diff --git a/.gitignore b/.gitignore
index 0ecb650..604f2df 100644
--- a/.gitignore
+++ b/.gitignore
@@ -137,7 +137,6 @@ dmypy.json
 .pytype/
 
 # customize
-flake8.sh
 log/
 MUJOCO_LOG.TXT
 *.pth
diff --git a/examples/box2d/mcc_sac.py b/examples/box2d/mcc_sac.py
index d73e1f5..9ca6845 100644
--- a/examples/box2d/mcc_sac.py
+++ b/examples/box2d/mcc_sac.py
@@ -26,7 +26,7 @@ def get_args():
     parser.add_argument('--noise_std', type=float, default=1.2)
     parser.add_argument('--gamma', type=float, default=0.99)
     parser.add_argument('--tau', type=float, default=0.005)
-    parser.add_argument('--auto_alpha', type=bool, default=True)
+    parser.add_argument('--auto_alpha', type=int, default=1)
     parser.add_argument('--alpha', type=float, default=0.2)
     parser.add_argument('--epoch', type=int, default=20)
     parser.add_argument('--step-per-epoch', type=int, default=2400)
diff --git a/test/discrete/test_sac.py b/test/discrete/test_sac.py
new file mode 100644
index 0000000..865924a
--- /dev/null
+++ b/test/discrete/test_sac.py
@@ -0,0 +1,117 @@
+import os
+import gym
+import torch
+import pprint
+import argparse
+import numpy as np
+from torch.utils.tensorboard import SummaryWriter
+
+from tianshou.env import SubprocVectorEnv
+from tianshou.utils.net.common import Net
+from tianshou.trainer import offpolicy_trainer
+from tianshou.data import Collector, ReplayBuffer
+from tianshou.policy import DiscreteSACPolicy
+from tianshou.utils.net.discrete import Actor, Critic
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--task', type=str, default='CartPole-v0')
+    parser.add_argument('--seed', type=int, default=1626)
+    parser.add_argument('--buffer-size', type=int, default=20000)
+    parser.add_argument('--actor-lr', type=float, default=3e-4)
+    parser.add_argument('--critic-lr', type=float, default=1e-3)
+    parser.add_argument('--alpha-lr', type=float, default=3e-4)
+    parser.add_argument('--gamma', type=float, default=0.95)
+    parser.add_argument('--tau', type=float, default=0.005)
+    parser.add_argument('--alpha', type=float, default=0.05)
+    parser.add_argument('--auto_alpha', type=int, default=0)
+    parser.add_argument('--epoch', type=int, default=5)
+    parser.add_argument('--step-per-epoch', type=int, default=1000)
+    parser.add_argument('--collect-per-step', type=int, default=5)
+    parser.add_argument('--batch-size', type=int, default=64)
+    parser.add_argument('--layer-num', type=int, default=1)
+    parser.add_argument('--training-num', type=int, default=16)
+    parser.add_argument('--test-num', type=int, default=100)
+    parser.add_argument('--logdir', type=str, default='log')
+    parser.add_argument('--render', type=float, default=0.0)
+    parser.add_argument('--rew-norm', type=int, default=0)
+    parser.add_argument('--ignore-done', type=int, default=0)
+    parser.add_argument(
+        '--device', type=str,
+        default='cuda' if torch.cuda.is_available() else 'cpu')
+    args = parser.parse_known_args()[0]
+    return args
+
+
+def test_discrete_sac(args=get_args()):
+    env = gym.make(args.task)
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.action_shape = env.action_space.shape or env.action_space.n
+
+    train_envs = SubprocVectorEnv(
+        [lambda: gym.make(args.task) for _ in range(args.training_num)])
+    test_envs = SubprocVectorEnv(
+        [lambda: gym.make(args.task) for _ in range(args.test_num)])
+    # seed
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    train_envs.seed(args.seed)
+    test_envs.seed(args.seed)
+    # model
+    net = Net(args.layer_num, args.state_shape, device=args.device)
+    actor = Actor(net, args.action_shape, softmax_output=False).to(args.device)
+    actor_optim = torch.optim.Adam(actor.parameters(), lr=args.actor_lr)
+    net = Net(args.layer_num, args.state_shape, device=args.device)
+    critic1 = Critic(net, last_size=args.action_shape).to(args.device)
+    critic1_optim = torch.optim.Adam(critic1.parameters(), lr=args.critic_lr)
+    net = Net(args.layer_num, args.state_shape, device=args.device)
+    critic2 = Critic(net, last_size=args.action_shape).to(args.device)
+    critic2_optim = torch.optim.Adam(critic2.parameters(), lr=args.critic_lr)
+
+    # better not to use auto alpha in CartPole
+    if args.auto_alpha:
+        target_entropy = 0.98 * np.log(np.prod(args.action_shape))
+        log_alpha = torch.zeros(1, requires_grad=True, device=args.device)
+        alpha_optim = torch.optim.Adam([log_alpha], lr=args.alpha_lr)
+        args.alpha = (target_entropy, log_alpha, alpha_optim)
+
+    policy = DiscreteSACPolicy(
+        actor, actor_optim, critic1, critic1_optim, critic2, critic2_optim,
+        args.tau, args.gamma, args.alpha,
+        reward_normalization=args.rew_norm,
+        ignore_done=args.ignore_done)
+    # collector
+    train_collector = Collector(
+        policy, train_envs, ReplayBuffer(args.buffer_size))
+    test_collector = Collector(policy, test_envs)
+    # train_collector.collect(n_step=args.buffer_size)
+    # log
+    log_path = os.path.join(args.logdir, args.task, 'discrete_sac')
+    writer = SummaryWriter(log_path)
+
+    def save_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, 'policy.pth'))
+
+    def stop_fn(x):
+        return x >= env.spec.reward_threshold
+
+    # trainer
+    result = offpolicy_trainer(
+        policy, train_collector, test_collector, args.epoch,
+        args.step_per_epoch, args.collect_per_step, args.test_num,
+        args.batch_size, stop_fn=stop_fn, save_fn=save_fn, writer=writer,
+        test_in_train=False)
+    assert stop_fn(result['best_reward'])
+    if __name__ == '__main__':
+        pprint.pprint(result)
+        # Let's watch its performance!
+        env = gym.make(args.task)
+        policy.eval()
+        collector = Collector(policy, env)
+        result = collector.collect(n_episode=1, render=args.render)
+        print(f'Final reward: {result["rew"]}, length: {result["len"]}')
+
+
+if __name__ == '__main__':
+    test_discrete_sac()
diff --git a/tianshou/policy/__init__.py b/tianshou/policy/__init__.py
index 7383390..cf1f4de 100644
--- a/tianshou/policy/__init__.py
+++ b/tianshou/policy/__init__.py
@@ -8,6 +8,7 @@ from tianshou.policy.modelfree.ddpg import DDPGPolicy
 from tianshou.policy.modelfree.ppo import PPOPolicy
 from tianshou.policy.modelfree.td3 import TD3Policy
 from tianshou.policy.modelfree.sac import SACPolicy
+from tianshou.policy.modelfree.discrete_sac import DiscreteSACPolicy
 from tianshou.policy.multiagent.mapolicy import MultiAgentPolicyManager
 
 
@@ -22,5 +23,6 @@ __all__ = [
     "PPOPolicy",
     "TD3Policy",
     "SACPolicy",
+    "DiscreteSACPolicy",
     "MultiAgentPolicyManager",
 ]
diff --git a/tianshou/policy/modelfree/ddpg.py b/tianshou/policy/modelfree/ddpg.py
index f19f56e..81bf7f6 100644
--- a/tianshou/policy/modelfree/ddpg.py
+++ b/tianshou/policy/modelfree/ddpg.py
@@ -140,7 +140,7 @@ class DDPGPolicy(BasePolicy):
             more detailed explanation.
         """
         model = getattr(self, model)
-        obs = getattr(batch, input)
+        obs = batch[input]
         actions, h = model(obs, state=state, info=batch.info)
         actions += self._action_bias
         if self._noise and self.training and explorating:
diff --git a/tianshou/policy/modelfree/discrete_sac.py b/tianshou/policy/modelfree/discrete_sac.py
new file mode 100644
index 0000000..d9fa35e
--- /dev/null
+++ b/tianshou/policy/modelfree/discrete_sac.py
@@ -0,0 +1,148 @@
+import torch
+import numpy as np
+from torch.distributions import Categorical
+from typing import Any, Dict, Tuple, Union, Optional
+
+from tianshou.policy import SACPolicy
+from tianshou.data import Batch, ReplayBuffer, to_torch
+
+
+class DiscreteSACPolicy(SACPolicy):
+    """Implementation of SAC for Discrete Action Settings. arXiv:1910.07207.
+
+    :param torch.nn.Module actor: the actor network following the rules in
+        :class:`~tianshou.policy.BasePolicy`. (s -> logits)
+    :param torch.optim.Optimizer actor_optim: the optimizer for actor network.
+    :param torch.nn.Module critic1: the first critic network. (s -> Q(s))
+    :param torch.optim.Optimizer critic1_optim: the optimizer for the first
+        critic network.
+    :param torch.nn.Module critic2: the second critic network. (s -> Q(s))
+    :param torch.optim.Optimizer critic2_optim: the optimizer for the second
+        critic network.
+    :param float tau: param for soft update of the target network, defaults to
+        0.005.
+    :param float gamma: discount factor, in [0, 1], defaults to 0.99.
+    :param (float, torch.Tensor, torch.optim.Optimizer) or float alpha: entropy
+        regularization coefficient, default to 0.2.
+        If a tuple (target_entropy, log_alpha, alpha_optim) is provided, then
+        alpha is automatatically tuned.
+    :param bool reward_normalization: normalize the reward to Normal(0, 1),
+        defaults to ``False``.
+    :param bool ignore_done: ignore the done flag while training the policy,
+        defaults to ``False``.
+
+    .. seealso::
+
+        Please refer to :class:`~tianshou.policy.BasePolicy` for more detailed
+        explanation.
+    """
+
+    def __init__(
+        self,
+        actor: torch.nn.Module,
+        actor_optim: torch.optim.Optimizer,
+        critic1: torch.nn.Module,
+        critic1_optim: torch.optim.Optimizer,
+        critic2: torch.nn.Module,
+        critic2_optim: torch.optim.Optimizer,
+        tau: float = 0.005,
+        gamma: float = 0.99,
+        alpha: Union[
+            float, Tuple[float, torch.Tensor, torch.optim.Optimizer]
+        ] = 0.2,
+        reward_normalization: bool = False,
+        ignore_done: bool = False,
+        estimation_step: int = 1,
+        **kwargs: Any,
+    ) -> None:
+        super().__init__(actor, actor_optim, critic1, critic1_optim, critic2,
+                         critic2_optim, (-np.inf, np.inf), tau, gamma, alpha,
+                         reward_normalization, ignore_done, estimation_step,
+                         **kwargs)
+        self._alpha: Union[float, torch.Tensor]
+
+    def forward(  # type: ignore
+        self,
+        batch: Batch,
+        state: Optional[Union[dict, Batch, np.ndarray]] = None,
+        input: str = "obs",
+        **kwargs: Any,
+    ) -> Batch:
+        obs = batch[input]
+        logits, h = self.actor(obs, state=state, info=batch.info)
+        dist = Categorical(logits=logits)
+        act = dist.sample()
+        return Batch(logits=logits, act=act, state=h, dist=dist)
+
+    def _target_q(
+        self, buffer: ReplayBuffer, indice: np.ndarray
+    ) -> torch.Tensor:
+        batch = buffer[indice]  # batch.obs: s_{t+n}
+        with torch.no_grad():
+            obs_next_result = self(batch, input="obs_next")
+            dist = obs_next_result.dist
+            target_q = dist.probs * torch.min(
+                self.critic1_old(batch.obs_next),
+                self.critic2_old(batch.obs_next),
+            )
+            target_q = target_q.sum(dim=-1) + self._alpha * dist.entropy()
+        return target_q
+
+    def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
+        weight = batch.pop("weight", 1.0)
+        target_q = batch.returns.flatten()
+        act = to_torch(
+            batch.act[:, np.newaxis], device=target_q.device, dtype=torch.long)
+
+        # critic 1
+        current_q1 = self.critic1(batch.obs).gather(1, act).flatten()
+        td1 = current_q1 - target_q
+        critic1_loss = (td1.pow(2) * weight).mean()
+
+        self.critic1_optim.zero_grad()
+        critic1_loss.backward()
+        self.critic1_optim.step()
+
+        # critic 2
+        current_q2 = self.critic2(batch.obs).gather(1, act).flatten()
+        td2 = current_q2 - target_q
+        critic2_loss = (td2.pow(2) * weight).mean()
+
+        self.critic2_optim.zero_grad()
+        critic2_loss.backward()
+        self.critic2_optim.step()
+        batch.weight = (td1 + td2) / 2.0  # prio-buffer
+
+        # actor
+        dist = self(batch).dist
+        entropy = dist.entropy()
+        with torch.no_grad():
+            current_q1a = self.critic1(batch.obs)
+            current_q2a = self.critic2(batch.obs)
+            q = torch.min(current_q1a, current_q2a)
+        actor_loss = -(self._alpha * entropy
+                       + (dist.probs * q).sum(dim=-1)).mean()
+        self.actor_optim.zero_grad()
+        actor_loss.backward()
+        self.actor_optim.step()
+
+        if self._is_auto_alpha:
+            log_prob = entropy.detach() - self._target_entropy
+            alpha_loss = (self._log_alpha * log_prob).mean()
+            self._alpha_optim.zero_grad()
+            alpha_loss.backward()
+            self._alpha_optim.step()
+            self._alpha = self._log_alpha.detach().exp()
+
+        self.sync_weight()
+
+        result = {
+            "loss/actor": actor_loss.item(),
+            "loss/critic1": critic1_loss.item(),
+            "loss/critic2": critic2_loss.item(),
+        }
+        if self._is_auto_alpha:
+            result["loss/alpha"] = alpha_loss.item()
+            result["alpha"] = self._alpha.item()  # type: ignore
+
+        return result
diff --git a/tianshou/policy/modelfree/dqn.py b/tianshou/policy/modelfree/dqn.py
index 070f11d..71d16f6 100644
--- a/tianshou/policy/modelfree/dqn.py
+++ b/tianshou/policy/modelfree/dqn.py
@@ -143,7 +143,7 @@ class DQNPolicy(BasePolicy):
             more detailed explanation.
         """
         model = getattr(self, model)
-        obs = getattr(batch, input)
+        obs = batch[input]
         obs_ = obs.obs if hasattr(obs, "obs") else obs
         q, h = model(obs_, state=state, info=batch.info)
         act: np.ndarray = to_numpy(q.max(dim=1)[1])
diff --git a/tianshou/policy/modelfree/sac.py b/tianshou/policy/modelfree/sac.py
index 83c7150..e44f8a1 100644
--- a/tianshou/policy/modelfree/sac.py
+++ b/tianshou/policy/modelfree/sac.py
@@ -28,8 +28,6 @@ class SACPolicy(DDPGPolicy):
     :param float tau: param for soft update of the target network, defaults to
         0.005.
     :param float gamma: discount factor, in [0, 1], defaults to 0.99.
-    :param float exploration_noise: the noise intensity, add to the action,
-        defaults to 0.1.
     :param (float, torch.Tensor, torch.optim.Optimizer) or float alpha: entropy
         regularization coefficient, default to 0.2.
         If a tuple (target_entropy, log_alpha, alpha_optim) is provided, then
@@ -38,8 +36,8 @@ class SACPolicy(DDPGPolicy):
         defaults to False.
     :param bool ignore_done: ignore the done flag while training the policy,
         defaults to False.
-    :param BaseNoise exploration_noise: add a noise to action for exploration.
-        This is useful when solving hard-exploration problem.
+    :param BaseNoise exploration_noise: add a noise to action for exploration,
+        defaults to None. This is useful when solving hard-exploration problem.
 
     .. seealso::
 
@@ -115,7 +113,7 @@ class SACPolicy(DDPGPolicy):
         explorating: bool = True,
         **kwargs: Any,
     ) -> Batch:
-        obs = getattr(batch, input)
+        obs = batch[input]
         logits, h = self.actor(obs, state=state, info=batch.info)
         assert isinstance(logits, tuple)
         dist = Independent(Normal(*logits), 1)
@@ -147,6 +145,7 @@ class SACPolicy(DDPGPolicy):
 
     def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
         weight = batch.pop("weight", 1.0)
+
         # critic 1
         current_q1 = self.critic1(batch.obs, batch.act).flatten()
         target_q = batch.returns.flatten()
@@ -156,6 +155,7 @@ class SACPolicy(DDPGPolicy):
         self.critic1_optim.zero_grad()
         critic1_loss.backward()
         self.critic1_optim.step()
+
         # critic 2
         current_q2 = self.critic2(batch.obs, batch.act).flatten()
         td2 = current_q2 - target_q
@@ -165,6 +165,7 @@ class SACPolicy(DDPGPolicy):
         critic2_loss.backward()
         self.critic2_optim.step()
         batch.weight = (td1 + td2) / 2.0  # prio-buffer
+
         # actor
         obs_result = self(batch, explorating=False)
         a = obs_result.act
@@ -193,5 +194,6 @@ class SACPolicy(DDPGPolicy):
         }
         if self._is_auto_alpha:
             result["loss/alpha"] = alpha_loss.item()
-            result["v/alpha"] = self._alpha.item()  # type: ignore
+            result["alpha"] = self._alpha.item()  # type: ignore
+
         return result
diff --git a/tianshou/utils/net/discrete.py b/tianshou/utils/net/discrete.py
index 58e44a7..547593f 100644
--- a/tianshou/utils/net/discrete.py
+++ b/tianshou/utils/net/discrete.py
@@ -19,10 +19,12 @@ class Actor(nn.Module):
         preprocess_net: nn.Module,
         action_shape: Sequence[int],
         hidden_layer_size: int = 128,
+        softmax_output: bool = True,
     ) -> None:
         super().__init__()
         self.preprocess = preprocess_net
         self.last = nn.Linear(hidden_layer_size, np.prod(action_shape))
+        self.softmax_output = softmax_output
 
     def forward(
         self,
@@ -32,7 +34,9 @@ class Actor(nn.Module):
     ) -> Tuple[torch.Tensor, Any]:
         r"""Mapping: s -> Q(s, \*)."""
         logits, h = self.preprocess(s, state)
-        logits = F.softmax(self.last(logits), dim=-1)
+        logits = self.last(logits)
+        if self.softmax_output:
+            logits = F.softmax(logits, dim=-1)
         return logits, h
 
 
@@ -44,11 +48,14 @@ class Critic(nn.Module):
     """
 
     def __init__(
-        self, preprocess_net: nn.Module, hidden_layer_size: int = 128
+        self,
+        preprocess_net: nn.Module,
+        hidden_layer_size: int = 128,
+        last_size: int = 1
     ) -> None:
         super().__init__()
         self.preprocess = preprocess_net
-        self.last = nn.Linear(hidden_layer_size, 1)
+        self.last = nn.Linear(hidden_layer_size, last_size)
 
     def forward(
         self, s: Union[np.ndarray, torch.Tensor], **kwargs: Any