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diff --git a/BreakoutNoFrameskip-v4/draw_return_Breakout.png b/BreakoutNoFrameskip-v4/draw_return_Breakout.png
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diff --git a/v4/ppo.py b/v4/ppo.py
new file mode 100644
index 0000000..ed646d0
--- /dev/null
+++ b/v4/ppo.py
@@ -0,0 +1,317 @@
+import argparse
+import os
+import random
+import time
+
+import gym
+import numpy as np
+import torch
+import torch.nn as nn
+import torch.optim as optim
+from stable_baselines3.common.atari_wrappers import (
+    ClipRewardEnv,
+    EpisodicLifeEnv,
+    FireResetEnv,
+    MaxAndSkipEnv,
+    NoopResetEnv
+)
+from torch.distributions.categorical import Categorical
+from torch.utils.tensorboard import SummaryWriter
+from tqdm import tqdm
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--exp_name', type=str, default=os.path.basename(__file__).rstrip('.py'))
+    parser.add_argument('--gym_id', type=str, default='BreakoutNoFrameskip-v4')
+    parser.add_argument('--learning_rate', type=float, default=2.5e-4)
+    parser.add_argument('--seed', type=int, default=1)
+    parser.add_argument('--total_steps', type=int, default=int(1e7))
+    parser.add_argument('--use_cuda', type=bool, default=True)
+    parser.add_argument('--num_envs', type=int, default=8)
+    parser.add_argument('--num_steps', type=int, default=128)
+    parser.add_argument('--lr_decay', type=bool, default=True)
+    parser.add_argument('--use_gae', type=bool, default=True)
+    parser.add_argument('--gae_lambda', type=float, default=0.95)
+    parser.add_argument('--gamma', type=float, default=0.99)
+    parser.add_argument('--num_mini_batches', type=int, default=4)
+    parser.add_argument('--update_epochs', type=int, default=4)
+    parser.add_argument('--norm_adv', type=bool, default=True)
+    parser.add_argument('--clip_value_loss', type=bool, default=True)
+    parser.add_argument('--c_1', type=float, default=1.0)
+    parser.add_argument('--c_2', type=float, default=0.01)
+    parser.add_argument('--max_grad_norm', type=float, default=0.5)
+    parser.add_argument('--clip_epsilon', type=float, default=0.2)
+    a = parser.parse_args()
+    a.batch_size = int(a.num_envs * a.num_steps)
+    a.minibatch_size = int(a.batch_size // a.num_mini_batches)
+    return a
+
+
+def make_env(gym_id, seed):
+    def thunk():
+        env = gym.make(gym_id)
+        env = gym.wrappers.RecordEpisodeStatistics(env)
+        env = NoopResetEnv(env, noop_max=30)
+        env = MaxAndSkipEnv(env, skip=4)
+        env = EpisodicLifeEnv(env)
+        if 'FIRE' in env.unwrapped.get_action_meanings():
+            env = FireResetEnv(env)
+        env = ClipRewardEnv(env)
+        env = gym.wrappers.ResizeObservation(env, (84, 84))
+        env = gym.wrappers.GrayScaleObservation(env)
+        env = gym.wrappers.FrameStack(env, 4)
+        env.seed(seed)
+        env.action_space.seed(seed)
+        env.observation_space.seed(seed)
+        return env
+    return thunk
+
+
+def layer_init(layer, std=np.sqrt(2), bias_const=0.0):
+    torch.nn.init.orthogonal_(layer.weight, std)
+    torch.nn.init.constant_(layer.bias, bias_const)
+    return layer
+
+
+class Agent(nn.Module):
+    def __init__(self, e):
+        super(Agent, self).__init__()
+        self.network = nn.Sequential(
+            layer_init(nn.Conv2d(4, 32, 8, stride=4)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(32, 64, 4, stride=2)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(64, 64, 3, stride=1)),
+            nn.ReLU(),
+            nn.Flatten(),
+            layer_init(nn.Linear(64 * 7 * 7, 512)),
+            nn.ReLU(),
+        )
+        self.actor = layer_init(nn.Linear(512, e.single_action_space.n), std=0.01)
+        self.critic = layer_init(nn.Linear(512, 1), std=1)
+
+    def get_value(self, x):
+        return self.critic(self.network(x / 255.0))
+
+    def get_action_and_value(self, x, a=None, show_all=False):
+        hidden = self.network(x / 255.0)
+        log = self.actor(hidden)
+        p = Categorical(logits=log)
+        if a is None:
+            a = p.sample()
+        if show_all:
+            return a, p.log_prob(a), p.entropy(), self.critic(hidden), p.probs
+        return a, p.log_prob(a), p.entropy(), self.critic(hidden)
+
+
+def main(env_id, seed):
+    args = get_args()
+    args.gym_id = env_id
+    args.seed = seed
+    run_name = (
+            'ppo' +
+            '_epoch_' + str(args.update_epochs) +
+            '_seed_' + str(args.seed)
+    )
+
+    # 保存训练日志
+    path_string = str(args.gym_id).split('NoFrameskip')[0] + '/' + run_name
+    writer = SummaryWriter(path_string)
+    writer.add_text(
+        'Hyperparameter',
+        '|param|value|\n|-|-|\n%s' % ('\n'.join([f'|{key}|{value}|' for key, value in vars(args).items()])),
+    )
+
+    # 随机数种子
+    random.seed(args.seed)
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+
+    # 初始化环境
+    device = torch.device('cuda' if torch.cuda.is_available() and args.use_cuda else 'cpu')
+    envs = gym.vector.SyncVectorEnv(
+        [make_env(args.gym_id, args.seed + i) for i in range(args.num_envs)]
+    )
+    assert isinstance(envs.single_action_space, gym.spaces.Discrete), 'only discrete action space is supported'
+    agent = Agent(envs).to(device)
+    optimizer = optim.Adam(agent.parameters(), lr=args.learning_rate, eps=1e-5)
+
+    # 初始化存储
+    obs = torch.zeros((args.num_steps, args.num_envs) + envs.single_observation_space.shape).to(device)
+    actions = torch.zeros((args.num_steps, args.num_envs) + envs.single_action_space.shape).to(device)
+    probs = torch.zeros((args.num_steps, args.num_envs, envs.single_action_space.n)).to(device)
+    log_probs = torch.zeros((args.num_steps, args.num_envs)).to(device)
+    rewards = torch.zeros((args.num_steps, args.num_envs)).to(device)
+    dones = torch.zeros((args.num_steps, args.num_envs)).to(device)
+    values = torch.zeros((args.num_steps, args.num_envs)).to(device)
+
+    # 开始收集数据
+    global_step = 0
+    start_time = time.time()
+    next_obs = torch.Tensor(envs.reset()).to(device)
+    next_done = torch.zeros(args.num_envs).to(device)
+    num_updates = int(args.total_steps // args.batch_size)
+
+    for update in tqdm(range(1, num_updates + 1)):
+
+        # 学习率是否衰减
+        if args.lr_decay:
+            frac = 1.0 - (update - 1.0) / num_updates
+            lr_now = frac * args.learning_rate
+            optimizer.param_groups[0]['lr'] = lr_now
+
+        for step in range(0, args.num_steps):
+
+            # 每一步更新步数还要乘上并行的环境数
+            global_step += 1 * args.num_envs
+            obs[step] = next_obs
+            dones[step] = next_done
+
+            # 计算旧的策略网络输出动作概率分布的对数
+            with torch.no_grad():
+                action, log_prob, _, value, prob = agent.get_action_and_value(next_obs, show_all=True)
+                values[step] = value.flatten()
+            actions[step] = action
+            probs[step] = prob
+            log_probs[step] = log_prob
+
+            # 更新环境
+            next_obs, reward, done, info = envs.step(action.cpu().numpy())
+            rewards[step] = torch.tensor(reward).to(device).view(-1)
+            next_obs, next_done = torch.Tensor(next_obs).to(device), torch.Tensor(done).to(device)
+
+            # 如果并行环境中有一个环境结束了，则输出总步数以及回合奖励和回合长度
+            for item in info:
+                if 'episode' in item.keys():
+                    # print(f"global_step={global_step}, episodic_return={item['episode']['r']}")
+                    writer.add_scalar('charts/episodic_return', item['episode']['r'], global_step)
+                    break
+
+        # 计算GAE
+        with torch.no_grad():
+            next_value = agent.get_value(next_obs).reshape(1, -1)
+            if args.use_gae:
+                advantages = torch.zeros_like(rewards).to(device)
+                last_gae_lam = 0
+                for t in reversed(range(args.num_steps)):
+                    if t == args.num_steps - 1:
+                        next_non_terminal = 1.0 - next_done
+                        next_values = next_value
+                    else:
+                        next_non_terminal = 1.0 - dones[t + 1]
+                        next_values = values[t + 1]
+                    delta = rewards[t] + args.gamma * next_values * next_non_terminal - values[t]
+                    advantages[t] = last_gae_lam = (
+                            delta + args.gamma * args.gae_lambda * next_non_terminal * last_gae_lam
+                    )
+                returns = advantages + values
+            else:
+                returns = torch.zeros_like(rewards).to(device)
+                for t in reversed(range(args.num_steps)):
+                    if t == args.num_steps - 1:
+                        next_non_terminal = 1.0 - next_done
+                        next_return = next_value
+                    else:
+                        next_non_terminal = 1.0 - dones[t + 1]
+                        next_return = returns[t + 1]
+                    returns[t] = rewards[t] + args.gamma * next_non_terminal * next_return
+                advantages = returns - values
+
+        # ------------------------------- 上面收集了足够的数据，下面开始更新 ------------------------------- #
+        # 将每个batch展平
+        b_obs = obs.reshape((-1,) + envs.single_observation_space.shape)
+        b_probs = probs.reshape((-1, envs.single_action_space.n))
+        b_log_probs = log_probs.reshape(-1)
+        b_actions = actions.reshape((-1,) + envs.single_action_space.shape)
+        b_advantages = advantages.reshape(-1)
+        b_returns = returns.reshape(-1)
+        b_values = values.reshape(-1)
+
+        # 更新策略网络和价值网络
+        b_index = np.arange(args.batch_size)
+        for epoch in range(1, args.update_epochs + 1):
+            np.random.shuffle(b_index)
+            for start in range(0, args.batch_size, args.minibatch_size):
+                end = start + args.minibatch_size
+                mb_index = b_index[start:end]
+
+                # 得到最新的策略网络和价值网络输出
+                _, new_log_prob, entropy, new_value, new_probs = (
+                    agent.get_action_and_value(b_obs[mb_index], b_actions.long()[mb_index], show_all=True)
+                )
+
+                # 计算kl散度
+                d = torch.sum(
+                    b_probs[mb_index] * torch.log((b_probs[mb_index] + 1e-12) / (new_probs + 1e-12)), 1
+                )
+                writer.add_scalar('charts/average_kld', d.mean(), global_step)
+                writer.add_scalar('others/min_kld', d.min(), global_step)
+                writer.add_scalar('others/max_kld', d.max(), global_step)
+                log_ratio = new_log_prob - b_log_probs[mb_index]
+                ratio = log_ratio.exp()
+
+                # 优势值归一化
+                mb_advantages = b_advantages[mb_index]
+                if args.norm_adv:
+                    mb_advantages = (mb_advantages - mb_advantages.mean()) / (mb_advantages.std() + 1e-12)
+
+                # 策略网络损失
+                pg_loss1 = -mb_advantages * ratio
+                pg_loss2 = -mb_advantages * torch.clamp(ratio, 1 - args.clip_epsilon, 1 + args.clip_epsilon)
+                pg_loss = torch.max(pg_loss1, pg_loss2).mean()
+
+                # 价值网络损失
+                new_value = new_value.view(-1)
+                if args.clip_value_loss:
+                    v_loss_un_clipped = (new_value - b_returns[mb_index]) ** 2
+                    v_clipped = b_values[mb_index] + torch.clamp(
+                        new_value - b_values[mb_index],
+                        -args.clip_epsilon,
+                        args.clip_epsilon,
+                    )
+                    v_loss_clipped = (v_clipped - b_returns[mb_index]) ** 2
+                    v_loss_max = torch.max(v_loss_un_clipped, v_loss_clipped)
+                    v_loss = 0.5 * v_loss_max.mean()
+                else:
+                    v_loss = 0.5 * ((new_value - b_returns[mb_index]) ** 2).mean()
+
+                entropy_loss = entropy.mean()
+
+                # 损失
+                loss = pg_loss + v_loss * args.c_1 - entropy_loss * args.c_2
+
+                # 写入训练过程的一些数据
+                writer.add_scalar('losses/value_loss', v_loss.item(), global_step)
+                writer.add_scalar('losses/policy_loss', pg_loss.item(), global_step)
+                writer.add_scalar('losses/entropy', entropy_loss.item(), global_step)
+                writer.add_scalar('losses/delta', torch.abs(ratio - 1).mean().item(), global_step)
+
+                # 更新网络参数
+                optimizer.zero_grad()
+                loss.backward()
+                nn.utils.clip_grad_norm_(agent.parameters(), args.max_grad_norm)
+                optimizer.step()
+
+        y_pre, y_true = b_values.cpu().numpy(), b_returns.cpu().numpy()
+        var_y = np.var(y_true)
+        explained_var = np.nan if var_y == 0 else 1 - np.var(y_true - y_pre) / var_y
+
+        # 写入训练过程的一些数据
+        writer.add_scalar('charts/learning_rate', optimizer.param_groups[0]['lr'], global_step)
+        writer.add_scalar('others/explained_variance', explained_var, global_step)
+        writer.add_scalar('charts/SPS', int(global_step / (time.time() - start_time)), global_step)
+
+    envs.close()
+    writer.close()
+
+
+def run():
+    for env_id in ['Breakout']:
+        for seed in [1, 2, 3]:
+            print(env_id + 'NoFrameskip-v4', 'seed:', seed)
+            main(env_id + 'NoFrameskip-v4', seed)
+
+
+if __name__ == '__main__':
+    run()
diff --git a/v4/spo.py b/v4/spo.py
new file mode 100644
index 0000000..e59cf2c
--- /dev/null
+++ b/v4/spo.py
@@ -0,0 +1,329 @@
+import argparse
+import os
+import random
+import time
+
+import gym
+import numpy as np
+import torch
+import torch.nn as nn
+import torch.optim as optim
+from stable_baselines3.common.atari_wrappers import (
+    ClipRewardEnv,
+    EpisodicLifeEnv,
+    FireResetEnv,
+    MaxAndSkipEnv,
+    NoopResetEnv
+)
+from torch.distributions.categorical import Categorical
+from torch.utils.tensorboard import SummaryWriter
+from tqdm import tqdm
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--exp_name', type=str, default=os.path.basename(__file__).rstrip('.py'))
+    parser.add_argument('--gym_id', type=str, default='BreakoutNoFrameskip-v4')
+    parser.add_argument('--learning_rate', type=float, default=2.5e-4)
+    parser.add_argument('--seed', type=int, default=1)
+    parser.add_argument('--total_steps', type=int, default=int(1e7))
+    parser.add_argument('--use_cuda', type=bool, default=True)
+    parser.add_argument('--num_envs', type=int, default=8)
+    parser.add_argument('--num_steps', type=int, default=128)
+    parser.add_argument('--lr_decay', type=bool, default=True)
+    parser.add_argument('--use_gae', type=bool, default=True)
+    parser.add_argument('--gae_lambda', type=float, default=0.95)
+    parser.add_argument('--gamma', type=float, default=0.99)
+    parser.add_argument('--num_mini_batches', type=int, default=4)
+    parser.add_argument('--update_epochs', type=int, default=8)
+    parser.add_argument('--norm_adv', type=bool, default=True)
+    parser.add_argument('--clip_value_loss', type=bool, default=True)
+    parser.add_argument('--c_1', type=float, default=1.0)
+    parser.add_argument('--c_2', type=float, default=0.01)
+    parser.add_argument('--max_grad_norm', type=float, default=0.5)
+    parser.add_argument('--kld_max', type=float, default=0.02)
+    a = parser.parse_args()
+    a.batch_size = int(a.num_envs * a.num_steps)
+    a.minibatch_size = int(a.batch_size // a.num_mini_batches)
+    return a
+
+
+def make_env(gym_id, seed):
+    def thunk():
+        env = gym.make(gym_id)
+        env = gym.wrappers.RecordEpisodeStatistics(env)
+        env = NoopResetEnv(env, noop_max=30)
+        env = MaxAndSkipEnv(env, skip=4)
+        env = EpisodicLifeEnv(env)
+        if 'FIRE' in env.unwrapped.get_action_meanings():
+            env = FireResetEnv(env)
+        env = ClipRewardEnv(env)
+        env = gym.wrappers.ResizeObservation(env, (84, 84))
+        env = gym.wrappers.GrayScaleObservation(env)
+        env = gym.wrappers.FrameStack(env, 4)
+        env.seed(seed)
+        env.action_space.seed(seed)
+        env.observation_space.seed(seed)
+        return env
+    return thunk
+
+
+def layer_init(layer, std=np.sqrt(2), bias_const=0.0):
+    torch.nn.init.orthogonal_(layer.weight, std)
+    torch.nn.init.constant_(layer.bias, bias_const)
+    return layer
+
+
+class Agent(nn.Module):
+    def __init__(self, e):
+        super(Agent, self).__init__()
+        self.network = nn.Sequential(
+            layer_init(nn.Conv2d(4, 32, 8, stride=4)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(32, 64, 4, stride=2)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(64, 64, 3, stride=1)),
+            nn.ReLU(),
+            nn.Flatten(),
+            layer_init(nn.Linear(64 * 7 * 7, 512)),
+            nn.ReLU(),
+        )
+        self.actor = layer_init(nn.Linear(512, e.single_action_space.n), std=0.01)
+        self.critic = layer_init(nn.Linear(512, 1), std=1)
+
+    def get_value(self, x):
+        return self.critic(self.network(x / 255.0))
+
+    def get_action_and_value(self, x, a=None, show_all=False):
+        hidden = self.network(x / 255.0)
+        log = self.actor(hidden)
+        p = Categorical(logits=log)
+        if a is None:
+            a = p.sample()
+        if show_all:
+            return a, p.log_prob(a), p.entropy(), self.critic(hidden), p.probs
+        return a, p.log_prob(a), p.entropy(), self.critic(hidden)
+
+
+def main(env_id, seed):
+    args = get_args()
+    args.gym_id = env_id
+    args.seed = seed
+    run_name = (
+            'spo_' + str(args.kld_max) +
+            '_epoch_' + str(args.update_epochs) +
+            '_seed_' + str(args.seed)
+    )
+
+    # 保存训练日志
+    path_string = str(args.gym_id).split('NoFrameskip')[0] + '/' + run_name
+    writer = SummaryWriter(path_string)
+    writer.add_text(
+        'Hyperparameter',
+        '|param|value|\n|-|-|\n%s' % ('\n'.join([f'|{key}|{value}|' for key, value in vars(args).items()])),
+    )
+
+    # 随机数种子
+    random.seed(args.seed)
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+
+    # 初始化环境
+    device = torch.device('cuda' if torch.cuda.is_available() and args.use_cuda else 'cpu')
+    envs = gym.vector.SyncVectorEnv(
+        [make_env(args.gym_id, args.seed + i) for i in range(args.num_envs)]
+    )
+    assert isinstance(envs.single_action_space, gym.spaces.Discrete), 'only discrete action space is supported'
+    agent = Agent(envs).to(device)
+    optimizer = optim.Adam(agent.parameters(), lr=args.learning_rate, eps=1e-5)
+
+    # 初始化存储
+    obs = torch.zeros((args.num_steps, args.num_envs) + envs.single_observation_space.shape).to(device)
+    actions = torch.zeros((args.num_steps, args.num_envs) + envs.single_action_space.shape).to(device)
+    probs = torch.zeros((args.num_steps, args.num_envs, envs.single_action_space.n)).to(device)
+    log_probs = torch.zeros((args.num_steps, args.num_envs)).to(device)
+    rewards = torch.zeros((args.num_steps, args.num_envs)).to(device)
+    dones = torch.zeros((args.num_steps, args.num_envs)).to(device)
+    values = torch.zeros((args.num_steps, args.num_envs)).to(device)
+
+    # 开始收集数据
+    global_step = 0
+    start_time = time.time()
+    next_obs = torch.Tensor(envs.reset()).to(device)
+    next_done = torch.zeros(args.num_envs).to(device)
+    num_updates = int(args.total_steps // args.batch_size)
+
+    for update in tqdm(range(1, num_updates + 1)):
+
+        # 学习率是否衰减
+        if args.lr_decay:
+            frac = 1.0 - (update - 1.0) / num_updates
+            lr_now = frac * args.learning_rate
+            optimizer.param_groups[0]['lr'] = lr_now
+
+        for step in range(0, args.num_steps):
+
+            # 每一步更新步数还要乘上并行的环境数
+            global_step += 1 * args.num_envs
+            obs[step] = next_obs
+            dones[step] = next_done
+
+            # 计算旧的策略网络输出动作概率分布的对数
+            with torch.no_grad():
+                action, log_prob, _, value, prob = agent.get_action_and_value(next_obs, show_all=True)
+                values[step] = value.flatten()
+            actions[step] = action
+            probs[step] = prob
+            log_probs[step] = log_prob
+
+            # 更新环境
+            next_obs, reward, done, info = envs.step(action.cpu().numpy())
+            rewards[step] = torch.tensor(reward).to(device).view(-1)
+            next_obs, next_done = torch.Tensor(next_obs).to(device), torch.Tensor(done).to(device)
+
+            # 如果并行环境中有一个环境结束了，则输出总步数以及回合奖励和回合长度
+            for item in info:
+                if 'episode' in item.keys():
+                    # print(f"global_step={global_step}, episodic_return={item['episode']['r']}")
+                    writer.add_scalar('charts/episodic_return', item['episode']['r'], global_step)
+                    break
+
+        # 计算GAE
+        with torch.no_grad():
+            next_value = agent.get_value(next_obs).reshape(1, -1)
+            if args.use_gae:
+                advantages = torch.zeros_like(rewards).to(device)
+                last_gae_lam = 0
+                for t in reversed(range(args.num_steps)):
+                    if t == args.num_steps - 1:
+                        next_non_terminal = 1.0 - next_done
+                        next_values = next_value
+                    else:
+                        next_non_terminal = 1.0 - dones[t + 1]
+                        next_values = values[t + 1]
+                    delta = rewards[t] + args.gamma * next_values * next_non_terminal - values[t]
+                    advantages[t] = last_gae_lam = (
+                            delta + args.gamma * args.gae_lambda * next_non_terminal * last_gae_lam
+                    )
+                returns = advantages + values
+            else:
+                returns = torch.zeros_like(rewards).to(device)
+                for t in reversed(range(args.num_steps)):
+                    if t == args.num_steps - 1:
+                        next_non_terminal = 1.0 - next_done
+                        next_return = next_value
+                    else:
+                        next_non_terminal = 1.0 - dones[t + 1]
+                        next_return = returns[t + 1]
+                    returns[t] = rewards[t] + args.gamma * next_non_terminal * next_return
+                advantages = returns - values
+
+        # ------------------------------- 上面收集了足够的数据，下面开始更新 ------------------------------- #
+        # 将每个batch展平
+        b_obs = obs.reshape((-1,) + envs.single_observation_space.shape)
+        b_probs = probs.reshape((-1, envs.single_action_space.n))
+        b_log_probs = log_probs.reshape(-1)
+        b_actions = actions.reshape((-1,) + envs.single_action_space.shape)
+        b_advantages = advantages.reshape(-1)
+        b_returns = returns.reshape(-1)
+        b_values = values.reshape(-1)
+
+        # 更新策略网络和价值网络
+        b_index = np.arange(args.batch_size)
+        for epoch in range(1, args.update_epochs + 1):
+            np.random.shuffle(b_index)
+            t = 0
+            for start in range(0, args.batch_size, args.minibatch_size):
+                t += 1
+                end = start + args.minibatch_size
+                mb_index = b_index[start:end]
+
+                # 得到最新的策略网络和价值网络输出
+                _, new_log_prob, entropy, new_value, new_probs = (
+                    agent.get_action_and_value(b_obs[mb_index], b_actions.long()[mb_index], show_all=True)
+                )
+
+                # 计算kl散度
+                d = torch.sum(
+                    b_probs[mb_index] * torch.log((b_probs[mb_index] + 1e-12) / (new_probs + 1e-12)), 1
+                )
+                writer.add_scalar('charts/average_kld', d.mean(), global_step)
+                writer.add_scalar('others/min_kld', d.min(), global_step)
+                writer.add_scalar('others/max_kld', d.max(), global_step)
+                log_ratio = new_log_prob - b_log_probs[mb_index]
+                ratios = log_ratio.exp()
+
+                # 优势值归一化
+                mb_advantages = b_advantages[mb_index]
+                if args.norm_adv:
+                    mb_advantages = (mb_advantages - mb_advantages.mean()) / (mb_advantages.std() + 1e-12)
+
+                # 策略网络损失
+                new_value = new_value.view(-1)
+                if epoch == 1 and t == 1:
+                    pg_loss = (-mb_advantages * ratios).mean()
+                else:
+                    d_clip = torch.clamp(input=d, min=0, max=args.kld_max)
+                    # d_clip / d
+                    ratio = d_clip / (d + 1e-12)
+                    # sign_a
+                    sign_a = torch.sign(mb_advantages)
+                    # (d_clip / d + sign_a - 1) * sign_a
+                    result = (ratio + sign_a - 1) * sign_a
+                    # 策略网络损失
+                    pg_loss = (-mb_advantages * ratios * result).mean()
+
+                # 价值网络损失
+                new_value = new_value.view(-1)
+                if args.clip_value_loss:
+                    v_loss_un_clipped = (new_value - b_returns[mb_index]) ** 2
+                    v_clipped = b_values[mb_index] + torch.clamp(
+                        new_value - b_values[mb_index],
+                        -0.2,
+                        0.2,
+                    )
+                    v_loss_clipped = (v_clipped - b_returns[mb_index]) ** 2
+                    v_loss_max = torch.max(v_loss_un_clipped, v_loss_clipped)
+                    v_loss = 0.5 * v_loss_max.mean()
+                else:
+                    v_loss = 0.5 * ((new_value - b_returns[mb_index]) ** 2).mean()
+
+                entropy_loss = entropy.mean()
+
+                # 损失
+                loss = pg_loss + v_loss * args.c_1 - entropy_loss * args.c_2
+
+                # 写入训练过程的一些数据
+                writer.add_scalar('losses/value_loss', v_loss.item(), global_step)
+                writer.add_scalar('losses/policy_loss', pg_loss.item(), global_step)
+                writer.add_scalar('losses/entropy', entropy_loss.item(), global_step)
+                writer.add_scalar('losses/delta', torch.abs(ratios - 1).mean().item(), global_step)
+
+                # 更新网络参数
+                optimizer.zero_grad()
+                loss.backward()
+                nn.utils.clip_grad_norm_(agent.parameters(), args.max_grad_norm)
+                optimizer.step()
+
+        y_pre, y_true = b_values.cpu().numpy(), b_returns.cpu().numpy()
+        var_y = np.var(y_true)
+        explained_var = np.nan if var_y == 0 else 1 - np.var(y_true - y_pre) / var_y
+
+        # 写入训练过程的一些数据
+        writer.add_scalar('charts/learning_rate', optimizer.param_groups[0]['lr'], global_step)
+        writer.add_scalar('others/explained_variance', explained_var, global_step)
+        writer.add_scalar('charts/SPS', int(global_step / (time.time() - start_time)), global_step)
+
+    envs.close()
+    writer.close()
+
+
+def run():
+    for env_id in ['Breakout']:
+        for seed in [1, 2, 3]:
+            print(env_id + 'NoFrameskip-v4', 'seed:', seed)
+            main(env_id + 'NoFrameskip-v4', seed)
+
+
+if __name__ == '__main__':
+    run()
diff --git a/v5/ppo_clip.py b/v5/ppo_clip.py
new file mode 100644
index 0000000..7021133
--- /dev/null
+++ b/v5/ppo_clip.py
@@ -0,0 +1,338 @@
+import argparse
+import os
+import time
+
+import gymnasium as gym
+import numpy as np
+import torch
+from stable_baselines3.common.atari_wrappers import FireResetEnv, EpisodicLifeEnv, ClipRewardEnv
+from torch import nn, optim
+from torch.distributions import Categorical
+from torch.nn.utils.clip_grad import clip_grad_norm_
+from torch.utils.tensorboard.writer import SummaryWriter
+from tqdm import tqdm
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--exp_name', type=str, default=os.path.basename(__file__).rstrip('.py'))
+    parser.add_argument('--env_id', type=str, default='ALE/Breakout-v5')
+    parser.add_argument('--seed', type=int, default=1)
+    parser.add_argument('--use_cuda', type=bool, default=True)
+    parser.add_argument('--learning_rate', type=float, default=2.5e-4)
+    parser.add_argument('--lr_decay', type=bool, default=True)
+    parser.add_argument('--total_steps', type=int, default=int(1e7))
+    parser.add_argument('--num_envs', type=int, default=8)
+    parser.add_argument('--num_steps', type=int, default=128)
+    parser.add_argument('--update_epochs', type=int, default=8)
+    parser.add_argument('--num_mini_batches', type=int, default=4)
+    parser.add_argument('--gae_lambda', type=float, default=0.95)
+    parser.add_argument('--gamma', type=float, default=0.99)
+    parser.add_argument('--clip_value_loss', type=bool, default=True)
+    parser.add_argument('--c_1', type=float, default=1.0)
+    parser.add_argument('--c_2', type=float, default=0.01)
+    parser.add_argument('--clip_grad_norm', type=float, default=0.5)
+    parser.add_argument('--clip_epsilon', type=float, default=0.2)
+    args = parser.parse_args()
+    args.device = torch.device('cuda' if torch.cuda.is_available() and args.use_cuda else 'cpu')
+    args.batch_size = int(args.num_envs * args.num_steps)
+    args.minibatch_size = int(args.batch_size // args.num_mini_batches)
+    args.num_updates = int(args.total_steps // args.batch_size)
+    return args
+
+
+def make_env(env_id):
+    def thunk():
+        env = gym.make(env_id, frameskip=1, repeat_action_probability=0.0, full_action_space=False)
+        env = gym.wrappers.RecordEpisodeStatistics(env)
+        if 'FIRE' in env.unwrapped.get_action_meanings():
+            env = FireResetEnv(env)
+        env = EpisodicLifeEnv(env)
+        env = ClipRewardEnv(env)
+        env = gym.wrappers.AtariPreprocessing(env, scale_obs=True)
+        env = gym.wrappers.FrameStack(env, 4)
+        return env
+    return thunk
+
+
+def compute_advantages(rewards, flags, values, last_value, args):
+    advantages = torch.zeros((args.num_steps, args.num_envs)).to(args.device)
+    adv = torch.zeros(args.num_envs).to(args.device)
+    for i in reversed(range(args.num_steps)):
+        returns = rewards[i] + args.gamma * flags[i] * last_value
+        delta = returns - values[i]
+        adv = delta + args.gamma * args.gae_lambda * flags[i] * adv
+        advantages[i] = adv
+        last_value = values[i]
+    return advantages
+
+
+class Buffer:
+    def __init__(self, num_steps, num_envs, observation_shape, action_dim, device):
+        self.states = np.zeros((num_steps, num_envs, *observation_shape), dtype=np.float32)
+        self.actions = np.zeros((num_steps, num_envs), dtype=np.int64)
+        self.rewards = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.flags = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.log_probs = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.probs = np.zeros((num_steps, num_envs, action_dim), dtype=np.float32)
+        self.values = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.step = 0
+        self.num_steps = num_steps
+        self.device = device
+
+    def push(self, state, action, reward, flag, log_prob, prob, value):
+        self.states[self.step] = state
+        self.actions[self.step] = action
+        self.rewards[self.step] = reward
+        self.flags[self.step] = flag
+        self.log_probs[self.step] = log_prob
+        self.probs[self.step] = prob
+        self.values[self.step] = value
+        self.step = (self.step + 1) % self.num_steps
+
+    def get(self):
+        return (
+            torch.from_numpy(self.states).to(self.device),
+            torch.from_numpy(self.actions).to(self.device),
+            torch.from_numpy(self.rewards).to(self.device),
+            torch.from_numpy(self.flags).to(self.device),
+            torch.from_numpy(self.log_probs).to(self.device),
+            torch.from_numpy(self.values).to(self.device),
+        )
+
+    def get_probs(self):
+        return torch.from_numpy(self.probs).to(self.device)
+
+
+def layer_init(layer, std=np.sqrt(2), bias_const=0.0):
+    torch.nn.init.orthogonal_(layer.weight, std)
+    torch.nn.init.constant_(layer.bias, bias_const)
+    return layer
+
+
+class Agent(nn.Module):
+    def __init__(self, action_dim, device):
+        super().__init__()
+        self.encoder = nn.Sequential(
+            layer_init(nn.Conv2d(4, 32, 8, stride=4)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(32, 64, 4, stride=2)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(64, 64, 3, stride=1)),
+            nn.ReLU(),
+            nn.Flatten(),
+            layer_init(nn.Linear(64 * 7 * 7, 512)),
+            nn.ReLU()
+        )
+        self.actor_net = layer_init(nn.Linear(512, action_dim), std=0.01)
+        self.critic_net = layer_init(nn.Linear(512, 1), std=1)
+
+        if device.type == 'cuda':
+            self.cuda()
+
+    def forward(self, state):
+        hidden = self.encoder(state)
+        actor_value = self.actor_net(hidden)
+        distribution = Categorical(logits=actor_value)
+        action = distribution.sample()
+        log_prob = distribution.log_prob(action)
+        value = self.critic_net(hidden).squeeze(-1)
+        return action, log_prob, value, distribution.probs
+
+    def evaluate(self, states, actions):
+        hidden = self.encoder(states)
+        actor_values = self.actor_net(hidden)
+        distribution = Categorical(logits=actor_values)
+        log_probs = distribution.log_prob(actions)
+        entropy = distribution.entropy()
+        values = self.critic_net(hidden).squeeze(-1)
+        return log_probs, values, entropy, distribution.probs
+
+    def critic(self, state):
+        return self.critic_net(self.encoder(state)).squeeze(-1)
+
+
+def train(env_id, seed):
+    args = get_args()
+    args.env_id = env_id
+    args.seed = seed
+    run_name = (
+            'ppo_clip' +
+            '_epoch_' + str(args.update_epochs) +
+            '_seed_' + str(args.seed)
+    )
+
+    # 保存训练日志
+    path_string = str(args.env_id)[4:] + '/' + run_name
+    writer = SummaryWriter(path_string)
+    writer.add_text(
+        'Hyperparameter',
+        '|param|value|\n|-|-|\n%s' % ('\n'.join([f'|{key}|{value}|' for key, value in vars(args).items()])),
+    )
+
+    # 初始化并行环境
+    envs = gym.vector.AsyncVectorEnv([make_env(args.env_id) for _ in range(args.num_envs)])
+
+    # 状态空间和动作空间
+    observation_shape = envs.single_observation_space.shape
+    action_dim = envs.single_action_space.n
+
+    # 随机数种子
+    if args.seed:
+        numpy_rng = np.random.default_rng(args.seed)
+        torch.manual_seed(args.seed)
+        state, _ = envs.reset(seed=args.seed)
+    else:
+        numpy_rng = np.random.default_rng()
+        state, _ = envs.reset()
+
+    # 价值网络和策略网络
+    agent = Agent(action_dim, args.device)
+
+    # 优化器
+    optimizer = optim.Adam(agent.parameters(), lr=args.learning_rate)
+
+    # 存储数据的buffer
+    rollout_buffer = Buffer(args.num_steps, args.num_envs, observation_shape, action_dim, args.device)
+    global_step = 0
+    start_time = time.time()
+
+    # 开始收集数据
+    for _ in tqdm(range(args.num_updates)):
+
+        # 学习率线性递减
+        if args.lr_decay:
+            optimizer.param_groups[0]['lr'] -= (args.learning_rate - 1e-12) / args.num_updates
+
+        for _ in range(args.num_steps):
+            global_step += 1 * args.num_envs
+
+            with torch.no_grad():
+                action, log_prob, value, prob = agent(torch.from_numpy(state).to(args.device).float())
+
+            action = action.cpu().numpy()
+            next_state, reward, terminated, truncated, all_info = envs.step(action)
+
+            # 存储数据
+            flag = 1.0 - np.logical_or(terminated, truncated)
+            log_prob = log_prob.cpu().numpy()
+            prob = prob.cpu().numpy()
+            value = value.cpu().numpy()
+            rollout_buffer.push(state, action, reward, flag, log_prob, prob, value)
+            state = next_state
+
+            if 'final_info' not in all_info:
+                continue
+
+            # 写入训练过程的数据
+            for info in all_info['final_info']:
+                if info is None:
+                    continue
+                if 'episode' in info.keys():
+                    writer.add_scalar('charts/episodic_return', info['episode']['r'], global_step)
+                    # print(float(info['episode']['r']))
+                    break
+
+        # ------------------------------- 上面收集了足够的数据，下面开始更新 ------------------------------- #
+        states, actions, rewards, flags, log_probs, values = rollout_buffer.get()
+        probs = rollout_buffer.get_probs()
+
+        with torch.no_grad():
+            last_value = agent.critic(torch.from_numpy(next_state).to(args.device).float())
+
+        # 计算优势值和TD目标
+        advantages = compute_advantages(rewards, flags, values, last_value, args)
+        td_target = advantages + values
+
+        # 将数据展平
+        states = states.reshape(-1, *observation_shape)
+        actions = actions.reshape(-1)
+        log_probs = log_probs.reshape(-1)
+        probs = probs.reshape((-1, action_dim))
+        td_target = td_target.reshape(-1)
+        advantages = advantages.reshape(-1)
+        values = values.reshape(-1)
+        batch_indexes = np.arange(args.batch_size)
+
+        # 更新策略网络和价值网络
+        for e in range(1, args.update_epochs + 1):
+            numpy_rng.shuffle(batch_indexes)
+            for start in range(0, args.batch_size, args.minibatch_size):
+                end = start + args.minibatch_size
+                index = batch_indexes[start:end]
+
+                # 得到最新的策略网络和价值网络输出
+                new_log_probs, td_predict, entropy, new_probs = agent.evaluate(states[index], actions[index])
+                log_ratio = new_log_probs - log_probs[index]
+                ratios = log_ratio.exp()
+
+                # 计算kl散度
+                d = torch.sum(
+                    probs[index] * torch.log((probs[index] + 1e-12) / (new_probs + 1e-12)), 1
+                )
+                writer.add_scalar('charts/average_kld', d.mean(), global_step)
+                writer.add_scalar('others/min_kld', d.min(), global_step)
+                writer.add_scalar('others/max_kld', d.max(), global_step)
+
+                # 优势值标准化
+                b_advantages = advantages[index]
+                b_advantages = (b_advantages - b_advantages.mean()) / (b_advantages.std() + 1e-12)
+
+                # 策略网络损失
+                policy_loss_1 = b_advantages * ratios
+                policy_loss_2 = b_advantages * torch.clamp(
+                    ratios, 1.0 - args.clip_epsilon, 1.0 + args.clip_epsilon
+                )
+                policy_loss = -torch.min(policy_loss_1, policy_loss_2).mean()
+
+                # 价值网络损失
+                if args.clip_value_loss:
+                    v_loss_un_clipped = (td_predict - td_target[index]) ** 2
+                    v_clipped = td_target[index] + torch.clamp(
+                        td_predict - td_target[index],
+                        -args.clip_epsilon,
+                        args.clip_epsilon,
+                    )
+                    v_loss_clipped = (v_clipped - td_target[index]) ** 2
+                    v_loss_max = torch.max(v_loss_un_clipped, v_loss_clipped)
+                    value_loss = 0.5 * v_loss_max.mean()
+                else:
+                    value_loss = 0.5 * ((td_predict - td_target[index]) ** 2).mean()
+
+                entropy_loss = entropy.mean()
+
+                # 保存训练过程中的一些数据
+                writer.add_scalar('losses/value_loss', value_loss.item(), global_step)
+                writer.add_scalar('losses/policy_loss', policy_loss.item(), global_step)
+                writer.add_scalar('losses/entropy', entropy_loss.item(), global_step)
+                writer.add_scalar('losses/delta', torch.abs(ratios - 1).mean().item(), global_step)
+
+                # 总的损失
+                loss = policy_loss + value_loss * args.c_1 - entropy_loss * args.c_2
+
+                # 更新网络参数
+                optimizer.zero_grad()
+                loss.backward()
+                clip_grad_norm_(agent.parameters(), args.clip_grad_norm)
+                optimizer.step()
+
+        explained_var = (
+            np.nan if torch.var(td_target) == 0 else 1 - torch.var(td_target - values) / torch.var(td_target)
+        )
+        writer.add_scalar('charts/learning_rate', optimizer.param_groups[0]['lr'], global_step)
+        writer.add_scalar('charts/SPS', int(global_step / (time.time() - start_time)), global_step)
+        writer.add_scalar('others/explained_var', explained_var, global_step)
+
+    envs.close()
+    writer.close()
+
+
+def main():
+    for env_id in ['Breakout']:
+        for seed in [1, 2, 3]:
+            print(env_id, seed)
+            train('ALE/' + env_id + '-v5', seed)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/v5/ppo_early_stop.py b/v5/ppo_early_stop.py
new file mode 100644
index 0000000..adcc0cb
--- /dev/null
+++ b/v5/ppo_early_stop.py
@@ -0,0 +1,347 @@
+import argparse
+import os
+import time
+
+import gymnasium as gym
+import numpy as np
+import torch
+from stable_baselines3.common.atari_wrappers import FireResetEnv, EpisodicLifeEnv, ClipRewardEnv
+from torch import nn, optim
+from torch.distributions import Categorical
+from torch.nn.utils.clip_grad import clip_grad_norm_
+from torch.utils.tensorboard.writer import SummaryWriter
+from tqdm import tqdm
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--exp_name', type=str, default=os.path.basename(__file__).rstrip('.py'))
+    parser.add_argument('--env_id', type=str, default='ALE/Breakout-v5')
+    parser.add_argument('--seed', type=int, default=1)
+    parser.add_argument('--use_cuda', type=bool, default=True)
+    parser.add_argument('--learning_rate', type=float, default=2.5e-4)
+    parser.add_argument('--lr_decay', type=bool, default=True)
+    parser.add_argument('--total_steps', type=int, default=int(1e7))
+    parser.add_argument('--num_envs', type=int, default=8)
+    parser.add_argument('--num_steps', type=int, default=128)
+    parser.add_argument('--update_epochs', type=int, default=8)
+    parser.add_argument('--num_mini_batches', type=int, default=4)
+    parser.add_argument('--gae_lambda', type=float, default=0.95)
+    parser.add_argument('--gamma', type=float, default=0.99)
+    parser.add_argument('--clip_value_loss', type=bool, default=True)
+    parser.add_argument('--c_1', type=float, default=1.0)
+    parser.add_argument('--c_2', type=float, default=0.01)
+    parser.add_argument('--clip_grad_norm', type=float, default=0.5)
+    parser.add_argument('--clip_epsilon', type=float, default=0.2)
+    args = parser.parse_args()
+    args.device = torch.device('cuda' if torch.cuda.is_available() and args.use_cuda else 'cpu')
+    args.batch_size = int(args.num_envs * args.num_steps)
+    args.minibatch_size = int(args.batch_size // args.num_mini_batches)
+    args.num_updates = int(args.total_steps // args.batch_size)
+    return args
+
+
+def make_env(env_id):
+    def thunk():
+        env = gym.make(env_id, frameskip=1, repeat_action_probability=0.0, full_action_space=False)
+        env = gym.wrappers.RecordEpisodeStatistics(env)
+        if 'FIRE' in env.unwrapped.get_action_meanings():
+            env = FireResetEnv(env)
+        env = EpisodicLifeEnv(env)
+        env = ClipRewardEnv(env)
+        env = gym.wrappers.AtariPreprocessing(env, scale_obs=True)
+        env = gym.wrappers.FrameStack(env, 4)
+        return env
+    return thunk
+
+
+def compute_advantages(rewards, flags, values, last_value, args):
+    advantages = torch.zeros((args.num_steps, args.num_envs)).to(args.device)
+    adv = torch.zeros(args.num_envs).to(args.device)
+    for i in reversed(range(args.num_steps)):
+        returns = rewards[i] + args.gamma * flags[i] * last_value
+        delta = returns - values[i]
+        adv = delta + args.gamma * args.gae_lambda * flags[i] * adv
+        advantages[i] = adv
+        last_value = values[i]
+    return advantages
+
+
+class Buffer:
+    def __init__(self, num_steps, num_envs, observation_shape, action_dim, device):
+        self.states = np.zeros((num_steps, num_envs, *observation_shape), dtype=np.float32)
+        self.actions = np.zeros((num_steps, num_envs), dtype=np.int64)
+        self.rewards = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.flags = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.log_probs = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.probs = np.zeros((num_steps, num_envs, action_dim), dtype=np.float32)
+        self.values = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.step = 0
+        self.num_steps = num_steps
+        self.device = device
+
+    def push(self, state, action, reward, flag, log_prob, prob, value):
+        self.states[self.step] = state
+        self.actions[self.step] = action
+        self.rewards[self.step] = reward
+        self.flags[self.step] = flag
+        self.log_probs[self.step] = log_prob
+        self.probs[self.step] = prob
+        self.values[self.step] = value
+        self.step = (self.step + 1) % self.num_steps
+
+    def get(self):
+        return (
+            torch.from_numpy(self.states).to(self.device),
+            torch.from_numpy(self.actions).to(self.device),
+            torch.from_numpy(self.rewards).to(self.device),
+            torch.from_numpy(self.flags).to(self.device),
+            torch.from_numpy(self.log_probs).to(self.device),
+            torch.from_numpy(self.values).to(self.device),
+        )
+
+    def get_probs(self):
+        return torch.from_numpy(self.probs).to(self.device)
+
+
+def layer_init(layer, std=np.sqrt(2), bias_const=0.0):
+    torch.nn.init.orthogonal_(layer.weight, std)
+    torch.nn.init.constant_(layer.bias, bias_const)
+    return layer
+
+
+class Agent(nn.Module):
+    def __init__(self, action_dim, device):
+        super().__init__()
+        self.encoder = nn.Sequential(
+            layer_init(nn.Conv2d(4, 32, 8, stride=4)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(32, 64, 4, stride=2)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(64, 64, 3, stride=1)),
+            nn.ReLU(),
+            nn.Flatten(),
+            layer_init(nn.Linear(64 * 7 * 7, 512)),
+            nn.ReLU()
+        )
+        self.actor_net = layer_init(nn.Linear(512, action_dim), std=0.01)
+        self.critic_net = layer_init(nn.Linear(512, 1), std=1)
+
+        if device.type == 'cuda':
+            self.cuda()
+
+    def forward(self, state):
+        hidden = self.encoder(state)
+        actor_value = self.actor_net(hidden)
+        distribution = Categorical(logits=actor_value)
+        action = distribution.sample()
+        log_prob = distribution.log_prob(action)
+        value = self.critic_net(hidden).squeeze(-1)
+        return action, log_prob, value, distribution.probs
+
+    def evaluate(self, states, actions):
+        hidden = self.encoder(states)
+        actor_values = self.actor_net(hidden)
+        distribution = Categorical(logits=actor_values)
+        log_probs = distribution.log_prob(actions)
+        entropy = distribution.entropy()
+        values = self.critic_net(hidden).squeeze(-1)
+        return log_probs, values, entropy, distribution.probs
+
+    def critic(self, state):
+        return self.critic_net(self.encoder(state)).squeeze(-1)
+
+
+def train(env_id, seed):
+    args = get_args()
+    args.env_id = env_id
+    args.seed = seed
+    run_name = (
+            'ppo_es' +
+            '_epoch_' + str(args.update_epochs) +
+            '_seed_' + str(args.seed)
+    )
+
+    # 保存训练日志
+    path_string = str(args.env_id)[4:] + '/' + run_name
+    writer = SummaryWriter(path_string)
+    writer.add_text(
+        'Hyperparameter',
+        '|param|value|\n|-|-|\n%s' % ('\n'.join([f'|{key}|{value}|' for key, value in vars(args).items()])),
+    )
+
+    # 初始化并行环境
+    envs = gym.vector.AsyncVectorEnv([make_env(args.env_id) for _ in range(args.num_envs)])
+
+    # 状态空间和动作空间
+    observation_shape = envs.single_observation_space.shape
+    action_dim = envs.single_action_space.n
+
+    # 随机数种子
+    if args.seed:
+        numpy_rng = np.random.default_rng(args.seed)
+        torch.manual_seed(args.seed)
+        state, _ = envs.reset(seed=args.seed)
+    else:
+        numpy_rng = np.random.default_rng()
+        state, _ = envs.reset()
+
+    # 价值网络和策略网络
+    agent = Agent(action_dim, args.device)
+
+    # 优化器
+    optimizer = optim.Adam(agent.parameters(), lr=args.learning_rate)
+
+    # 存储数据的buffer
+    rollout_buffer = Buffer(args.num_steps, args.num_envs, observation_shape, action_dim, args.device)
+    global_step = 0
+    start_time = time.time()
+
+    # 开始收集数据
+    for _ in tqdm(range(args.num_updates)):
+
+        # 学习率线性递减
+        if args.lr_decay:
+            optimizer.param_groups[0]['lr'] -= (args.learning_rate - 1e-12) / args.num_updates
+
+        for _ in range(args.num_steps):
+            global_step += 1 * args.num_envs
+
+            with torch.no_grad():
+                action, log_prob, value, prob = agent(torch.from_numpy(state).to(args.device).float())
+
+            action = action.cpu().numpy()
+            next_state, reward, terminated, truncated, all_info = envs.step(action)
+
+            # 存储数据
+            flag = 1.0 - np.logical_or(terminated, truncated)
+            log_prob = log_prob.cpu().numpy()
+            prob = prob.cpu().numpy()
+            value = value.cpu().numpy()
+            rollout_buffer.push(state, action, reward, flag, log_prob, prob, value)
+            state = next_state
+
+            if 'final_info' not in all_info:
+                continue
+
+            # 写入训练过程的数据
+            for info in all_info['final_info']:
+                if info is None:
+                    continue
+                if 'episode' in info.keys():
+                    writer.add_scalar('charts/episodic_return', info['episode']['r'], global_step)
+                    # print(float(info['episode']['r']))
+                    break
+
+        # ------------------------------- 上面收集了足够的数据，下面开始更新 ------------------------------- #
+        states, actions, rewards, flags, log_probs, values = rollout_buffer.get()
+        probs = rollout_buffer.get_probs()
+
+        with torch.no_grad():
+            last_value = agent.critic(torch.from_numpy(next_state).to(args.device).float())
+
+        # 计算优势值和TD目标
+        advantages = compute_advantages(rewards, flags, values, last_value, args)
+        td_target = advantages + values
+
+        # 将数据展平
+        states = states.reshape(-1, *observation_shape)
+        actions = actions.reshape(-1)
+        log_probs = log_probs.reshape(-1)
+        probs = probs.reshape((-1, action_dim))
+        td_target = td_target.reshape(-1)
+        advantages = advantages.reshape(-1)
+        values = values.reshape(-1)
+        batch_indexes = np.arange(args.batch_size)
+
+        # 更新策略网络和价值网络
+        flag = True
+        for e in range(1, args.update_epochs + 1):
+            numpy_rng.shuffle(batch_indexes)
+            for start in range(0, args.batch_size, args.minibatch_size):
+                end = start + args.minibatch_size
+                index = batch_indexes[start:end]
+
+                # 得到最新的策略网络和价值网络输出
+                new_log_probs, td_predict, entropy, new_probs = agent.evaluate(states[index], actions[index])
+                log_ratio = new_log_probs - log_probs[index]
+                ratios = log_ratio.exp()
+
+                # 计算kl散度
+                d = torch.sum(
+                    probs[index] * torch.log((probs[index] + 1e-12) / (new_probs + 1e-12)), 1
+                )
+                writer.add_scalar('charts/average_kld', d.mean(), global_step)
+                writer.add_scalar('others/min_kld', d.min(), global_step)
+                writer.add_scalar('others/max_kld', d.max(), global_step)
+
+                # 早停策略
+                if d.mean() > 0.02:
+                    flag = False
+                    break
+
+                # 优势值标准化
+                b_advantages = advantages[index]
+                b_advantages = (b_advantages - b_advantages.mean()) / (b_advantages.std() + 1e-12)
+
+                # 策略网络损失
+                policy_loss_1 = b_advantages * ratios
+                policy_loss_2 = b_advantages * torch.clamp(
+                    ratios, 1.0 - args.clip_epsilon, 1.0 + args.clip_epsilon
+                )
+                policy_loss = -torch.min(policy_loss_1, policy_loss_2).mean()
+
+                # 价值网络损失
+                if args.clip_value_loss:
+                    v_loss_un_clipped = (td_predict - td_target[index]) ** 2
+                    v_clipped = td_target[index] + torch.clamp(
+                        td_predict - td_target[index],
+                        -args.clip_epsilon,
+                        args.clip_epsilon,
+                    )
+                    v_loss_clipped = (v_clipped - td_target[index]) ** 2
+                    v_loss_max = torch.max(v_loss_un_clipped, v_loss_clipped)
+                    value_loss = 0.5 * v_loss_max.mean()
+                else:
+                    value_loss = 0.5 * ((td_predict - td_target[index]) ** 2).mean()
+
+                entropy_loss = entropy.mean()
+
+                # 保存训练过程中的一些数据
+                writer.add_scalar('losses/value_loss', value_loss.item(), global_step)
+                writer.add_scalar('losses/policy_loss', policy_loss.item(), global_step)
+                writer.add_scalar('losses/entropy', entropy_loss.item(), global_step)
+                writer.add_scalar('losses/delta', torch.abs(ratios - 1).mean().item(), global_step)
+
+                # 总的损失
+                loss = policy_loss + value_loss * args.c_1 - entropy_loss * args.c_2
+
+                # 更新网络参数
+                optimizer.zero_grad()
+                loss.backward()
+                clip_grad_norm_(agent.parameters(), args.clip_grad_norm)
+                optimizer.step()
+
+            if flag is False:
+                break
+
+        explained_var = (
+            np.nan if torch.var(td_target) == 0 else 1 - torch.var(td_target - values) / torch.var(td_target)
+        )
+        writer.add_scalar('charts/learning_rate', optimizer.param_groups[0]['lr'], global_step)
+        writer.add_scalar('charts/SPS', int(global_step / (time.time() - start_time)), global_step)
+        writer.add_scalar('others/explained_var', explained_var, global_step)
+
+    envs.close()
+    writer.close()
+
+
+def main():
+    for env_id in ['Breakout']:
+        for seed in [1, 2, 3]:
+            print(env_id, seed)
+            train('ALE/' + env_id + '-v5', seed)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/v5/ppo_penalty.py b/v5/ppo_penalty.py
new file mode 100644
index 0000000..89ccf03
--- /dev/null
+++ b/v5/ppo_penalty.py
@@ -0,0 +1,339 @@
+import argparse
+import os
+import time
+
+import gymnasium as gym
+import numpy as np
+import torch
+from stable_baselines3.common.atari_wrappers import FireResetEnv, EpisodicLifeEnv, ClipRewardEnv
+from torch import nn, optim
+from torch.distributions import Categorical
+from torch.nn.utils.clip_grad import clip_grad_norm_
+from torch.utils.tensorboard.writer import SummaryWriter
+from tqdm import tqdm
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--exp_name', type=str, default=os.path.basename(__file__).rstrip('.py'))
+    parser.add_argument('--env_id', type=str, default='ALE/Breakout-v5')
+    parser.add_argument('--seed', type=int, default=1)
+    parser.add_argument('--use_cuda', type=bool, default=True)
+    parser.add_argument('--learning_rate', type=float, default=2.5e-4)
+    parser.add_argument('--lr_decay', type=bool, default=True)
+    parser.add_argument('--total_steps', type=int, default=int(1e7))
+    parser.add_argument('--num_envs', type=int, default=8)
+    parser.add_argument('--num_steps', type=int, default=128)
+    parser.add_argument('--update_epochs', type=int, default=8)
+    parser.add_argument('--num_mini_batches', type=int, default=4)
+    parser.add_argument('--gae_lambda', type=float, default=0.95)
+    parser.add_argument('--gamma', type=float, default=0.99)
+    parser.add_argument('--clip_value_loss', type=bool, default=True)
+    parser.add_argument('--c_1', type=float, default=1.0)
+    parser.add_argument('--c_2', type=float, default=0.01)
+    parser.add_argument('--clip_grad_norm', type=float, default=0.5)
+    parser.add_argument('--beta', type=float, default=1.0)
+    args = parser.parse_args()
+    args.device = torch.device('cuda' if torch.cuda.is_available() and args.use_cuda else 'cpu')
+    args.batch_size = int(args.num_envs * args.num_steps)
+    args.minibatch_size = int(args.batch_size // args.num_mini_batches)
+    args.num_updates = int(args.total_steps // args.batch_size)
+    return args
+
+
+def make_env(env_id):
+    def thunk():
+        env = gym.make(env_id, frameskip=1, repeat_action_probability=0.0, full_action_space=False)
+        env = gym.wrappers.RecordEpisodeStatistics(env)
+        if 'FIRE' in env.unwrapped.get_action_meanings():
+            env = FireResetEnv(env)
+        env = EpisodicLifeEnv(env)
+        env = ClipRewardEnv(env)
+        env = gym.wrappers.AtariPreprocessing(env, scale_obs=True)
+        env = gym.wrappers.FrameStack(env, 4)
+        return env
+    return thunk
+
+
+def compute_advantages(rewards, flags, values, last_value, args):
+    advantages = torch.zeros((args.num_steps, args.num_envs)).to(args.device)
+    adv = torch.zeros(args.num_envs).to(args.device)
+    for i in reversed(range(args.num_steps)):
+        returns = rewards[i] + args.gamma * flags[i] * last_value
+        delta = returns - values[i]
+        adv = delta + args.gamma * args.gae_lambda * flags[i] * adv
+        advantages[i] = adv
+        last_value = values[i]
+    return advantages
+
+
+class Buffer:
+    def __init__(self, num_steps, num_envs, observation_shape, action_dim, device):
+        self.states = np.zeros((num_steps, num_envs, *observation_shape), dtype=np.float32)
+        self.actions = np.zeros((num_steps, num_envs), dtype=np.int64)
+        self.rewards = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.flags = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.log_probs = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.probs = np.zeros((num_steps, num_envs, action_dim), dtype=np.float32)
+        self.values = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.step = 0
+        self.num_steps = num_steps
+        self.device = device
+
+    def push(self, state, action, reward, flag, log_prob, prob, value):
+        self.states[self.step] = state
+        self.actions[self.step] = action
+        self.rewards[self.step] = reward
+        self.flags[self.step] = flag
+        self.log_probs[self.step] = log_prob
+        self.probs[self.step] = prob
+        self.values[self.step] = value
+        self.step = (self.step + 1) % self.num_steps
+
+    def get(self):
+        return (
+            torch.from_numpy(self.states).to(self.device),
+            torch.from_numpy(self.actions).to(self.device),
+            torch.from_numpy(self.rewards).to(self.device),
+            torch.from_numpy(self.flags).to(self.device),
+            torch.from_numpy(self.log_probs).to(self.device),
+            torch.from_numpy(self.values).to(self.device),
+        )
+
+    def get_probs(self):
+        return torch.from_numpy(self.probs).to(self.device)
+
+
+def layer_init(layer, std=np.sqrt(2), bias_const=0.0):
+    torch.nn.init.orthogonal_(layer.weight, std)
+    torch.nn.init.constant_(layer.bias, bias_const)
+    return layer
+
+
+class Agent(nn.Module):
+    def __init__(self, action_dim, device):
+        super().__init__()
+        self.encoder = nn.Sequential(
+            layer_init(nn.Conv2d(4, 32, 8, stride=4)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(32, 64, 4, stride=2)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(64, 64, 3, stride=1)),
+            nn.ReLU(),
+            nn.Flatten(),
+            layer_init(nn.Linear(64 * 7 * 7, 512)),
+            nn.ReLU()
+        )
+        self.actor_net = layer_init(nn.Linear(512, action_dim), std=0.01)
+        self.critic_net = layer_init(nn.Linear(512, 1), std=1)
+
+        if device.type == 'cuda':
+            self.cuda()
+
+    def forward(self, state):
+        hidden = self.encoder(state)
+        actor_value = self.actor_net(hidden)
+        distribution = Categorical(logits=actor_value)
+        action = distribution.sample()
+        log_prob = distribution.log_prob(action)
+        value = self.critic_net(hidden).squeeze(-1)
+        return action, log_prob, value, distribution.probs
+
+    def evaluate(self, states, actions):
+        hidden = self.encoder(states)
+        actor_values = self.actor_net(hidden)
+        distribution = Categorical(logits=actor_values)
+        log_probs = distribution.log_prob(actions)
+        entropy = distribution.entropy()
+        values = self.critic_net(hidden).squeeze(-1)
+        return log_probs, values, entropy, distribution.probs
+
+    def critic(self, state):
+        return self.critic_net(self.encoder(state)).squeeze(-1)
+
+
+def train(env_id, seed):
+    args = get_args()
+    args.env_id = env_id
+    args.seed = seed
+    run_name = (
+            'ppo_penalty' +
+            '_epoch_' + str(args.update_epochs) +
+            '_seed_' + str(args.seed)
+    )
+
+    # 保存训练日志
+    path_string = str(args.env_id)[4:] + '/' + run_name
+    writer = SummaryWriter(path_string)
+    writer.add_text(
+        'Hyperparameter',
+        '|param|value|\n|-|-|\n%s' % ('\n'.join([f'|{key}|{value}|' for key, value in vars(args).items()])),
+    )
+
+    # 初始化并行环境
+    envs = gym.vector.AsyncVectorEnv([make_env(args.env_id) for _ in range(args.num_envs)])
+
+    # 状态空间和动作空间
+    observation_shape = envs.single_observation_space.shape
+    action_dim = envs.single_action_space.n
+
+    # 随机数种子
+    if args.seed:
+        numpy_rng = np.random.default_rng(args.seed)
+        torch.manual_seed(args.seed)
+        state, _ = envs.reset(seed=args.seed)
+    else:
+        numpy_rng = np.random.default_rng()
+        state, _ = envs.reset()
+
+    # 价值网络和策略网络
+    agent = Agent(action_dim, args.device)
+
+    # 优化器
+    optimizer = optim.Adam(agent.parameters(), lr=args.learning_rate)
+
+    # 存储数据的buffer
+    rollout_buffer = Buffer(args.num_steps, args.num_envs, observation_shape, action_dim, args.device)
+    global_step = 0
+    start_time = time.time()
+
+    # 开始收集数据
+    for _ in tqdm(range(args.num_updates)):
+
+        # 学习率线性递减
+        if args.lr_decay:
+            optimizer.param_groups[0]['lr'] -= (args.learning_rate - 1e-12) / args.num_updates
+
+        for _ in range(args.num_steps):
+            global_step += 1 * args.num_envs
+
+            with torch.no_grad():
+                action, log_prob, value, prob = agent(torch.from_numpy(state).to(args.device).float())
+
+            action = action.cpu().numpy()
+            next_state, reward, terminated, truncated, all_info = envs.step(action)
+
+            # 存储数据
+            flag = 1.0 - np.logical_or(terminated, truncated)
+            log_prob = log_prob.cpu().numpy()
+            prob = prob.cpu().numpy()
+            value = value.cpu().numpy()
+            rollout_buffer.push(state, action, reward, flag, log_prob, prob, value)
+            state = next_state
+
+            if 'final_info' not in all_info:
+                continue
+
+            # 写入训练过程的数据
+            for info in all_info['final_info']:
+                if info is None:
+                    continue
+                if 'episode' in info.keys():
+                    writer.add_scalar('charts/episodic_return', info['episode']['r'], global_step)
+                    # print(float(info['episode']['r']))
+                    break
+
+        # ------------------------------- 上面收集了足够的数据，下面开始更新 ------------------------------- #
+        states, actions, rewards, flags, log_probs, values = rollout_buffer.get()
+        probs = rollout_buffer.get_probs()
+
+        with torch.no_grad():
+            last_value = agent.critic(torch.from_numpy(next_state).to(args.device).float())
+
+        # 计算优势值和TD目标
+        advantages = compute_advantages(rewards, flags, values, last_value, args)
+        td_target = advantages + values
+
+        # 将数据展平
+        states = states.reshape(-1, *observation_shape)
+        actions = actions.reshape(-1)
+        log_probs = log_probs.reshape(-1)
+        probs = probs.reshape((-1, action_dim))
+        td_target = td_target.reshape(-1)
+        advantages = advantages.reshape(-1)
+        values = values.reshape(-1)
+        batch_indexes = np.arange(args.batch_size)
+
+        # 更新策略网络和价值网络
+        for e in range(1, args.update_epochs + 1):
+            numpy_rng.shuffle(batch_indexes)
+            for start in range(0, args.batch_size, args.minibatch_size):
+                end = start + args.minibatch_size
+                index = batch_indexes[start:end]
+
+                # 得到最新的策略网络和价值网络输出
+                new_log_probs, td_predict, entropy, new_probs = agent.evaluate(states[index], actions[index])
+                log_ratio = new_log_probs - log_probs[index]
+                ratios = log_ratio.exp()
+
+                # 计算kl散度
+                d = torch.sum(
+                    probs[index] * torch.log((probs[index] + 1e-12) / (new_probs + 1e-12)), 1
+                )
+                writer.add_scalar('charts/average_kld', d.mean(), global_step)
+                writer.add_scalar('others/min_kld', d.min(), global_step)
+                writer.add_scalar('others/max_kld', d.max(), global_step)
+
+                # 优势值标准化
+                b_advantages = advantages[index]
+                b_advantages = (b_advantages - b_advantages.mean()) / (b_advantages.std() + 1e-12)
+
+                # 策略网络损失
+                if d.mean() < 0.02 / 1.5:
+                    args.beta = args.beta / 2
+                if d.mean() > 0.02 * 1.5:
+                    args.beta = args.beta * 2
+
+                policy_loss = -(b_advantages * ratios - args.beta * d).mean()
+
+                # 价值网络损失
+                if args.clip_value_loss:
+                    v_loss_un_clipped = (td_predict - td_target[index]) ** 2
+                    v_clipped = td_target[index] + torch.clamp(
+                        td_predict - td_target[index],
+                        -0.2,
+                        0.2,
+                    )
+                    v_loss_clipped = (v_clipped - td_target[index]) ** 2
+                    v_loss_max = torch.max(v_loss_un_clipped, v_loss_clipped)
+                    value_loss = 0.5 * v_loss_max.mean()
+                else:
+                    value_loss = 0.5 * ((td_predict - td_target[index]) ** 2).mean()
+
+                entropy_loss = entropy.mean()
+
+                # 保存训练过程中的一些数据
+                writer.add_scalar('losses/value_loss', value_loss.item(), global_step)
+                writer.add_scalar('losses/policy_loss', policy_loss.item(), global_step)
+                writer.add_scalar('losses/entropy', entropy_loss.item(), global_step)
+                writer.add_scalar('losses/delta', torch.abs(ratios - 1).mean().item(), global_step)
+
+                # 总的损失
+                loss = policy_loss + value_loss * args.c_1 - entropy_loss * args.c_2
+
+                # 更新网络参数
+                optimizer.zero_grad()
+                loss.backward()
+                clip_grad_norm_(agent.parameters(), args.clip_grad_norm)
+                optimizer.step()
+
+        explained_var = (
+            np.nan if torch.var(td_target) == 0 else 1 - torch.var(td_target - values) / torch.var(td_target)
+        )
+        writer.add_scalar('charts/learning_rate', optimizer.param_groups[0]['lr'], global_step)
+        writer.add_scalar('charts/SPS', int(global_step / (time.time() - start_time)), global_step)
+        writer.add_scalar('others/explained_var', explained_var, global_step)
+
+    envs.close()
+    writer.close()
+
+
+def main():
+    for env_id in ['Breakout']:
+        for seed in [1, 2, 3]:
+            print(env_id, seed)
+            train('ALE/' + env_id + '-v5', seed)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/v5/spo.py b/v5/spo.py
new file mode 100644
index 0000000..ff2bedf
--- /dev/null
+++ b/v5/spo.py
@@ -0,0 +1,348 @@
+import argparse
+import os
+import time
+
+import gymnasium as gym
+import numpy as np
+import torch
+from stable_baselines3.common.atari_wrappers import FireResetEnv, EpisodicLifeEnv, ClipRewardEnv
+from torch import nn, optim
+from torch.distributions import Categorical
+from torch.nn.utils.clip_grad import clip_grad_norm_
+from torch.utils.tensorboard.writer import SummaryWriter
+from tqdm import tqdm
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--exp_name', type=str, default=os.path.basename(__file__).rstrip('.py'))
+    parser.add_argument('--env_id', type=str, default='ALE/Breakout-v5')
+    parser.add_argument('--seed', type=int, default=1)
+    parser.add_argument('--use_cuda', type=bool, default=True)
+    parser.add_argument('--learning_rate', type=float, default=2.5e-4)
+    parser.add_argument('--lr_decay', type=bool, default=True)
+    parser.add_argument('--total_steps', type=int, default=int(1e7))
+    parser.add_argument('--num_envs', type=int, default=8)
+    parser.add_argument('--num_steps', type=int, default=128)
+    parser.add_argument('--update_epochs', type=int, default=8)
+    parser.add_argument('--num_mini_batches', type=int, default=4)
+    parser.add_argument('--gae_lambda', type=float, default=0.95)
+    parser.add_argument('--gamma', type=float, default=0.99)
+    parser.add_argument('--clip_value_loss', type=bool, default=True)
+    parser.add_argument('--c_1', type=float, default=1.0)
+    parser.add_argument('--c_2', type=float, default=0.01)
+    parser.add_argument('--clip_grad_norm', type=float, default=0.5)
+    parser.add_argument('--kld_max', type=float, default=0.01)
+    args = parser.parse_args()
+    args.device = torch.device('cuda' if torch.cuda.is_available() and args.use_cuda else 'cpu')
+    args.batch_size = int(args.num_envs * args.num_steps)
+    args.minibatch_size = int(args.batch_size // args.num_mini_batches)
+    args.num_updates = int(args.total_steps // args.batch_size)
+    return args
+
+
+def make_env(env_id):
+    def thunk():
+        env = gym.make(env_id, frameskip=1, repeat_action_probability=0.0, full_action_space=False)
+        env = gym.wrappers.RecordEpisodeStatistics(env)
+        if 'FIRE' in env.unwrapped.get_action_meanings():
+            env = FireResetEnv(env)
+        env = EpisodicLifeEnv(env)
+        env = ClipRewardEnv(env)
+        env = gym.wrappers.AtariPreprocessing(env, scale_obs=True)
+        env = gym.wrappers.FrameStack(env, 4)
+        return env
+    return thunk
+
+
+def compute_advantages(rewards, flags, values, last_value, args):
+    advantages = torch.zeros((args.num_steps, args.num_envs)).to(args.device)
+    adv = torch.zeros(args.num_envs).to(args.device)
+    for i in reversed(range(args.num_steps)):
+        returns = rewards[i] + args.gamma * flags[i] * last_value
+        delta = returns - values[i]
+        adv = delta + args.gamma * args.gae_lambda * flags[i] * adv
+        advantages[i] = adv
+        last_value = values[i]
+    return advantages
+
+
+class Buffer:
+    def __init__(self, num_steps, num_envs, observation_shape, action_dim, device):
+        self.states = np.zeros((num_steps, num_envs, *observation_shape), dtype=np.float32)
+        self.actions = np.zeros((num_steps, num_envs), dtype=np.int64)
+        self.rewards = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.flags = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.log_probs = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.probs = np.zeros((num_steps, num_envs, action_dim), dtype=np.float32)
+        self.values = np.zeros((num_steps, num_envs), dtype=np.float32)
+        self.step = 0
+        self.num_steps = num_steps
+        self.device = device
+
+    def push(self, state, action, reward, flag, log_prob, prob, value):
+        self.states[self.step] = state
+        self.actions[self.step] = action
+        self.rewards[self.step] = reward
+        self.flags[self.step] = flag
+        self.log_probs[self.step] = log_prob
+        self.probs[self.step] = prob
+        self.values[self.step] = value
+        self.step = (self.step + 1) % self.num_steps
+
+    def get(self):
+        return (
+            torch.from_numpy(self.states).to(self.device),
+            torch.from_numpy(self.actions).to(self.device),
+            torch.from_numpy(self.rewards).to(self.device),
+            torch.from_numpy(self.flags).to(self.device),
+            torch.from_numpy(self.log_probs).to(self.device),
+            torch.from_numpy(self.values).to(self.device),
+        )
+
+    def get_probs(self):
+        return torch.from_numpy(self.probs).to(self.device)
+
+
+def layer_init(layer, std=np.sqrt(2), bias_const=0.0):
+    torch.nn.init.orthogonal_(layer.weight, std)
+    torch.nn.init.constant_(layer.bias, bias_const)
+    return layer
+
+
+class Agent(nn.Module):
+    def __init__(self, action_dim, device):
+        super().__init__()
+        self.encoder = nn.Sequential(
+            layer_init(nn.Conv2d(4, 32, 8, stride=4)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(32, 64, 4, stride=2)),
+            nn.ReLU(),
+            layer_init(nn.Conv2d(64, 64, 3, stride=1)),
+            nn.ReLU(),
+            nn.Flatten(),
+            layer_init(nn.Linear(64 * 7 * 7, 512)),
+            nn.ReLU()
+        )
+        self.actor_net = layer_init(nn.Linear(512, action_dim), std=0.01)
+        self.critic_net = layer_init(nn.Linear(512, 1), std=1)
+
+        if device.type == 'cuda':
+            self.cuda()
+
+    def forward(self, state):
+        hidden = self.encoder(state)
+        actor_value = self.actor_net(hidden)
+        distribution = Categorical(logits=actor_value)
+        action = distribution.sample()
+        log_prob = distribution.log_prob(action)
+        value = self.critic_net(hidden).squeeze(-1)
+        return action, log_prob, value, distribution.probs
+
+    def evaluate(self, states, actions):
+        hidden = self.encoder(states)
+        actor_values = self.actor_net(hidden)
+        distribution = Categorical(logits=actor_values)
+        log_probs = distribution.log_prob(actions)
+        entropy = distribution.entropy()
+        values = self.critic_net(hidden).squeeze(-1)
+        return log_probs, values, entropy, distribution.probs
+
+    def critic(self, state):
+        return self.critic_net(self.encoder(state)).squeeze(-1)
+
+
+def train(env_id, seed):
+    args = get_args()
+    args.env_id = env_id
+    args.seed = seed
+    run_name = (
+            'spo_' + str(args.kld_max) +
+            '_epoch_' + str(args.update_epochs) +
+            '_seed_' + str(args.seed)
+    )
+
+    # 保存训练日志
+    path_string = str(args.env_id)[4:] + '/' + run_name
+    writer = SummaryWriter(path_string)
+    writer.add_text(
+        'Hyperparameter',
+        '|param|value|\n|-|-|\n%s' % ('\n'.join([f'|{key}|{value}|' for key, value in vars(args).items()])),
+    )
+
+    # 初始化并行环境
+    envs = gym.vector.AsyncVectorEnv([make_env(args.env_id) for _ in range(args.num_envs)])
+
+    # 状态空间和动作空间
+    observation_shape = envs.single_observation_space.shape
+    action_dim = envs.single_action_space.n
+
+    # 随机数种子
+    if args.seed:
+        numpy_rng = np.random.default_rng(args.seed)
+        torch.manual_seed(args.seed)
+        state, _ = envs.reset(seed=args.seed)
+    else:
+        numpy_rng = np.random.default_rng()
+        state, _ = envs.reset()
+
+    # 价值网络和策略网络
+    agent = Agent(action_dim, args.device)
+
+    # 优化器
+    optimizer = optim.Adam(agent.parameters(), lr=args.learning_rate)
+
+    # 存储数据的buffer
+    rollout_buffer = Buffer(args.num_steps, args.num_envs, observation_shape, action_dim, args.device)
+    global_step = 0
+    start_time = time.time()
+
+    # 开始收集数据
+    for _ in tqdm(range(args.num_updates)):
+
+        # 学习率线性递减
+        if args.lr_decay:
+            optimizer.param_groups[0]['lr'] -= (args.learning_rate - 1e-12) / args.num_updates
+
+        for _ in range(args.num_steps):
+            global_step += 1 * args.num_envs
+
+            with torch.no_grad():
+                action, log_prob, value, prob = agent(torch.from_numpy(state).to(args.device).float())
+
+            action = action.cpu().numpy()
+            next_state, reward, terminated, truncated, all_info = envs.step(action)
+
+            # 存储数据
+            flag = 1.0 - np.logical_or(terminated, truncated)
+            log_prob = log_prob.cpu().numpy()
+            prob = prob.cpu().numpy()
+            value = value.cpu().numpy()
+            rollout_buffer.push(state, action, reward, flag, log_prob, prob, value)
+            state = next_state
+
+            if 'final_info' not in all_info:
+                continue
+
+            # 写入训练过程的数据
+            for info in all_info['final_info']:
+                if info is None:
+                    continue
+                if 'episode' in info.keys():
+                    writer.add_scalar('charts/episodic_return', info['episode']['r'], global_step)
+                    # print(float(info['episode']['r']))
+                    break
+
+        # ------------------------------- 上面收集了足够的数据，下面开始更新 ------------------------------- #
+        states, actions, rewards, flags, log_probs, values = rollout_buffer.get()
+        probs = rollout_buffer.get_probs()
+
+        with torch.no_grad():
+            last_value = agent.critic(torch.from_numpy(next_state).to(args.device).float())
+
+        # 计算优势值和TD目标
+        advantages = compute_advantages(rewards, flags, values, last_value, args)
+        td_target = advantages + values
+
+        # 将数据展平
+        states = states.reshape(-1, *observation_shape)
+        actions = actions.reshape(-1)
+        log_probs = log_probs.reshape(-1)
+        probs = probs.reshape((-1, action_dim))
+        td_target = td_target.reshape(-1)
+        advantages = advantages.reshape(-1)
+        values = values.reshape(-1)
+        batch_indexes = np.arange(args.batch_size)
+
+        # 更新策略网络和价值网络
+        for e in range(1, args.update_epochs + 1):
+            numpy_rng.shuffle(batch_indexes)
+            t = 0
+            for start in range(0, args.batch_size, args.minibatch_size):
+                t += 1
+                end = start + args.minibatch_size
+                index = batch_indexes[start:end]
+
+                # 得到最新的策略网络和价值网络输出
+                new_log_probs, td_predict, entropy, new_probs = agent.evaluate(states[index], actions[index])
+                log_ratio = new_log_probs - log_probs[index]
+                ratios = log_ratio.exp()
+
+                # 计算kl散度
+                d = torch.sum(
+                    probs[index] * torch.log((probs[index] + 1e-12) / (new_probs + 1e-12)), 1
+                )
+                writer.add_scalar('charts/average_kld', d.mean(), global_step)
+                writer.add_scalar('others/min_kld', d.min(), global_step)
+                writer.add_scalar('others/max_kld', d.max(), global_step)
+
+                # 优势值标准化
+                b_advantages = advantages[index]
+                b_advantages = (b_advantages - b_advantages.mean()) / (b_advantages.std() + 1e-12)
+
+                # 策略网络和价值网络损失
+                if e == 1 and t == 1:
+                    policy_loss = (-b_advantages * ratios).mean()
+                else:
+                    # d_clip
+                    d_clip = torch.clamp(input=d, min=0, max=args.kld_max)
+                    # d_clip / d
+                    ratio = d_clip / (d + 1e-12)
+                    # sign_a
+                    sign_a = torch.sign(b_advantages)
+                    # (d_clip / d + sign_a - 1) * sign_a
+                    result = (ratio + sign_a - 1) * sign_a
+                    # 策略网络损失
+                    policy_loss = (-b_advantages * ratios * result).mean()
+
+                # 价值网络损失
+                if args.clip_value_loss:
+                    v_loss_un_clipped = (td_predict - td_target[index]) ** 2
+                    v_clipped = td_target[index] + torch.clamp(
+                        td_predict - td_target[index],
+                        -0.2,
+                        0.2,
+                    )
+                    v_loss_clipped = (v_clipped - td_target[index]) ** 2
+                    v_loss_max = torch.max(v_loss_un_clipped, v_loss_clipped)
+                    value_loss = 0.5 * v_loss_max.mean()
+                else:
+                    value_loss = 0.5 * ((td_predict - td_target[index]) ** 2).mean()
+
+                entropy_loss = entropy.mean()
+
+                # 保存训练过程中的一些数据
+                writer.add_scalar('losses/value_loss', value_loss.item(), global_step)
+                writer.add_scalar('losses/policy_loss', policy_loss.item(), global_step)
+                writer.add_scalar('losses/entropy', entropy_loss.item(), global_step)
+                writer.add_scalar('losses/delta', torch.abs(ratios - 1).mean().item(), global_step)
+
+                # 总的损失
+                loss = policy_loss + value_loss * args.c_1 - entropy_loss * args.c_2
+
+                # 更新网络参数
+                optimizer.zero_grad()
+                loss.backward()
+                clip_grad_norm_(agent.parameters(), args.clip_grad_norm)
+                optimizer.step()
+
+        explained_var = (
+            np.nan if torch.var(td_target) == 0 else 1 - torch.var(td_target - values) / torch.var(td_target)
+        )
+        writer.add_scalar('charts/learning_rate', optimizer.param_groups[0]['lr'], global_step)
+        writer.add_scalar('charts/SPS', int(global_step / (time.time() - start_time)), global_step)
+        writer.add_scalar('others/explained_var', explained_var, global_step)
+
+    envs.close()
+    writer.close()
+
+
+def main():
+    for env_id in ['Breakout']:
+        for seed in [1, 2, 3]:
+            print(env_id, seed)
+            train('ALE/' + env_id + '-v5', seed)
+
+
+if __name__ == '__main__':
+    main()