深度确定性策略梯度(Deep Deterministic Policy Gradient, DDPG)是受Deep Q-Network启发的无模型、非策略深度强化算法，是基于应用策略梯度的Actor-Critic，本文将应用pytorch对其进行残缺的实现和解说
DDPG的要害组成部分是
- Replay Buffer
- Actor-Critic neural network
- Exploration Noise
- Target network
- Soft Target Updates for Target Network
上面咱们一个一个来逐渐实现：
Replay Buffer
DDPG应用Replay Buffer存储通过摸索环境采样的过程和处分(S，a，R，S+)。Replay Buffer在帮忙代理减速学习以及DDPG的稳定性方面起着至关重要的作用:
- 最小化样本之间的相关性：将过来的教训存储在 Replay Buffer 中，从而容许代理从各种教训中学习。
- 启用离线策略学习：容许代理从重播缓冲区采样转换，而不是从以后策略采样转换。
- 高效采样：将过来的教训存储在缓冲区中，容许代理屡次从不同的教训中学习。
classReplay_buffer(): ''' Code based on: https://github.com/openai/baselines/blob/master/baselines/deepq/replay_buffer.py Expects tuples of (state, next_state, action, reward, done) ''' def__init__(self, max_size=capacity): """Create Replay buffer. Parameters ---------- size: int Max number of transitions to store in the buffer. When the buffer overflows the old memories are dropped. """ self.storage= [] self.max_size=max_size self.ptr=0 defpush(self, data): iflen(self.storage) ==self.max_size: self.storage[int(self.ptr)] =data self.ptr= (self.ptr+1) %self.max_size else: self.storage.append(data) defsample(self, batch_size): """Sample a batch of experiences. Parameters ---------- batch_size: int How many transitions to sample. Returns ------- state: np.array batch of state or observations action: np.array batch of actions executed given a state reward: np.array rewards received as results of executing action next_state: np.array next state next state or observations seen after executing action done: np.array done[i] = 1 if executing ation[i] resulted in the end of an episode and 0 otherwise. """ ind=np.random.randint(0, len(self.storage), size=batch_size) state, next_state, action, reward, done= [], [], [], [], [] foriinind: st, n_st, act, rew, dn=self.storage[i] state.append(np.array(st, copy=False)) next_state.append(np.array(n_st, copy=False)) action.append(np.array(act, copy=False)) reward.append(np.array(rew, copy=False)) done.append(np.array(dn, copy=False)) returnnp.array(state), np.array(next_state), np.array(action), np.array(reward).reshape(-1, 1), np.array(done).reshape(-1, 1)Actor-Critic Neural Network
这是Actor-Critic 强化学习算法的 PyTorch 实现。该代码定义了两个神经网络模型，一个 Actor 和一个 Critic。
Actor 模型的输出：环境状态；Actor 模型的输入：具备间断值的动作。
Critic 模型的输出：环境状态和动作；Critic 模型的输入：Q 值，即以后状态-动作对的预期总处分。
classActor(nn.Module): """ The Actor model takes in a state observation as input and outputs an action, which is a continuous value. It consists of four fully connected linear layers with ReLU activation functions and a final output layer selects one single optimized action for the state """ def__init__(self, n_states, action_dim, hidden1): super(Actor, self).__init__() self.net=nn.Sequential( nn.Linear(n_states, hidden1), nn.ReLU(), nn.Linear(hidden1, hidden1), nn.ReLU(), nn.Linear(hidden1, hidden1), nn.ReLU(), nn.Linear(hidden1, 1) ) defforward(self, state): returnself.net(state) classCritic(nn.Module): """ The Critic model takes in both a state observation and an action as input and outputs a Q-value, which estimates the expected total reward for the current state-action pair. It consists of four linear layers with ReLU activation functions, State and action inputs are concatenated before being fed into the first linear layer. The output layer has a single output, representing the Q-value """ def__init__(self, n_states, action_dim, hidden2): super(Critic, self).__init__() self.net=nn.Sequential( nn.Linear(n_states+action_dim, hidden2), nn.ReLU(), nn.Linear(hidden2, hidden2), nn.ReLU(), nn.Linear(hidden2, hidden2), nn.ReLU(), nn.Linear(hidden2, action_dim) ) defforward(self, state, action): returnself.net(torch.cat((state, action), 1))Exploration Noise
向 Actor 抉择的动作增加噪声是 DDPG 中用来激励摸索和改良学习过程的一种技术。
能够应用高斯噪声或 Ornstein-Uhlenbeck 噪声。 高斯噪声简略且易于实现，Ornstein-Uhlenbeck 噪声会生成工夫相干的噪声，能够帮忙代理更无效地摸索动作空间。然而与高斯噪声办法相比，Ornstein-Uhlenbeck 噪声稳定更平滑且随机性更低。
importnumpyasnp importrandom importcopy classOU_Noise(object): """Ornstein-Uhlenbeck process. code from : https://math.stackexchange.com/questions/1287634/implementing-ornstein-uhlenbeck-in-matlab The OU_Noise class has four attributes size: the size of the noise vector to be generated mu: the mean of the noise, set to 0 by default theta: the rate of mean reversion, controlling how quickly the noise returns to the mean sigma: the volatility of the noise, controlling the magnitude of fluctuations """ def__init__(self, size, seed, mu=0., theta=0.15, sigma=0.2): self.mu=mu*np.ones(size) self.theta=theta self.sigma=sigma self.seed=random.seed(seed) self.reset() defreset(self): """Reset the internal state (= noise) to mean (mu).""" self.state=copy.copy(self.mu) defsample(self): """Update internal state and return it as a noise sample. This method uses the current state of the noise and generates the next sample """ dx=self.theta* (self.mu-self.state) +self.sigma*np.array([np.random.normal() for_inrange(len(self.state))]) self.state+=dx returnself.state要在DDPG中应用高斯噪声，能够间接将高斯噪声增加到代理的动作抉择过程中。
DDPG
DDPG (Deep Deterministic Policy Gradient)采纳两组Actor-Critic神经网络进行函数迫近。在DDPG中，指标网络是Actor-Critic ，它指标网络具备与Actor-Critic网络雷同的构造和参数化。
在训练期时，代理应用其 Actor-Critic 网络与环境交互，并将教训元组（S、A、R、S+）存储在Replay Buffer中。 而后代理从 Replay Buffer 中采样并应用数据更新 Actor-Critic 网络。 DDPG 算法不是通过间接从 Actor-Critic 网络复制来更新指标网络权重，而是通过称为软指标更新的过程迟缓更新指标网络权重。
软指标的更新是从Actor-Critic网络传输到指标网络的称为指标更新率()的权重的一小部分。
软指标的更新公式如下:
通过应用软指标技术，能够大大提高学习的稳定性。
#Set Hyperparameters # Hyperparameters adapted for performance from capacity=1000000 batch_size=64 update_iteration=200 tau=0.001# tau for soft updating gamma=0.99# discount factor directory='./' hidden1=20# hidden layer for actor hidden2=64.#hiiden laye for critic classDDPG(object): def__init__(self, state_dim, action_dim): """ Initializes the DDPG agent. Takes three arguments: state_dim which is the dimensionality of the state space, action_dim which is the dimensionality of the action space, and max_action which is the maximum value an action can take. Creates a replay buffer, an actor-critic networks and their corresponding target networks. It also initializes the optimizer for both actor and critic networks alog with counters to track the number of training iterations. """ self.replay_buffer=Replay_buffer() self.actor=Actor(state_dim, action_dim, hidden1).to(device) self.actor_target=Actor(state_dim, action_dim, hidden1).to(device) self.actor_target.load_state_dict(self.actor.state_dict()) self.actor_optimizer=optim.Adam(self.actor.parameters(), lr=3e-3) self.critic=Critic(state_dim, action_dim, hidden2).to(device) self.critic_target=Critic(state_dim, action_dim, hidden2).to(device) self.critic_target.load_state_dict(self.critic.state_dict()) self.critic_optimizer=optim.Adam(self.critic.parameters(), lr=2e-2) # learning rate self.num_critic_update_iteration=0 self.num_actor_update_iteration=0 self.num_training=0 defselect_action(self, state): """ takes the current state as input and returns an action to take in that state. It uses the actor network to map the state to an action. """ state=torch.FloatTensor(state.reshape(1, -1)).to(device) returnself.actor(state).cpu().data.numpy().flatten() defupdate(self): """ updates the actor and critic networks using a batch of samples from the replay buffer. For each sample in the batch, it computes the target Q value using the target critic network and the target actor network. It then computes the current Q value using the critic network and the action taken by the actor network. It computes the critic loss as the mean squared error between the target Q value and the current Q value, and updates the critic network using gradient descent. It then computes the actor loss as the negative mean Q value using the critic network and the actor network, and updates the actor network using gradient ascent. Finally, it updates the target networks using soft updates, where a small fraction of the actor and critic network weights are transferred to their target counterparts. This process is repeated for a fixed number of iterations. """ foritinrange(update_iteration): # For each Sample in replay buffer batch state, next_state, action, reward, done=self.replay_buffer.sample(batch_size) state=torch.FloatTensor(state).to(device) action=torch.FloatTensor(action).to(device) next_state=torch.FloatTensor(next_state).to(device) done=torch.FloatTensor(1-done).to(device) reward=torch.FloatTensor(reward).to(device) # Compute the target Q value target_Q=self.critic_target(next_state, self.actor_target(next_state)) target_Q=reward+ (done*gamma*target_Q).detach() # Get current Q estimate current_Q=self.critic(state, action) # Compute critic loss critic_loss=F.mse_loss(current_Q, target_Q) # Optimize the critic self.critic_optimizer.zero_grad() critic_loss.backward() self.critic_optimizer.step() # Compute actor loss as the negative mean Q value using the critic network and the actor network actor_loss=-self.critic(state, self.actor(state)).mean() # Optimize the actor self.actor_optimizer.zero_grad() actor_loss.backward() self.actor_optimizer.step() """ Update the frozen target models using soft updates, where tau,a small fraction of the actor and critic network weights are transferred to their target counterparts. """ forparam, target_paraminzip(self.critic.parameters(), self.critic_target.parameters()): target_param.data.copy_(tau*param.data+ (1-tau) *target_param.data) forparam, target_paraminzip(self.actor.parameters(), self.actor_target.parameters()): target_param.data.copy_(tau*param.data+ (1-tau) *target_param.data) self.num_actor_update_iteration+=1 self.num_critic_update_iteration+=1 defsave(self): """ Saves the state dictionaries of the actor and critic networks to files """ torch.save(self.actor.state_dict(), directory+'actor.pth') torch.save(self.critic.state_dict(), directory+'critic.pth') defload(self): """ Loads the state dictionaries of the actor and critic networks to files """ self.actor.load_state_dict(torch.load(directory+'actor.pth')) self.critic.load_state_dict(torch.load(directory+'critic.pth'))训练DDPG
这里咱们应用 OpenAI Gym 的“MountainCarContinuous-v0”来训练咱们的DDPG RL 模型，这里的环境提供间断的口头和察看空间，指标是尽快让小车达到山顶。
上面定义算法的各种参数，例如最大训练次数、摸索噪声和记录距离等等。 应用固定的随机种子能够使得过程可能回溯。
importgym # create the environment env_name='MountainCarContinuous-v0' env=gym.make(env_name) device='cuda'iftorch.cuda.is_available() else'cpu' # Define different parameters for training the agent max_episode=100 max_time_steps=5000 ep_r=0 total_step=0 score_hist=[] # for rensering the environmnet render=True render_interval=10 # for reproducibility env.seed(0) torch.manual_seed(0) np.random.seed(0) #Environment action ans states state_dim=env.observation_space.shape[0] action_dim=env.action_space.shape[0] max_action=float(env.action_space.high[0]) min_Val=torch.tensor(1e-7).float().to(device) # Exploration Noise exploration_noise=0.1 exploration_noise=0.1*max_action创立DDPG代理类的实例，以训练代理达到指定的次数。在每轮完结时调用代理的update()办法来更新参数，并且在每十轮之后应用save()办法将代理的参数保留到一个文件中。
# Create a DDPG instance agent=DDPG(state_dim, action_dim) # Train the agent for max_episodes foriinrange(max_episode): total_reward=0 step=0 state=env.reset() for tinrange(max_time_steps): action=agent.select_action(state) # Add Gaussian noise to actions for exploration action= (action+np.random.normal(0, 1, size=action_dim)).clip(-max_action, max_action) #action += ou_noise.sample() next_state, reward, done, info=env.step(action) total_reward+=reward ifrenderandi>=render_interval : env.render() agent.replay_buffer.push((state, next_state, action, reward, np.float(done))) state=next_state ifdone: break step+=1 score_hist.append(total_reward) total_step+=step+1 print("Episode: \t{} Total Reward: \t{:0.2f}".format( i, total_reward)) agent.update() ifi%10==0: agent.save() env.close()测试DDPG
test_iteration=100 foriinrange(test_iteration): state=env.reset() fortincount(): action=agent.select_action(state) next_state, reward, done, info=env.step(np.float32(action)) ep_r+=reward print(reward) env.render() ifdone: print("reward{}".format(reward)) print("Episode \t{}, the episode reward is \t{:0.2f}".format(i, ep_r)) ep_r=0 env.render() break state=next_state咱们应用上面的参数让模型收敛：
- 从规范正态分布中采样噪声，而不是随机采样。
- 将polyak常数(tau)从0.99更改为0.001
- 批改Critic 网络的暗藏层大小为[64,64]。在Critic 网络的第二层之后删除了ReLU激活。改成(Linear, ReLU, Linear, Linear)。
- 最大缓冲区大小更改为1000000
- 将batch_size的大小从128更改为64
训练了75轮之后的成果如下：
总结
DDPG算法是一种受deep Q-Network (DQN)算法启发的无模型off-policy Actor-Critic算法。它联合了策略梯度办法和Q-learning的长处来学习间断动作空间的确定性策略。
与DQN相似，它应用重播缓冲区存储过来的教训和指标网络，用于训练网络，从而进步了训练过程的稳定性。
DDPG算法须要认真的超参数调优以获得最佳性能。超参数包含学习率、批大小、指标网络更新速率和探测噪声参数。超参数的渺小变动会对算法的性能产生重大影响。
下面的参数来自：
https://avoid.overfit.cn/post/9951ac196ec84629968ce7168215e461
作者：Renu Khandelwal