diff --git a/v4/ppo.py b/v4/ppo.py
new file mode 100644
index 0000000..80bc2f8
--- /dev/null
+++ b/v4/ppo.py
@@ -0,0 +1,314 @@
+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('--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)
+    )
+
+    # Save training logs
+    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()])),
+    )
+
+    # Random seed
+    random.seed(args.seed)
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+
+    # Initialize environments
+    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)
+
+    # Initialize buffer
+    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)
+
+    # Data collection
+    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)):
+
+        # Linear decay of learning rate
+        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):
+            global_step += 1 * args.num_envs
+            obs[step] = next_obs
+            dones[step] = next_done
+
+            # Compute the logarithm of the action probability output by the old policy network
+            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
+
+            # Update the environments
+            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)
+
+            for item in info:
+                if 'episode' in item.keys():
+                    writer.add_scalar('charts/episodic_return', item['episode']['r'], global_step)
+                    break
+
+        # Use GAE (Generalized Advantage Estimation) technique to estimate the advantage function
+        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
+
+        # ---------------------- We have collected enough data, now let's start training ---------------------- #
+        # Flatten each batch
+        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)
+
+        # Update the policy network and value network
+        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]
+
+                # The latest outputs of the policy network and value network
+                _, 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)
+                )
+
+                # Compute KL divergence
+                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()
+
+                # Advantage normalization
+                mb_advantages = b_advantages[mb_index]
+                if args.norm_adv:
+                    mb_advantages = (mb_advantages - mb_advantages.mean()) / (mb_advantages.std() + 1e-12)
+
+                # Policy loss
+                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()
+
+                # Value loss
+                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()
+
+                # Policy entropy
+                entropy_loss = entropy.mean()
+
+                # Total loss
+                loss = pg_loss + v_loss * args.c_1 - entropy_loss * args.c_2
+
+                # Save the data during the training process
+                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)
+
+                # Update network parameters
+                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
+
+        # Save the data during the training process
+        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..c2ce712
--- /dev/null
+++ b/v4/spo.py
@@ -0,0 +1,325 @@
+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)
+    )
+
+    # Save training logs
+    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()])),
+    )
+
+    # Random seed
+    random.seed(args.seed)
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+
+    # Initialize environments
+    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)
+
+    # Initialize buffer
+    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)
+
+    # Data collection
+    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)):
+
+        # Linear decay of learning rate
+        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):
+            global_step += 1 * args.num_envs
+            obs[step] = next_obs
+            dones[step] = next_done
+
+            # Compute the logarithm of the action probability output by the old policy network
+            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
+
+            # Update the environments
+            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)
+
+            for item in info:
+                if 'episode' in item.keys():
+                    writer.add_scalar('charts/episodic_return', item['episode']['r'], global_step)
+                    break
+
+        # Use GAE (Generalized Advantage Estimation) technique to estimate the advantage function
+        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
+
+        # ---------------------- We have collected enough data, now let's start training ---------------------- #
+        # Flatten each batch
+        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)
+
+        # Update the policy network and value network
+        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]
+
+                # The latest outputs of the policy network and value network
+                _, 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)
+                )
+
+                # Compute KL divergence
+                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()
+
+                # Advantage normalization
+                mb_advantages = b_advantages[mb_index]
+                if args.norm_adv:
+                    mb_advantages = (mb_advantages - mb_advantages.mean()) / (mb_advantages.std() + 1e-12)
+
+                # Policy loss (main code of SPO)
+                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
+                    pg_loss = (-mb_advantages * ratios * result).mean()
+
+                # Value loss
+                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()
+
+                # Policy entropy
+                entropy_loss = entropy.mean()
+
+                # Total loss
+                loss = pg_loss + v_loss * args.c_1 - entropy_loss * args.c_2
+
+                # Save the data during the training process
+                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)
+
+                # Update network parameters
+                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
+
+        # Save the data during the training process
+        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()