diff --git a/README.md b/README.md
index 0807fd8..a39da24 100644
--- a/README.md
+++ b/README.md
@@ -12,6 +12,7 @@
 - [Deep Q-Network (DQN)](https://storage.googleapis.com/deepmind-media/dqn/DQNNaturePaper.pdf)
 - [Double DQN](https://arxiv.org/pdf/1509.06461.pdf)
 - [Dueling DQN](https://arxiv.org/pdf/1511.06581.pdf)
+- [Branching DQN](https://arxiv.org/pdf/1711.08946.pdf)
 - [Categorical DQN (C51)](https://arxiv.org/pdf/1707.06887.pdf)
 - [Rainbow DQN (Rainbow)](https://arxiv.org/pdf/1710.02298.pdf)
 - [Quantile Regression DQN (QRDQN)](https://arxiv.org/pdf/1710.10044.pdf)
diff --git a/docs/api/tianshou.env.rst b/docs/api/tianshou.env.rst
index 77713f4..bf0c8e0 100644
--- a/docs/api/tianshou.env.rst
+++ b/docs/api/tianshou.env.rst
@@ -49,6 +49,14 @@ RayVectorEnv
 Wrapper
 -------
 
+ContinuousToDiscrete
+~~~~~~~~~~~~~~~~~~~~
+
+.. autoclass:: tianshou.env.ContinuousToDiscrete
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
 VectorEnvWrapper
 ~~~~~~~~~~~~~~~~
 
diff --git a/docs/api/tianshou.policy.rst b/docs/api/tianshou.policy.rst
index 2719757..fe129d8 100644
--- a/docs/api/tianshou.policy.rst
+++ b/docs/api/tianshou.policy.rst
@@ -25,6 +25,11 @@ DQN Family
    :undoc-members:
    :show-inheritance:
 
+.. autoclass:: tianshou.policy.BranchingDQNPolicy
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
 .. autoclass:: tianshou.policy.C51Policy
    :members:
    :undoc-members:
diff --git a/docs/index.rst b/docs/index.rst
index 49453ad..c187827 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -12,6 +12,7 @@ Welcome to Tianshou!
 * :class:`~tianshou.policy.DQNPolicy` `Deep Q-Network <https://storage.googleapis.com/deepmind-media/dqn/DQNNaturePaper.pdf>`_
 * :class:`~tianshou.policy.DQNPolicy` `Double DQN <https://arxiv.org/pdf/1509.06461.pdf>`_
 * :class:`~tianshou.policy.DQNPolicy` `Dueling DQN <https://arxiv.org/pdf/1511.06581.pdf>`_
+* :class:`~tianshou.policy.BranchingDQNPolicy` `Branching DQN <https://arxiv.org/pdf/1711.08946.pdf>`_
 * :class:`~tianshou.policy.C51Policy` `Categorical DQN <https://arxiv.org/pdf/1707.06887.pdf>`_
 * :class:`~tianshou.policy.RainbowPolicy` `Rainbow DQN <https://arxiv.org/pdf/1710.02298.pdf>`_
 * :class:`~tianshou.policy.QRDQNPolicy` `Quantile Regression DQN <https://arxiv.org/pdf/1710.10044.pdf>`_
diff --git a/examples/box2d/README.md b/examples/box2d/README.md
index f438b2a..f42f19a 100644
--- a/examples/box2d/README.md
+++ b/examples/box2d/README.md
@@ -4,3 +4,10 @@
 - If the done penalty is not removed, it converges much slower than before, about 200 epochs (20M env steps) to reach the same performance (\~200 reward)
 
 ![](results/sac/BipedalHardcore.png)
+
+
+# BipedalWalker-BDQ
+
+- To demonstrate the cpabilities of the BDQ to scale up to big discrete action spaces, we run it on a discretized version of the BipedalWalker-v3 environment, where the number of possible actions in each dimension is 25, for a total of 25^4 = 390 625 possible actions. A usaual DQN architecture would use 25^4 output neurons for the Q-network, thus scaling exponentially with the number of action space dimensions, while the Branching architecture scales linearly and uses only 25*4 output neurons. 
+
+![](results/bdq/BipedalWalker.png)
\ No newline at end of file
diff --git a/examples/box2d/bipedal_bdq.py b/examples/box2d/bipedal_bdq.py
new file mode 100644
index 0000000..bb9d4d2
--- /dev/null
+++ b/examples/box2d/bipedal_bdq.py
@@ -0,0 +1,163 @@
+import argparse
+import datetime
+import os
+import pprint
+
+import gym
+import numpy as np
+import torch
+from torch.utils.tensorboard import SummaryWriter
+
+from tianshou.data import Collector, VectorReplayBuffer
+from tianshou.env import ContinuousToDiscrete, SubprocVectorEnv
+from tianshou.policy import BranchingDQNPolicy
+from tianshou.trainer import offpolicy_trainer
+from tianshou.utils import TensorboardLogger
+from tianshou.utils.net.common import BranchingNet
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    # task
+    parser.add_argument("--task", type=str, default="BipedalWalker-v3")
+    # network architecture
+    parser.add_argument(
+        "--common-hidden-sizes", type=int, nargs="*", default=[512, 256]
+    )
+    parser.add_argument("--action-hidden-sizes", type=int, nargs="*", default=[128])
+    parser.add_argument("--value-hidden-sizes", type=int, nargs="*", default=[128])
+    parser.add_argument("--action-per-branch", type=int, default=25)
+    # training hyperparameters
+    parser.add_argument("--seed", type=int, default=0)
+    parser.add_argument("--eps-test", type=float, default=0.)
+    parser.add_argument("--eps-train", type=float, default=0.73)
+    parser.add_argument("--eps-decay", type=float, default=5e-6)
+    parser.add_argument("--buffer-size", type=int, default=100000)
+    parser.add_argument("--lr", type=float, default=1e-4)
+    parser.add_argument("--gamma", type=float, default=0.99)
+    parser.add_argument("--target-update-freq", type=int, default=1000)
+    parser.add_argument("--epoch", type=int, default=1000)
+    parser.add_argument("--step-per-epoch", type=int, default=80000)
+    parser.add_argument("--step-per-collect", type=int, default=16)
+    parser.add_argument("--update-per-step", type=float, default=0.0625)
+    parser.add_argument("--batch-size", type=int, default=512)
+    parser.add_argument("--training-num", type=int, default=20)
+    parser.add_argument("--test-num", type=int, default=10)
+    # other
+    parser.add_argument("--logdir", type=str, default="log")
+    parser.add_argument("--render", type=float, default=0.)
+    parser.add_argument(
+        "--device", type=str, default="cuda" if torch.cuda.is_available() else "cpu"
+    )
+    return parser.parse_args()
+
+
+def test_bdq(args=get_args()):
+    env = gym.make(args.task)
+    env = ContinuousToDiscrete(env, args.action_per_branch)
+
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.action_shape = env.action_space.shape or env.action_space.n
+    args.num_branches = args.action_shape if isinstance(args.action_shape,
+                                                        int) else args.action_shape[0]
+
+    print("Observations shape:", args.state_shape)
+    print("Num branches:", args.num_branches)
+    print("Actions per branch:", args.action_per_branch)
+
+    # train_envs = ContinuousToDiscrete(gym.make(args.task), args.action_per_branch)
+    # you can also use tianshou.env.SubprocVectorEnv
+    train_envs = SubprocVectorEnv(
+        [
+            lambda: ContinuousToDiscrete(gym.make(args.task), args.action_per_branch)
+            for _ in range(args.training_num)
+        ]
+    )
+    # test_envs = ContinuousToDiscrete(gym.make(args.task), args.action_per_branch)
+    test_envs = SubprocVectorEnv(
+        [
+            lambda: ContinuousToDiscrete(gym.make(args.task), args.action_per_branch)
+            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 = BranchingNet(
+        args.state_shape,
+        args.num_branches,
+        args.action_per_branch,
+        args.common_hidden_sizes,
+        args.value_hidden_sizes,
+        args.action_hidden_sizes,
+        device=args.device,
+    ).to(args.device)
+    optim = torch.optim.Adam(net.parameters(), lr=args.lr)
+    policy = BranchingDQNPolicy(
+        net, optim, args.gamma, target_update_freq=args.target_update_freq
+    )
+    # collector
+    train_collector = Collector(
+        policy,
+        train_envs,
+        VectorReplayBuffer(args.buffer_size, len(train_envs)),
+        exploration_noise=True
+    )
+    test_collector = Collector(policy, test_envs, exploration_noise=False)
+    # policy.set_eps(1)
+    train_collector.collect(n_step=args.batch_size * args.training_num)
+    # log
+    current_time = datetime.datetime.now().strftime("%Y%m%d-%H%M%S")
+    log_path = os.path.join(args.logdir, "bdq", args.task, current_time)
+    writer = SummaryWriter(log_path)
+    logger = TensorboardLogger(writer)
+
+    def save_best_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, "policy.pth"))
+
+    def stop_fn(mean_rewards):
+        return mean_rewards >= getattr(env.spec.reward_threshold)
+
+    def train_fn(epoch, env_step):  # exp decay
+        eps = max(args.eps_train * (1 - args.eps_decay)**env_step, args.eps_test)
+        policy.set_eps(eps)
+
+    def test_fn(epoch, env_step):
+        policy.set_eps(args.eps_test)
+
+    # trainer
+    result = offpolicy_trainer(
+        policy,
+        train_collector,
+        test_collector,
+        args.epoch,
+        args.step_per_epoch,
+        args.step_per_collect,
+        args.test_num,
+        args.batch_size,
+        update_per_step=args.update_per_step,
+        # stop_fn=stop_fn,
+        train_fn=train_fn,
+        test_fn=test_fn,
+        save_best_fn=save_best_fn,
+        logger=logger
+    )
+
+    # assert stop_fn(result["best_reward"])
+    if __name__ == "__main__":
+        pprint.pprint(result)
+        # Let's watch its performance!
+        policy.eval()
+        policy.set_eps(args.eps_test)
+        test_envs.seed(args.seed)
+        test_collector.reset()
+        result = test_collector.collect(n_episode=args.test_num, render=args.render)
+        rews, lens = result["rews"], result["lens"]
+        print(f"Final reward: {rews.mean()}, length: {lens.mean()}")
+
+
+if __name__ == "__main__":
+    test_bdq(get_args())
diff --git a/examples/box2d/results/bdq/BipedalWalker.png b/examples/box2d/results/bdq/BipedalWalker.png
new file mode 100644
index 0000000..ee4b240
Binary files /dev/null and b/examples/box2d/results/bdq/BipedalWalker.png differ
diff --git a/test/discrete/test_bdq.py b/test/discrete/test_bdq.py
new file mode 100644
index 0000000..604fd88
--- /dev/null
+++ b/test/discrete/test_bdq.py
@@ -0,0 +1,150 @@
+import argparse
+import pprint
+
+import gym
+import numpy as np
+import torch
+
+from tianshou.data import Collector, VectorReplayBuffer
+from tianshou.env import ContinuousToDiscrete, DummyVectorEnv
+from tianshou.policy import BranchingDQNPolicy
+from tianshou.trainer import offpolicy_trainer
+from tianshou.utils.net.common import BranchingNet
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    # task
+    parser.add_argument("--task", type=str, default="Pendulum-v1")
+    parser.add_argument('--reward-threshold', type=float, default=None)
+    # network architecture
+    parser.add_argument("--common-hidden-sizes", type=int, nargs="*", default=[64, 64])
+    parser.add_argument("--action-hidden-sizes", type=int, nargs="*", default=[64])
+    parser.add_argument("--value-hidden-sizes", type=int, nargs="*", default=[64])
+    parser.add_argument("--action-per-branch", type=int, default=40)
+    # training hyperparameters
+    parser.add_argument("--seed", type=int, default=1626)
+    parser.add_argument("--eps-test", type=float, default=0.01)
+    parser.add_argument("--eps-train", type=float, default=0.76)
+    parser.add_argument("--eps-decay", type=float, default=1e-4)
+    parser.add_argument("--buffer-size", type=int, default=20000)
+    parser.add_argument("--lr", type=float, default=1e-3)
+    parser.add_argument("--gamma", type=float, default=0.9)
+    parser.add_argument("--target-update-freq", type=int, default=200)
+    parser.add_argument("--epoch", type=int, default=10)
+    parser.add_argument("--step-per-epoch", type=int, default=80000)
+    parser.add_argument("--step-per-collect", type=int, default=10)
+    parser.add_argument("--update-per-step", type=float, default=0.1)
+    parser.add_argument("--batch-size", type=int, default=128)
+    parser.add_argument("--training-num", type=int, default=10)
+    parser.add_argument("--test-num", type=int, default=10)
+    parser.add_argument("--logdir", type=str, default="log")
+    parser.add_argument('--render', type=float, 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_bdq(args=get_args()):
+    env = gym.make(args.task)
+    env = ContinuousToDiscrete(env, args.action_per_branch)
+
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.num_branches = env.action_space.shape[0]
+
+    if args.reward_threshold is None:
+        default_reward_threshold = {"Pendulum-v0": -250, "Pendulum-v1": -250}
+        args.reward_threshold = default_reward_threshold.get(
+            args.task, env.spec.reward_threshold
+        )
+
+    print("Observations shape:", args.state_shape)
+    print("Num branches:", args.num_branches)
+    print("Actions per branch:", args.action_per_branch)
+
+    train_envs = DummyVectorEnv(
+        [
+            lambda: ContinuousToDiscrete(gym.make(args.task), args.action_per_branch)
+            for _ in range(args.training_num)
+        ]
+    )
+    test_envs = DummyVectorEnv(
+        [
+            lambda: ContinuousToDiscrete(gym.make(args.task), args.action_per_branch)
+            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 = BranchingNet(
+        args.state_shape,
+        args.num_branches,
+        args.action_per_branch,
+        args.common_hidden_sizes,
+        args.value_hidden_sizes,
+        args.action_hidden_sizes,
+        device=args.device,
+    ).to(args.device)
+    optim = torch.optim.Adam(net.parameters(), lr=args.lr)
+    policy = BranchingDQNPolicy(
+        net, optim, args.gamma, target_update_freq=args.target_update_freq
+    )
+    # collector
+    train_collector = Collector(
+        policy,
+        train_envs,
+        VectorReplayBuffer(args.buffer_size, args.training_num),
+        exploration_noise=True
+    )
+    test_collector = Collector(policy, test_envs, exploration_noise=False)
+    # policy.set_eps(1)
+    train_collector.collect(n_step=args.batch_size * args.training_num)
+
+    def train_fn(epoch, env_step):  # exp decay
+        eps = max(args.eps_train * (1 - args.eps_decay)**env_step, args.eps_test)
+        policy.set_eps(eps)
+
+    def test_fn(epoch, env_step):
+        policy.set_eps(args.eps_test)
+
+    def stop_fn(mean_rewards):
+        return mean_rewards >= args.reward_threshold
+
+    # trainer
+    result = offpolicy_trainer(
+        policy,
+        train_collector,
+        test_collector,
+        args.epoch,
+        args.step_per_epoch,
+        args.step_per_collect,
+        args.test_num,
+        args.batch_size,
+        update_per_step=args.update_per_step,
+        train_fn=train_fn,
+        test_fn=test_fn,
+        stop_fn=stop_fn,
+    )
+
+    # assert stop_fn(result["best_reward"])
+    if __name__ == "__main__":
+        pprint.pprint(result)
+        # Let's watch its performance!
+        policy.eval()
+        policy.set_eps(args.eps_test)
+        test_envs.seed(args.seed)
+        test_collector.reset()
+        result = test_collector.collect(n_episode=args.test_num, render=args.render)
+        rews, lens = result["rews"], result["lens"]
+        print(f"Final reward: {rews.mean()}, length: {lens.mean()}")
+
+
+if __name__ == "__main__":
+    test_bdq(get_args())
diff --git a/tianshou/data/utils/converter.py b/tianshou/data/utils/converter.py
index e23143b..ed705e2 100644
--- a/tianshou/data/utils/converter.py
+++ b/tianshou/data/utils/converter.py
@@ -1,7 +1,7 @@
 import pickle
 from copy import deepcopy
 from numbers import Number
-from typing import Any, Dict, Optional, Union
+from typing import Any, Dict, Optional, Union, no_type_check
 
 import h5py
 import numpy as np
@@ -10,6 +10,7 @@ import torch
 from tianshou.data.batch import Batch, _parse_value
 
 
+@no_type_check
 def to_numpy(x: Any) -> Union[Batch, np.ndarray]:
     """Return an object without torch.Tensor."""
     if isinstance(x, torch.Tensor):  # most often case
@@ -30,6 +31,7 @@ def to_numpy(x: Any) -> Union[Batch, np.ndarray]:
         return np.asanyarray(x)
 
 
+@no_type_check
 def to_torch(
     x: Any,
     dtype: Optional[torch.dtype] = None,
@@ -39,14 +41,14 @@ def to_torch(
     if isinstance(x, np.ndarray) and issubclass(
         x.dtype.type, (np.bool_, np.number)
     ):  # most often case
-        x = torch.from_numpy(x).to(device)  # type: ignore
+        x = torch.from_numpy(x).to(device)
         if dtype is not None:
             x = x.type(dtype)
         return x
     elif isinstance(x, torch.Tensor):  # second often case
         if dtype is not None:
             x = x.type(dtype)
-        return x.to(device)  # type: ignore
+        return x.to(device)
     elif isinstance(x, (np.number, np.bool_, Number)):
         return to_torch(np.asanyarray(x), dtype, device)
     elif isinstance(x, (dict, Batch)):
@@ -59,6 +61,7 @@ def to_torch(
         raise TypeError(f"object {x} cannot be converted to torch.")
 
 
+@no_type_check
 def to_torch_as(x: Any, y: torch.Tensor) -> Union[Batch, torch.Tensor]:
     """Return an object without np.ndarray.
 
diff --git a/tianshou/env/__init__.py b/tianshou/env/__init__.py
index 66fbc68..8b1c71a 100644
--- a/tianshou/env/__init__.py
+++ b/tianshou/env/__init__.py
@@ -1,5 +1,6 @@
 """Env package."""
 
+from tianshou.env.gym_wrappers import ContinuousToDiscrete
 from tianshou.env.venv_wrappers import VectorEnvNormObs, VectorEnvWrapper
 from tianshou.env.venvs import (
     BaseVectorEnv,
@@ -23,4 +24,5 @@ __all__ = [
     "VectorEnvWrapper",
     "VectorEnvNormObs",
     "PettingZooEnv",
+    "ContinuousToDiscrete",
 ]
diff --git a/tianshou/env/gym_wrappers.py b/tianshou/env/gym_wrappers.py
new file mode 100644
index 0000000..f63bc9e
--- /dev/null
+++ b/tianshou/env/gym_wrappers.py
@@ -0,0 +1,28 @@
+import gym
+import numpy as np
+
+
+class ContinuousToDiscrete(gym.ActionWrapper):
+    """Gym environment wrapper to take discrete action in a continuous environment.
+
+    :param gym.Env env: gym environment with continuous action space.
+    :param int action_per_branch: number of discrete actions in each dimension
+        of the action space.
+    """
+
+    def __init__(self, env: gym.Env, action_per_branch: int) -> None:
+        super().__init__(env)
+        assert isinstance(env.action_space, gym.spaces.Box)
+        low, high = env.action_space.low, env.action_space.high
+        num_branches = env.action_space.shape[0]
+        self.action_space = gym.spaces.MultiDiscrete(
+            [action_per_branch] * num_branches
+        )
+        mesh = []
+        for lo, hi in zip(low, high):
+            mesh.append(np.linspace(lo, hi, action_per_branch))
+        self.mesh = np.array(mesh)
+
+    def action(self, act: np.ndarray) -> np.ndarray:
+        # modify act
+        return np.array([self.mesh[i][a] for i, a in enumerate(act)])
diff --git a/tianshou/policy/__init__.py b/tianshou/policy/__init__.py
index f7774cb..8007bad 100644
--- a/tianshou/policy/__init__.py
+++ b/tianshou/policy/__init__.py
@@ -4,6 +4,7 @@
 from tianshou.policy.base import BasePolicy
 from tianshou.policy.random import RandomPolicy
 from tianshou.policy.modelfree.dqn import DQNPolicy
+from tianshou.policy.modelfree.bdq import BranchingDQNPolicy
 from tianshou.policy.modelfree.c51 import C51Policy
 from tianshou.policy.modelfree.rainbow import RainbowPolicy
 from tianshou.policy.modelfree.qrdqn import QRDQNPolicy
@@ -34,6 +35,7 @@ __all__ = [
     "BasePolicy",
     "RandomPolicy",
     "DQNPolicy",
+    "BranchingDQNPolicy",
     "C51Policy",
     "RainbowPolicy",
     "QRDQNPolicy",
diff --git a/tianshou/policy/base.py b/tianshou/policy/base.py
index 325a85b..893905d 100644
--- a/tianshou/policy/base.py
+++ b/tianshou/policy/base.py
@@ -339,7 +339,7 @@ class BasePolicy(ABC, nn.Module):
             assert np.isclose(gae_lambda, 1.0)
             v_s_ = np.zeros_like(rew)
         else:
-            v_s_ = to_numpy(v_s_.flatten())  # type: ignore
+            v_s_ = to_numpy(v_s_.flatten())
             v_s_ = v_s_ * BasePolicy.value_mask(buffer, indices)
         v_s = np.roll(v_s_, 1) if v_s is None else to_numpy(v_s.flatten())
 
diff --git a/tianshou/policy/imitation/base.py b/tianshou/policy/imitation/base.py
index 20c6a62..211c093 100644
--- a/tianshou/policy/imitation/base.py
+++ b/tianshou/policy/imitation/base.py
@@ -54,11 +54,11 @@ class ImitationPolicy(BasePolicy):
         if self.action_type == "continuous":  # regression
             act = self(batch).act
             act_target = to_torch(batch.act, dtype=torch.float32, device=act.device)
-            loss = F.mse_loss(act, act_target)  # type: ignore
+            loss = F.mse_loss(act, act_target)
         elif self.action_type == "discrete":  # classification
             act = F.log_softmax(self(batch).logits, dim=-1)
             act_target = to_torch(batch.act, dtype=torch.long, device=act.device)
-            loss = F.nll_loss(act, act_target)  # type: ignore
+            loss = F.nll_loss(act, act_target)
         loss.backward()
         self.optim.step()
         return {"loss": loss.item()}
diff --git a/tianshou/policy/imitation/bcq.py b/tianshou/policy/imitation/bcq.py
index 89facd7..883400d 100644
--- a/tianshou/policy/imitation/bcq.py
+++ b/tianshou/policy/imitation/bcq.py
@@ -104,9 +104,7 @@ class BCQPolicy(BasePolicy):
         """Compute action over the given batch data."""
         # There is "obs" in the Batch
         # obs_group: several groups. Each group has a state.
-        obs_group: torch.Tensor = to_torch(  # type: ignore
-            batch.obs, device=self.device
-        )
+        obs_group: torch.Tensor = to_torch(batch.obs, device=self.device)
         act_group = []
         for obs in obs_group:
             # now obs is (state_dim)
@@ -132,9 +130,7 @@ class BCQPolicy(BasePolicy):
     def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
         # batch: obs, act, rew, done, obs_next. (numpy array)
         # (batch_size, state_dim)
-        batch: Batch = to_torch(  # type: ignore
-            batch, dtype=torch.float, device=self.device
-        )
+        batch: Batch = to_torch(batch, dtype=torch.float, device=self.device)
         obs, act = batch.obs, batch.act
         batch_size = obs.shape[0]
 
diff --git a/tianshou/policy/imitation/cql.py b/tianshou/policy/imitation/cql.py
index dd890ab..7d9cea9 100644
--- a/tianshou/policy/imitation/cql.py
+++ b/tianshou/policy/imitation/cql.py
@@ -160,9 +160,7 @@ class CQLPolicy(SACPolicy):
         return batch
 
     def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
-        batch: Batch = to_torch(  # type: ignore
-            batch, dtype=torch.float, device=self.device,
-        )
+        batch: Batch = to_torch(batch, dtype=torch.float, device=self.device)
         obs, act, rew, obs_next = batch.obs, batch.act, batch.rew, batch.obs_next
         batch_size = obs.shape[0]
 
@@ -208,12 +206,12 @@ class CQLPolicy(SACPolicy):
         random_actions = torch.FloatTensor(
             batch_size * self.num_repeat_actions, act.shape[-1]
         ).uniform_(-self.min_action, self.max_action).to(self.device)
-        tmp_obs = obs.unsqueeze(1) \
-            .repeat(1, self.num_repeat_actions, 1) \
-            .view(batch_size * self.num_repeat_actions, obs.shape[-1])
-        tmp_obs_next = obs_next.unsqueeze(1) \
-            .repeat(1, self.num_repeat_actions, 1) \
-            .view(batch_size * self.num_repeat_actions, obs.shape[-1])
+
+        obs_len = len(obs.shape)
+        repeat_size = [1, self.num_repeat_actions] + [1] * (obs_len - 1)
+        view_size = [batch_size * self.num_repeat_actions] + list(obs.shape[1:])
+        tmp_obs = obs.unsqueeze(1).repeat(*repeat_size).view(*view_size)
+        tmp_obs_next = obs_next.unsqueeze(1).repeat(*repeat_size).view(*view_size)
         # tmp_obs & tmp_obs_next: (batch_size * num_repeat, state_dim)
 
         current_pi_value1, current_pi_value2 = self.calc_pi_values(tmp_obs, tmp_obs)
diff --git a/tianshou/policy/imitation/discrete_bcq.py b/tianshou/policy/imitation/discrete_bcq.py
index 95b5dea..1f713b5 100644
--- a/tianshou/policy/imitation/discrete_bcq.py
+++ b/tianshou/policy/imitation/discrete_bcq.py
@@ -113,10 +113,7 @@ class DiscreteBCQPolicy(DQNPolicy):
         current_q = result.q_value[np.arange(len(target_q)), batch.act]
         act = to_torch(batch.act, dtype=torch.long, device=target_q.device)
         q_loss = F.smooth_l1_loss(current_q, target_q)
-        i_loss = F.nll_loss(
-            F.log_softmax(imitation_logits, dim=-1),
-            act  # type: ignore
-        )
+        i_loss = F.nll_loss(F.log_softmax(imitation_logits, dim=-1), act)
         reg_loss = imitation_logits.pow(2).mean()
         loss = q_loss + i_loss + self._weight_reg * reg_loss
 
diff --git a/tianshou/policy/imitation/gail.py b/tianshou/policy/imitation/gail.py
index 434e12e..b85f52d 100644
--- a/tianshou/policy/imitation/gail.py
+++ b/tianshou/policy/imitation/gail.py
@@ -108,9 +108,9 @@ class GAILPolicy(PPOPolicy):
         return super().process_fn(batch, buffer, indices)
 
     def disc(self, batch: Batch) -> torch.Tensor:
-        obs = to_torch(batch.obs, device=self.disc_net.device)  # type: ignore
-        act = to_torch(batch.act, device=self.disc_net.device)  # type: ignore
-        return self.disc_net(torch.cat([obs, act], dim=1))  # type: ignore
+        obs = to_torch(batch.obs, device=self.disc_net.device)
+        act = to_torch(batch.act, device=self.disc_net.device)
+        return self.disc_net(torch.cat([obs, act], dim=1))
 
     def learn(  # type: ignore
         self, batch: Batch, batch_size: int, repeat: int, **kwargs: Any
diff --git a/tianshou/policy/modelbased/icm.py b/tianshou/policy/modelbased/icm.py
index 66ab1bb..97fcde2 100644
--- a/tianshou/policy/modelbased/icm.py
+++ b/tianshou/policy/modelbased/icm.py
@@ -105,7 +105,7 @@ class ICMPolicy(BasePolicy):
         self.optim.zero_grad()
         act_hat = batch.policy.act_hat
         act = to_torch(batch.act, dtype=torch.long, device=act_hat.device)
-        inverse_loss = F.cross_entropy(act_hat, act).mean()  # type: ignore
+        inverse_loss = F.cross_entropy(act_hat, act).mean()
         forward_loss = batch.policy.mse_loss.mean()
         loss = (
             (1 - self.forward_loss_weight) * inverse_loss +
diff --git a/tianshou/policy/modelfree/bdq.py b/tianshou/policy/modelfree/bdq.py
new file mode 100644
index 0000000..b02514c
--- /dev/null
+++ b/tianshou/policy/modelfree/bdq.py
@@ -0,0 +1,144 @@
+from typing import Any, Dict, Optional, Union
+
+import numpy as np
+import torch
+
+from tianshou.data import Batch, ReplayBuffer, to_numpy, to_torch, to_torch_as
+from tianshou.policy import DQNPolicy
+from tianshou.utils.net.common import BranchingNet
+
+
+class BranchingDQNPolicy(DQNPolicy):
+    """Implementation of the Branching dual Q network arXiv:1711.08946.
+
+    :param torch.nn.Module model: a model following the rules in
+        :class:`~tianshou.policy.BasePolicy`. (s -> logits)
+    :param torch.optim.Optimizer optim: a torch.optim for optimizing the model.
+    :param float discount_factor: in [0, 1].
+    :param int estimation_step: the number of steps to look ahead. Default to 1.
+    :param int target_update_freq: the target network update frequency (0 if
+        you do not use the target network). Default to 0.
+    :param bool reward_normalization: normalize the reward to Normal(0, 1).
+        Default to False.
+    :param bool is_double: use double network. Default to True.
+
+    .. seealso::
+
+        Please refer to :class:`~tianshou.policy.BasePolicy` for more detailed
+        explanation.
+    """
+
+    def __init__(
+        self,
+        model: BranchingNet,
+        optim: torch.optim.Optimizer,
+        discount_factor: float = 0.99,
+        estimation_step: int = 1,
+        target_update_freq: int = 0,
+        reward_normalization: bool = False,
+        is_double: bool = True,
+        **kwargs: Any,
+    ) -> None:
+        super().__init__(
+            model, optim, discount_factor, estimation_step, target_update_freq,
+            reward_normalization, is_double
+        )
+        assert estimation_step == 1, "N-step bigger than one is not supported by BDQ"
+        self.max_action_num = model.action_per_branch
+        self.num_branches = model.num_branches
+
+    def _target_q(self, buffer: ReplayBuffer, indices: np.ndarray) -> torch.Tensor:
+        batch = buffer[indices]  # batch.obs_next: s_{t+n}
+        result = self(batch, input="obs_next")
+        if self._target:
+            # target_Q = Q_old(s_, argmax(Q_new(s_, *)))
+            target_q = self(batch, model="model_old", input="obs_next").logits
+        else:
+            target_q = result.logits
+        if self._is_double:
+            act = np.expand_dims(self(batch, input="obs_next").act, -1)
+            act = to_torch(act, dtype=torch.long, device=target_q.device)
+        else:
+            act = target_q.max(-1).indices.unsqueeze(-1)
+        return torch.gather(target_q, -1, act).squeeze()
+
+    def _compute_return(
+        self,
+        batch: Batch,
+        buffer: ReplayBuffer,
+        indice: np.ndarray,
+        gamma: float = 0.99,
+    ) -> Batch:
+        rew = batch.rew
+        with torch.no_grad():
+            target_q_torch = self._target_q(buffer, indice)  # (bsz, ?)
+        target_q = to_numpy(target_q_torch)
+        end_flag = buffer.done.copy()
+        end_flag[buffer.unfinished_index()] = True
+        end_flag = end_flag[indice]
+        mean_target_q = np.mean(target_q, -1) if len(target_q.shape) > 1 else target_q
+        _target_q = rew + gamma * mean_target_q * (1 - end_flag)
+        target_q = np.repeat(_target_q[..., None], self.num_branches, axis=-1)
+        target_q = np.repeat(target_q[..., None], self.max_action_num, axis=-1)
+
+        batch.returns = to_torch_as(target_q, target_q_torch)
+        if hasattr(batch, "weight"):  # prio buffer update
+            batch.weight = to_torch_as(batch.weight, target_q_torch)
+        return batch
+
+    def process_fn(
+        self, batch: Batch, buffer: ReplayBuffer, indices: np.ndarray
+    ) -> Batch:
+        """Compute the 1-step return for BDQ targets."""
+        return self._compute_return(batch, buffer, indices)
+
+    def forward(
+        self,
+        batch: Batch,
+        state: Optional[Union[Dict, Batch, np.ndarray]] = None,
+        model: str = "model",
+        input: str = "obs",
+        **kwargs: Any,
+    ) -> Batch:
+        model = getattr(self, model)
+        obs = batch[input]
+        obs_next = obs.obs if hasattr(obs, "obs") else obs
+        logits, hidden = model(obs_next, state=state, info=batch.info)
+        act = to_numpy(logits.max(dim=-1)[1])
+        return Batch(logits=logits, act=act, state=hidden)
+
+    def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
+        if self._target and self._iter % self._freq == 0:
+            self.sync_weight()
+        self.optim.zero_grad()
+        weight = batch.pop("weight", 1.0)
+        act = to_torch(batch.act, dtype=torch.long, device=batch.returns.device)
+        q = self(batch).logits
+        act_mask = torch.zeros_like(q)
+        act_mask = act_mask.scatter_(-1, act.unsqueeze(-1), 1)
+        act_q = q * act_mask
+        returns = batch.returns
+        returns = returns * act_mask
+        td_error = returns - act_q
+        loss = (td_error.pow(2).sum(-1).mean(-1) * weight).mean()
+        batch.weight = td_error.sum(-1).sum(-1)  # prio-buffer
+        loss.backward()
+        self.optim.step()
+        self._iter += 1
+        return {"loss": loss.item()}
+
+    def exploration_noise(
+        self,
+        act: Union[np.ndarray, Batch],
+        batch: Batch,
+    ) -> Union[np.ndarray, Batch]:
+        if isinstance(act, np.ndarray) and not np.isclose(self.eps, 0.0):
+            bsz = len(act)
+            rand_mask = np.random.rand(bsz) < self.eps
+            rand_act = np.random.randint(
+                low=0, high=self.max_action_num, size=(bsz, act.shape[-1])
+            )
+            if hasattr(batch.obs, "mask"):
+                rand_act += batch.obs.mask
+            act[rand_mask] = rand_act[rand_mask]
+        return act
diff --git a/tianshou/policy/modelfree/dqn.py b/tianshou/policy/modelfree/dqn.py
index 593de15..e36b7f5 100644
--- a/tianshou/policy/modelfree/dqn.py
+++ b/tianshou/policy/modelfree/dqn.py
@@ -138,8 +138,6 @@ class DQNPolicy(BasePolicy):
                 ...
             )
 
-        :param float eps: in [0, 1], for epsilon-greedy exploration method.
-
         :return: A :class:`~tianshou.data.Batch` which has 3 keys:
 
             * ``act`` the action.
@@ -177,8 +175,11 @@ class DQNPolicy(BasePolicy):
         self._iter += 1
         return {"loss": loss.item()}
 
-    def exploration_noise(self, act: Union[np.ndarray, Batch],
-                          batch: Batch) -> Union[np.ndarray, Batch]:
+    def exploration_noise(
+        self,
+        act: Union[np.ndarray, Batch],
+        batch: Batch,
+    ) -> Union[np.ndarray, Batch]:
         if isinstance(act, np.ndarray) and not np.isclose(self.eps, 0.0):
             bsz = len(act)
             rand_mask = np.random.rand(bsz) < self.eps
diff --git a/tianshou/utils/net/common.py b/tianshou/utils/net/common.py
index 64283b4..1fc58f7 100644
--- a/tianshou/utils/net/common.py
+++ b/tianshou/utils/net/common.py
@@ -363,3 +363,93 @@ class EnsembleLinear(nn.Module):
         if self.bias is not None:
             x = x + self.bias
         return x
+
+
+class BranchingNet(nn.Module):
+    """Branching dual Q network.
+
+    Network for the BranchingDQNPolicy, it uses a common network module, a value module
+    and action "branches" one for each dimension.It allows for a linear scaling
+    of Q-value the output w.r.t. the number of dimensions in the action space.
+    For more info please refer to: arXiv:1711.08946.
+    :param state_shape: int or a sequence of int of the shape of state.
+    :param action_shape: int or a sequence of int of the shape of action.
+    :param action_peer_branch: int or a sequence of int of the number of actions in
+    each dimension.
+    :param common_hidden_sizes: shape of the common MLP network passed in as a list.
+    :param value_hidden_sizes: shape of the value MLP network passed in as a list.
+    :param action_hidden_sizes: shape of the action MLP network passed in as a list.
+    :param norm_layer: use which normalization before activation, e.g.,
+    ``nn.LayerNorm`` and ``nn.BatchNorm1d``. Default to no normalization.
+    You can also pass a list of normalization modules with the same length
+    of hidden_sizes, to use different normalization module in different
+    layers. Default to no normalization.
+    :param activation: which activation to use after each layer, can be both
+    the same activation for all layers if passed in nn.Module, or different
+    activation for different Modules if passed in a list. Default to
+    nn.ReLU.
+    :param device: specify the device when the network actually runs. Default
+    to "cpu".
+    :param bool softmax: whether to apply a softmax layer over the last layer's
+    output.
+    """
+
+    def __init__(
+        self,
+        state_shape: Union[int, Sequence[int]],
+        num_branches: int = 0,
+        action_per_branch: int = 2,
+        common_hidden_sizes: List[int] = [],
+        value_hidden_sizes: List[int] = [],
+        action_hidden_sizes: List[int] = [],
+        norm_layer: Optional[ModuleType] = None,
+        activation: Optional[ModuleType] = nn.ReLU,
+        device: Union[str, int, torch.device] = "cpu",
+    ) -> None:
+        super().__init__()
+        self.device = device
+        self.num_branches = num_branches
+        self.action_per_branch = action_per_branch
+        # common network
+        common_input_dim = int(np.prod(state_shape))
+        common_output_dim = 0
+        self.common = MLP(
+            common_input_dim, common_output_dim, common_hidden_sizes, norm_layer,
+            activation, device
+        )
+        # value network
+        value_input_dim = common_hidden_sizes[-1]
+        value_output_dim = 1
+        self.value = MLP(
+            value_input_dim, value_output_dim, value_hidden_sizes, norm_layer,
+            activation, device
+        )
+        # action branching network
+        action_input_dim = common_hidden_sizes[-1]
+        action_output_dim = action_per_branch
+        self.branches = nn.ModuleList(
+            [
+                MLP(
+                    action_input_dim, action_output_dim, action_hidden_sizes,
+                    norm_layer, activation, device
+                ) for _ in range(self.num_branches)
+            ]
+        )
+
+    def forward(
+        self,
+        obs: Union[np.ndarray, torch.Tensor],
+        state: Any = None,
+        info: Dict[str, Any] = {},
+    ) -> Tuple[torch.Tensor, Any]:
+        """Mapping: obs -> model -> logits."""
+        common_out = self.common(obs)
+        value_out = self.value(common_out)
+        value_out = torch.unsqueeze(value_out, 1)
+        action_out = []
+        for b in self.branches:
+            action_out.append(b(common_out))
+        action_scores = torch.stack(action_out, 1)
+        action_scores = action_scores - torch.mean(action_scores, 2, keepdim=True)
+        logits = value_out + action_scores
+        return logits, state