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PPO 算法

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1. 简介

TRPO 算法的改进版——PPO 算法在 2017 年被提出，PPO 基于 TRPO 的思想，但是其算法实现更加简单。并且大量的实验结果表明，与 TRPO 相比，PPO 能学习得一样好（甚至更快），这使得 PPO 成为非常流行的强化学习算法。如果我们想要尝试在一个新的环境中使用强化学习算法，那么 PPO 就属于可以首先尝试的算法。

回忆一下 TRPO 的优化目标：

TRPO 使用泰勒展开近似、共轭梯度、线性搜索等方法直接求解。PPO 的优化目标与 TRPO 相同，但 PPO 用了一些相对简单的方法来求解。具体来说，PPO 有两种形式，一是 PPO-惩罚，二是 PPO-截断，我们接下来对这两种形式进行介绍。

2.PPO-惩罚

PPO-惩罚（PPO-Penalty）用拉格朗日乘数法直接将 KL 散度的限制放进了目标函数中，这就变成了一个无约束的优化问题，在迭代的过程中不断更新 KL 散度前的系数。即：

3.PPO-截断

PPO 的另一种形式 PPO-截断（PPO-Clip）更加直接，它在目标函数中进行限制，以保证新的参数和旧的参数的差距不会太大，即：

4.PPO 代码实践

与 TRPO 相同，我们仍然在车杆和倒立摆两个环境中测试 PPO 算法。大量实验表明，PPO-截断总是比 PPO-惩罚表现得更好。因此下面我们专注于 PPO-截断的代码实现。

首先导入一些必要的库，并定义策略网络和价值网络。

import gym
import torch
import torch.nn.functional as F
import numpy as np
import matplotlib.pyplot as plt
import rl_utilsclass PolicyNet(torch.nn.Module):def __init__(self, state_dim, hidden_dim, action_dim):super(PolicyNet, self).__init__()self.fc1 = torch.nn.Linear(state_dim, hidden_dim)self.fc2 = torch.nn.Linear(hidden_dim, action_dim)def forward(self, x):x = F.relu(self.fc1(x))return F.softmax(self.fc2(x), dim=1)class ValueNet(torch.nn.Module):def __init__(self, state_dim, hidden_dim):super(ValueNet, self).__init__()self.fc1 = torch.nn.Linear(state_dim, hidden_dim)self.fc2 = torch.nn.Linear(hidden_dim, 1)def forward(self, x):x = F.relu(self.fc1(x))return self.fc2(x)class PPO:''' PPO算法,采用截断方式 '''def __init__(self, state_dim, hidden_dim, action_dim, actor_lr, critic_lr,lmbda, epochs, eps, gamma, device):self.actor = PolicyNet(state_dim, hidden_dim, action_dim).to(device)self.critic = ValueNet(state_dim, hidden_dim).to(device)self.actor_optimizer = torch.optim.Adam(self.actor.parameters(),lr=actor_lr)self.critic_optimizer = torch.optim.Adam(self.critic.parameters(),lr=critic_lr)self.gamma = gammaself.lmbda = lmbdaself.epochs = epochs  # 一条序列的数据用来训练轮数self.eps = eps  # PPO中截断范围的参数self.device = devicedef take_action(self, state):state = torch.tensor([state], dtype=torch.float).to(self.device)probs = self.actor(state)action_dist = torch.distributions.Categorical(probs)action = action_dist.sample()return action.item()def update(self, transition_dict):states = torch.tensor(transition_dict['states'],dtype=torch.float).to(self.device)actions = torch.tensor(transition_dict['actions']).view(-1, 1).to(self.device)rewards = torch.tensor(transition_dict['rewards'],dtype=torch.float).view(-1, 1).to(self.device)next_states = torch.tensor(transition_dict['next_states'],dtype=torch.float).to(self.device)dones = torch.tensor(transition_dict['dones'],dtype=torch.float).view(-1, 1).to(self.device)td_target = rewards + self.gamma * self.critic(next_states) * (1 -dones)td_delta = td_target - self.critic(states)advantage = rl_utils.compute_advantage(self.gamma, self.lmbda,td_delta.cpu()).to(self.device)old_log_probs = torch.log(self.actor(states).gather(1,actions)).detach()for _ in range(self.epochs):log_probs = torch.log(self.actor(states).gather(1, actions))ratio = torch.exp(log_probs - old_log_probs)surr1 = ratio * advantagesurr2 = torch.clamp(ratio, 1 - self.eps,1 + self.eps) * advantage  # 截断actor_loss = torch.mean(-torch.min(surr1, surr2))  # PPO损失函数critic_loss = torch.mean(F.mse_loss(self.critic(states), td_target.detach()))self.actor_optimizer.zero_grad()self.critic_optimizer.zero_grad()actor_loss.backward()critic_loss.backward()self.actor_optimizer.step()self.critic_optimizer.step()

接下来在车杆环境中训练 PPO 算法。

actor_lr = 1e-3
critic_lr = 1e-2
num_episodes = 500
hidden_dim = 128
gamma = 0.98
lmbda = 0.95
epochs = 10
eps = 0.2
device = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")env_name = 'CartPole-v0'
env = gym.make(env_name)
env.seed(0)
torch.manual_seed(0)
state_dim = env.observation_space.shape[0]
action_dim = env.action_space.n
agent = PPO(state_dim, hidden_dim, action_dim, actor_lr, critic_lr, lmbda,epochs, eps, gamma, device)return_list = rl_utils.train_on_policy_agent(env, agent, num_episodes)

episodes_list = list(range(len(return_list)))
plt.plot(episodes_list, return_list)
plt.xlabel('Episodes')
plt.ylabel('Returns')
plt.title('PPO on {}'.format(env_name))
plt.show()mv_return = rl_utils.moving_average(return_list, 9)
plt.plot(episodes_list, mv_return)
plt.xlabel('Episodes')
plt.ylabel('Returns')
plt.title('PPO on {}'.format(env_name))
plt.show()

倒立摆是与连续动作交互的环境，同 TRPO 算法一样，我们做一些修改，让策略网络输出连续动作高斯分布（Gaussian distribution）的均值和标准差。后续的连续动作则在该高斯分布中采样得到。

class PolicyNetContinuous(torch.nn.Module):def __init__(self, state_dim, hidden_dim, action_dim):super(PolicyNetContinuous, self).__init__()self.fc1 = torch.nn.Linear(state_dim, hidden_dim)self.fc_mu = torch.nn.Linear(hidden_dim, action_dim)self.fc_std = torch.nn.Linear(hidden_dim, action_dim)def forward(self, x):x = F.relu(self.fc1(x))mu = 2.0 * torch.tanh(self.fc_mu(x))std = F.softplus(self.fc_std(x))return mu, stdclass PPOContinuous:''' 处理连续动作的PPO算法 '''def __init__(self, state_dim, hidden_dim, action_dim, actor_lr, critic_lr,lmbda, epochs, eps, gamma, device):self.actor = PolicyNetContinuous(state_dim, hidden_dim,action_dim).to(device)self.critic = ValueNet(state_dim, hidden_dim).to(device)self.actor_optimizer = torch.optim.Adam(self.actor.parameters(),lr=actor_lr)self.critic_optimizer = torch.optim.Adam(self.critic.parameters(),lr=critic_lr)self.gamma = gammaself.lmbda = lmbdaself.epochs = epochsself.eps = epsself.device = devicedef take_action(self, state):state = torch.tensor([state], dtype=torch.float).to(self.device)mu, sigma = self.actor(state)action_dist = torch.distributions.Normal(mu, sigma)action = action_dist.sample()return [action.item()]def update(self, transition_dict):states = torch.tensor(transition_dict['states'],dtype=torch.float).to(self.device)actions = torch.tensor(transition_dict['actions'],dtype=torch.float).view(-1, 1).to(self.device)rewards = torch.tensor(transition_dict['rewards'],dtype=torch.float).view(-1, 1).to(self.device)next_states = torch.tensor(transition_dict['next_states'],dtype=torch.float).to(self.device)dones = torch.tensor(transition_dict['dones'],dtype=torch.float).view(-1, 1).to(self.device)rewards = (rewards + 8.0) / 8.0  # 和TRPO一样,对奖励进行修改,方便训练td_target = rewards + self.gamma * self.critic(next_states) * (1 -dones)td_delta = td_target - self.critic(states)advantage = rl_utils.compute_advantage(self.gamma, self.lmbda,td_delta.cpu()).to(self.device)mu, std = self.actor(states)action_dists = torch.distributions.Normal(mu.detach(), std.detach())# 动作是正态分布old_log_probs = action_dists.log_prob(actions)for _ in range(self.epochs):mu, std = self.actor(states)action_dists = torch.distributions.Normal(mu, std)log_probs = action_dists.log_prob(actions)ratio = torch.exp(log_probs - old_log_probs)surr1 = ratio * advantagesurr2 = torch.clamp(ratio, 1 - self.eps, 1 + self.eps) * advantageactor_loss = torch.mean(-torch.min(surr1, surr2))critic_loss = torch.mean(F.mse_loss(self.critic(states), td_target.detach()))self.actor_optimizer.zero_grad()self.critic_optimizer.zero_grad()actor_loss.backward()critic_loss.backward()self.actor_optimizer.step()self.critic_optimizer.step()

创建环境Pendulum-v0，并设定随机数种子以便重复实现。接下来我们在倒立摆环境中训练 PPO 算法。

actor_lr = 1e-4
critic_lr = 5e-3
num_episodes = 2000
hidden_dim = 128
gamma = 0.9
lmbda = 0.9
epochs = 10
eps = 0.2
device = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")env_name = 'Pendulum-v0'
env = gym.make(env_name)
env.seed(0)
torch.manual_seed(0)
state_dim = env.observation_space.shape[0]
action_dim = env.action_space.shape[0]  # 连续动作空间
agent = PPOContinuous(state_dim, hidden_dim, action_dim, actor_lr, critic_lr,lmbda, epochs, eps, gamma, device)return_list = rl_utils.train_on_policy_agent(env, agent, num_episodes)

episodes_list = list(range(len(return_list)))
plt.plot(episodes_list, return_list)
plt.xlabel('Episodes')
plt.ylabel('Returns')
plt.title('PPO on {}'.format(env_name))
plt.show()mv_return = rl_utils.moving_average(return_list, 21)
plt.plot(episodes_list, mv_return)
plt.xlabel('Episodes')
plt.ylabel('Returns')
plt.title('PPO on {}'.format(env_name))
plt.show()

5.总结

PPO 是 TRPO 的一种改进算法，它在实现上简化了 TRPO 中的复杂计算，并且它在实验中的性能大多数情况下会比 TRPO 更好，因此目前常被用作一种常用的基准算法。需要注意的是，TRPO 和 PPO 都属于在线策略学习算法，即使优化目标中包含重要性采样的过程，但其只是用到了上一轮策略的数据，而不是过去所有策略的数据。

PPO 是 TRPO 的第一作者 John Schulman 从加州大学伯克利分校博士毕业后在 OpenAI 公司研究出来的。通过对 TRPO 计算方式的改进，PPO 成为了最受关注的深度强化学习算法之一，并且其论文的引用量也超越了 TRPO。