个简单的例子:

import gym
 from baselines.common.vec_env.dummy_vec_env import DummyVecEnv
 from baselines.trpo_mpi import trpo_mpi
 
 #Initialize the environment
 env = gym.make("CartPole-v1")
 env = DummyVecEnv([lambda: env])
 
 # Define the policy network
 policy_fn = mlp_policy
 
 #Train the TRPO model
 model = trpo_mpi.learn(env, policy_fn, max_iters=1000)

我们使用Gym库初始化环境。然后定义策略网络，并调用TRPO模块中的learn()函数来训练模型。

还有许多其他库也提供了TRPO的实现，例如TensorFlow、PyTorch和RLLib。下面时一个使用TF 2.0实现的样例

import tensorflow as tf
 import gym
 
 # Define the policy network
 class PolicyNetwork(tf.keras.Model):
     def __init__(self):
         super(PolicyNetwork, self).__init__()
         self.dense1 = tf.keras.layers.Dense(16, activation='relu')
         self.dense2 = tf.keras.layers.Dense(16, activation='relu')
         self.dense3 = tf.keras.layers.Dense(1, activation='sigmoid')
 
     def call(self, inputs):
         x = self.dense1(inputs)
         x = self.dense2(x)
         x = self.dense3(x)
         return x
 
 # Initialize the environment
 env = gym.make("CartPole-v1")
 
 # Initialize the policy network
 policy_network = PolicyNetwork()
 
 # Define the optimizer
 optimizer = tf.optimizers.Adam()
 
 # Define the loss function
 loss_fn = tf.losses.BinaryCrossentropy()
 
 # Set the maximum number of iterations
 max_iters = 1000
 
 # Start the training loop
 for i in range(max_iters):
     # Sample an action from the policy network
     action = tf.squeeze(tf.random.categorical(policy_network(observation), 1))
 
     # Take a step in the environment
     observation, reward, done, _ = env.step(action)
 
     with tf.GradientTape() as tape:
         # Compute the loss
         loss = loss_fn(reward, policy_network(observation))
 
     # Compute the gradients
     grads = tape.gradient(loss, policy_network.trainable_variables)
 
     # Perform the update step
     optimizer.apply_gradients(zip(grads, policy_network.trainable_variables))
 
     if done:
         # Reset the environment
         observation = env.reset()

在这个例子中，我们首先使用TensorFlow的Keras API定义一个策略网络。然后使用Gym库和策略网络初始化环境。然后定义用于训练策略网络的优化器和损失函数。

在训练循环中，从策略网络中采样一个动作，在环境中前进一步，然后使用TensorFlow的GradientTape计算损失和梯度。然后我们使用优化器执行更新步骤。

这是一个简单的例子，只展示了如何在TensorFlow 2.0中实现TRPO。TRPO是一个非常复杂的算法，这个例子没有涵盖所有的细节，但它是试验TRPO的一个很好的起点。

总结

以上就是我们总结的7个常用的强化学习算法，这些算法并不相互排斥，通常与其他技术(如值函数逼近、基于模型的方法和集成方法)结合使用，可以获得更好的结果。