diff --git a/.gitignore b/.gitignore
index 082dcef..be8453a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -145,3 +145,5 @@ MUJOCO_LOG.TXT
 *.zip
 *.pstats
 *.swp
+*.pkl
+*.hdf5
diff --git a/README.md b/README.md
index 69f95ce..2848f9c 100644
--- a/README.md
+++ b/README.md
@@ -31,6 +31,7 @@
 - [Soft Actor-Critic (SAC)](https://arxiv.org/pdf/1812.05905.pdf)
 - [Discrete Soft Actor-Critic (SAC-Discrete)](https://arxiv.org/pdf/1910.07207.pdf)
 - Vanilla Imitation Learning
+- [Discrete Batch-Constrained deep Q-Learning (BCQ-Discrete)](https://arxiv.org/pdf/1910.01708.pdf)
 - [Prioritized Experience Replay (PER)](https://arxiv.org/pdf/1511.05952.pdf)
 - [Generalized Advantage Estimator (GAE)](https://arxiv.org/pdf/1506.02438.pdf)
 - [Posterior Sampling Reinforcement Learning (PSRL)](https://www.ece.uvic.ca/~bctill/papers/learning/Strens_2000.pdf)
diff --git a/docs/index.rst b/docs/index.rst
index 3b1fe02..72704f4 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -20,8 +20,9 @@ Welcome to Tianshou!
 * :class:`~tianshou.policy.TD3Policy` `Twin Delayed DDPG <https://arxiv.org/pdf/1802.09477.pdf>`_
 * :class:`~tianshou.policy.SACPolicy` `Soft Actor-Critic <https://arxiv.org/pdf/1812.05905.pdf>`_
 * :class:`~tianshou.policy.DiscreteSACPolicy` `Discrete Soft Actor-Critic <https://arxiv.org/pdf/1910.07207.pdf>`_
-* :class:`~tianshou.policy.PSRLPolicy` `Posterior Sampling Reinforcement Learning <https://www.ece.uvic.ca/~bctill/papers/learning/Strens_2000.pdf>`_
 * :class:`~tianshou.policy.ImitationPolicy` Imitation Learning
+* :class:`~tianshou.policy.DiscreteBCQPolicy` `Discrete Batch-Constrained deep Q-Learning <https://arxiv.org/pdf/1910.01708.pdf>`_
+* :class:`~tianshou.policy.PSRLPolicy` `Posterior Sampling Reinforcement Learning <https://www.ece.uvic.ca/~bctill/papers/learning/Strens_2000.pdf>`_
 * :class:`~tianshou.data.PrioritizedReplayBuffer` `Prioritized Experience Replay <https://arxiv.org/pdf/1511.05952.pdf>`_
 * :meth:`~tianshou.policy.BasePolicy.compute_episodic_return` `Generalized Advantage Estimator <https://arxiv.org/pdf/1506.02438.pdf>`_
 
diff --git a/docs/tutorials/concepts.rst b/docs/tutorials/concepts.rst
index 7d64458..8ea2d27 100644
--- a/docs/tutorials/concepts.rst
+++ b/docs/tutorials/concepts.rst
@@ -201,7 +201,7 @@ Trainer
 
 Once you have a collector and a policy, you can start writing the training method for your RL agent. Trainer, to be honest, is a simple wrapper. It helps you save energy for writing the training loop. You can also construct your own trainer: :ref:`customized_trainer`.
 
-Tianshou has two types of trainer: :func:`~tianshou.trainer.onpolicy_trainer` and :func:`~tianshou.trainer.offpolicy_trainer`, corresponding to on-policy algorithms (such as Policy Gradient) and off-policy algorithms (such as DQN). Please check out :doc:`/api/tianshou.trainer` for the usage.
+Tianshou has three types of trainer: :func:`~tianshou.trainer.onpolicy_trainer` for on-policy algorithms such as Policy Gradient, :func:`~tianshou.trainer.offpolicy_trainer` for off-policy algorithms such as DQN, and :func:`~tianshou.trainer.offline_trainer` for offline algorithms such as BCQ. Please check out :doc:`/api/tianshou.trainer` for the usage.
 
 
 .. _pseudocode:
diff --git a/docs/tutorials/dqn.rst b/docs/tutorials/dqn.rst
index b1971ea..faea6a8 100644
--- a/docs/tutorials/dqn.rst
+++ b/docs/tutorials/dqn.rst
@@ -120,7 +120,7 @@ In each step, the collector will let the policy perform (at least) a specified n
 Train Policy with a Trainer
 ---------------------------
 
-Tianshou provides :class:`~tianshou.trainer.onpolicy_trainer` and :class:`~tianshou.trainer.offpolicy_trainer`. The trainer will automatically stop training when the policy reach the stop condition ``stop_fn`` on test collector. Since DQN is an off-policy algorithm, we use the :class:`~tianshou.trainer.offpolicy_trainer` as follows:
+Tianshou provides :func:`~tianshou.trainer.onpolicy_trainer`, :func:`~tianshou.trainer.offpolicy_trainer`, and :func:`~tianshou.trainer.offline_trainer`. The trainer will automatically stop training when the policy reach the stop condition ``stop_fn`` on test collector. Since DQN is an off-policy algorithm, we use the :func:`~tianshou.trainer.offpolicy_trainer` as follows:
 ::
 
     result = ts.trainer.offpolicy_trainer(
@@ -133,7 +133,7 @@ Tianshou provides :class:`~tianshou.trainer.onpolicy_trainer` and :class:`~tians
         writer=None)
     print(f'Finished training! Use {result["duration"]}')
 
-The meaning of each parameter is as follows (full description can be found at :meth:`~tianshou.trainer.offpolicy_trainer`):
+The meaning of each parameter is as follows (full description can be found at :func:`~tianshou.trainer.offpolicy_trainer`):
 
 * ``max_epoch``: The maximum of epochs for training. The training process might be finished before reaching the ``max_epoch``;
 * ``step_per_epoch``: The number of step for updating policy network in one epoch;
diff --git a/examples/atari/README.md b/examples/atari/README.md
index 7fd0344..933415e 100644
--- a/examples/atari/README.md
+++ b/examples/atari/README.md
@@ -38,4 +38,15 @@ One epoch here is equal to 100,000 env step, 100 epochs stand for 10M.
 | SeaquestNoFrameskip-v4      | 6226        | ![](results/c51/Seaquest_rew.png)     | `python3 atari_c51.py --task "SeaquestNoFrameskip-v4"`  |
 | SpaceInvadersNoFrameskip-v4 | 988.5      | ![](results/c51/SpaceInvader_rew.png) | `python3 atari_c51.py --task "SpaceInvadersNoFrameskip-v4"`  |
 
-Note: The selection of `n_step` is based on Figure 6 in the [Rainbow](https://arxiv.org/abs/1710.02298) paper.
\ No newline at end of file
+Note: The selection of `n_step` is based on Figure 6 in the [Rainbow](https://arxiv.org/abs/1710.02298) paper.
+
+# BCQ
+
+TODO: after the `done` issue fixed, the result should be re-tuned and place here.
+
+To running BCQ algorithm on Atari, you need to do the following things:
+
+- Train an expert, by using the command listed in the above DQN section;
+- Generate buffer with noise: `python3 atari_dqn.py --task {your_task} --watch --resume-path log/{your_task}/dqn/policy.pth --eps-test 0.2 --buffer-size 1000000 --save-buffer-name expert.hdf5` (note that 1M Atari buffer cannot be saved as `.pkl` format because it is too large and will cause error);
+- Train BCQ: `python3 atari_bcq.py --task {your_task} --load-buffer-name expert.hdf5`.
+
diff --git a/examples/atari/atari_bcq.py b/examples/atari/atari_bcq.py
new file mode 100644
index 0000000..e9edb83
--- /dev/null
+++ b/examples/atari/atari_bcq.py
@@ -0,0 +1,153 @@
+import os
+import torch
+import pickle
+import pprint
+import argparse
+import numpy as np
+from torch.utils.tensorboard import SummaryWriter
+
+from tianshou.env import SubprocVectorEnv
+from tianshou.trainer import offline_trainer
+from tianshou.utils.net.discrete import Actor
+from tianshou.policy import DiscreteBCQPolicy
+from tianshou.data import Collector, ReplayBuffer
+
+from atari_network import DQN
+from atari_wrapper import wrap_deepmind
+
+
+def get_args():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--task", type=str, default="PongNoFrameskip-v4")
+    parser.add_argument("--seed", type=int, default=1626)
+    parser.add_argument("--eps-test", type=float, default=0.001)
+    parser.add_argument("--lr", type=float, default=6.25e-5)
+    parser.add_argument("--gamma", type=float, default=0.99)
+    parser.add_argument("--n-step", type=int, default=3)
+    parser.add_argument("--target-update-freq", type=int, default=8000)
+    parser.add_argument("--unlikely-action-threshold", type=float, default=0.3)
+    parser.add_argument("--imitation-logits-penalty", type=float, default=0.01)
+    parser.add_argument("--epoch", type=int, default=100)
+    parser.add_argument("--step-per-epoch", type=int, default=10000)
+    parser.add_argument("--batch-size", type=int, default=32)
+    parser.add_argument('--hidden-sizes', type=int,
+                        nargs='*', default=[512])
+    parser.add_argument("--test-num", type=int, default=100)
+    parser.add_argument('--frames_stack', type=int, default=4)
+    parser.add_argument("--logdir", type=str, default="log")
+    parser.add_argument("--render", type=float, default=0.)
+    parser.add_argument("--resume-path", type=str, default=None)
+    parser.add_argument("--watch", default=False, action="store_true",
+                        help="watch the play of pre-trained policy only")
+    parser.add_argument("--log-interval", type=int, default=1000)
+    parser.add_argument(
+        "--load-buffer-name", type=str,
+        default="./expert_DQN_PongNoFrameskip-v4.hdf5",
+    )
+    parser.add_argument(
+        "--device", type=str,
+        default="cuda" if torch.cuda.is_available() else "cpu",
+    )
+    args = parser.parse_known_args()[0]
+    return args
+
+
+def make_atari_env(args):
+    return wrap_deepmind(args.task, frame_stack=args.frames_stack)
+
+
+def make_atari_env_watch(args):
+    return wrap_deepmind(args.task, frame_stack=args.frames_stack,
+                         episode_life=False, clip_rewards=False)
+
+
+def test_discrete_bcq(args=get_args()):
+    # envs
+    env = make_atari_env(args)
+    args.state_shape = env.observation_space.shape or env.observation_space.n
+    args.action_shape = env.action_space.shape or env.action_space.n
+    # should be N_FRAMES x H x W
+    print("Observations shape:", args.state_shape)
+    print("Actions shape:", args.action_shape)
+    # make environments
+    test_envs = SubprocVectorEnv([lambda: make_atari_env_watch(args)
+                                  for _ in range(args.test_num)])
+    # seed
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    test_envs.seed(args.seed)
+    # model
+    feature_net = DQN(*args.state_shape, args.action_shape,
+                      device=args.device, features_only=True).to(args.device)
+    policy_net = Actor(feature_net, args.action_shape,
+                       hidden_sizes=args.hidden_sizes).to(args.device)
+    imitation_net = Actor(feature_net, args.action_shape,
+                          hidden_sizes=args.hidden_sizes).to(args.device)
+    optim = torch.optim.Adam(
+        set(policy_net.parameters()).union(imitation_net.parameters()),
+        lr=args.lr,
+    )
+    # define policy
+    policy = DiscreteBCQPolicy(
+        policy_net, imitation_net, optim, args.gamma, args.n_step,
+        args.target_update_freq, args.eps_test,
+        args.unlikely_action_threshold, args.imitation_logits_penalty,
+    )
+    # load a previous policy
+    if args.resume_path:
+        policy.load_state_dict(torch.load(
+            args.resume_path, map_location=args.device
+        ))
+        print("Loaded agent from: ", args.resume_path)
+    # buffer
+    assert os.path.exists(args.load_buffer_name), \
+        "Please run atari_dqn.py first to get expert's data buffer."
+    if args.load_buffer_name.endswith('.pkl'):
+        buffer = pickle.load(open(args.load_buffer_name, "rb"))
+    elif args.load_buffer_name.endswith('.hdf5'):
+        buffer = ReplayBuffer.load_hdf5(args.load_buffer_name)
+    else:
+        print(f"Unknown buffer format: {args.load_buffer_name}")
+        exit(0)
+
+    # collector
+    test_collector = Collector(policy, test_envs)
+
+    log_path = os.path.join(args.logdir, args.task, 'discrete_bcq')
+    writer = SummaryWriter(log_path)
+
+    def save_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, 'policy.pth'))
+
+    def stop_fn(mean_rewards):
+        return False
+
+    # watch agent's performance
+    def watch():
+        print("Setup test envs ...")
+        policy.eval()
+        policy.set_eps(args.eps_test)
+        test_envs.seed(args.seed)
+        print("Testing agent ...")
+        test_collector.reset()
+        result = test_collector.collect(n_episode=[1] * args.test_num,
+                                        render=args.render)
+        pprint.pprint(result)
+
+    if args.watch:
+        watch()
+        exit(0)
+
+    result = offline_trainer(
+        policy, buffer, test_collector,
+        args.epoch, args.step_per_epoch, args.test_num, args.batch_size,
+        stop_fn=stop_fn, save_fn=save_fn, writer=writer,
+        log_interval=args.log_interval,
+    )
+
+    pprint.pprint(result)
+    watch()
+
+
+if __name__ == "__main__":
+    test_discrete_bcq(get_args())
diff --git a/examples/atari/atari_dqn.py b/examples/atari/atari_dqn.py
index cf43189..4f4c4f2 100644
--- a/examples/atari/atari_dqn.py
+++ b/examples/atari/atari_dqn.py
@@ -41,6 +41,7 @@ def get_args():
     parser.add_argument('--resume-path', type=str, default=None)
     parser.add_argument('--watch', default=False, action='store_true',
                         help='watch the play of pre-trained policy only')
+    parser.add_argument('--save-buffer-name', type=str, default=None)
     return parser.parse_args()
 
 
@@ -120,13 +121,25 @@ def test_dqn(args=get_args()):
 
     # watch agent's performance
     def watch():
-        print("Testing agent ...")
+        print("Setup test envs ...")
         policy.eval()
         policy.set_eps(args.eps_test)
         test_envs.seed(args.seed)
-        test_collector.reset()
-        result = test_collector.collect(n_episode=[1] * args.test_num,
-                                        render=args.render)
+        if args.save_buffer_name:
+            print(f"Generate buffer with size {args.buffer_size}")
+            buffer = ReplayBuffer(
+                args.buffer_size, ignore_obs_next=True,
+                save_only_last_obs=True, stack_num=args.frames_stack)
+            collector = Collector(policy, test_envs, buffer)
+            result = collector.collect(n_step=args.buffer_size)
+            print(f"Save buffer into {args.save_buffer_name}")
+            # Unfortunately, pickle will cause oom with 1M buffer size
+            buffer.save_hdf5(args.save_buffer_name)
+        else:
+            print("Testing agent ...")
+            test_collector.reset()
+            result = test_collector.collect(n_episode=[1] * args.test_num,
+                                            render=args.render)
         pprint.pprint(result)
 
     if args.watch:
diff --git a/examples/atari/atari_network.py b/examples/atari/atari_network.py
index 0b7adaa..c31a6c8 100644
--- a/examples/atari/atari_network.py
+++ b/examples/atari/atari_network.py
@@ -44,8 +44,7 @@ class DQN(nn.Module):
         info: Dict[str, Any] = {},
     ) -> Tuple[torch.Tensor, Any]:
         r"""Mapping: x -> Q(x, \*)."""
-        x = torch.as_tensor(
-            x, device=self.device, dtype=torch.float32)  # type: ignore
+        x = torch.as_tensor(x, device=self.device, dtype=torch.float32)
         return self.net(x), state
 
 
diff --git a/setup.py b/setup.py
index 5af0b20..4b22472 100644
--- a/setup.py
+++ b/setup.py
@@ -51,7 +51,7 @@ setup(
         "tensorboard",
         "torch>=1.4.0",
         "numba>=0.51.0",
-        "h5py>=3.1.0"
+        "h5py>=2.10.0",  # to match tensorflow's minimal requirements
     ],
     extras_require={
         "dev": [
diff --git a/test/discrete/test_dqn.py b/test/discrete/test_dqn.py
index 541f249..1e9f089 100644
--- a/test/discrete/test_dqn.py
+++ b/test/discrete/test_dqn.py
@@ -1,6 +1,7 @@
 import os
 import gym
 import torch
+import pickle
 import pprint
 import argparse
 import numpy as np
@@ -38,6 +39,9 @@ def get_args():
                         action="store_true", default=False)
     parser.add_argument('--alpha', type=float, default=0.6)
     parser.add_argument('--beta', type=float, default=0.4)
+    parser.add_argument(
+        '--save-buffer-name', type=str,
+        default="./expert_DQN_CartPole-v0.pkl")
     parser.add_argument(
         '--device', type=str,
         default='cuda' if torch.cuda.is_available() else 'cpu')
@@ -114,6 +118,7 @@ def test_dqn(args=get_args()):
         stop_fn=stop_fn, save_fn=save_fn, writer=writer)
 
     assert stop_fn(result['best_reward'])
+
     if __name__ == '__main__':
         pprint.pprint(result)
         # Let's watch its performance!
@@ -124,6 +129,12 @@ def test_dqn(args=get_args()):
         result = collector.collect(n_episode=1, render=args.render)
         print(f'Final reward: {result["rew"]}, length: {result["len"]}')
 
+    # save buffer in pickle format, for imitation learning unittest
+    buf = ReplayBuffer(args.buffer_size)
+    collector = Collector(policy, test_envs, buf)
+    collector.collect(n_step=args.buffer_size)
+    pickle.dump(buf, open(args.save_buffer_name, "wb"))
+
 
 def test_pdqn(args=get_args()):
     args.prioritized_replay = True
diff --git a/test/discrete/test_il_bcq.py b/test/discrete/test_il_bcq.py
new file mode 100644
index 0000000..e9e857e
--- /dev/null
+++ b/test/discrete/test_il_bcq.py
@@ -0,0 +1,111 @@
+import os
+import gym
+import torch
+import pickle
+import pprint
+import argparse
+import numpy as np
+from torch.utils.tensorboard import SummaryWriter
+
+from tianshou.data import Collector
+from tianshou.env import DummyVectorEnv
+from tianshou.utils.net.common import Net
+from tianshou.trainer import offline_trainer
+from tianshou.policy import DiscreteBCQPolicy
+
+
+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("--eps-test", type=float, default=0.001)
+    parser.add_argument("--lr", type=float, default=3e-4)
+    parser.add_argument("--gamma", type=float, default=0.9)
+    parser.add_argument("--n-step", type=int, default=3)
+    parser.add_argument("--target-update-freq", type=int, default=320)
+    parser.add_argument("--unlikely-action-threshold", type=float, default=0.3)
+    parser.add_argument("--imitation-logits-penalty", type=float, default=0.01)
+    parser.add_argument("--epoch", type=int, default=5)
+    parser.add_argument("--step-per-epoch", type=int, default=1000)
+    parser.add_argument("--batch-size", type=int, default=64)
+    parser.add_argument('--hidden-sizes', type=int,
+                        nargs='*', default=[128, 128, 128])
+    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.)
+    parser.add_argument(
+        "--load-buffer-name", type=str,
+        default="./expert_DQN_CartPole-v0.pkl",
+    )
+    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_bcq(args=get_args()):
+    # envs
+    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
+    test_envs = DummyVectorEnv(
+        [lambda: gym.make(args.task) for _ in range(args.test_num)])
+    # seed
+    np.random.seed(args.seed)
+    torch.manual_seed(args.seed)
+    test_envs.seed(args.seed)
+    # model
+    policy_net = Net(
+        args.state_shape, args.action_shape,
+        hidden_sizes=args.hidden_sizes, device=args.device).to(args.device)
+    imitation_net = Net(
+        args.state_shape, args.action_shape,
+        hidden_sizes=args.hidden_sizes, device=args.device).to(args.device)
+    optim = torch.optim.Adam(
+        set(policy_net.parameters()).union(imitation_net.parameters()),
+        lr=args.lr)
+
+    policy = DiscreteBCQPolicy(
+        policy_net, imitation_net, optim, args.gamma, args.n_step,
+        args.target_update_freq, args.eps_test,
+        args.unlikely_action_threshold, args.imitation_logits_penalty,
+    )
+    # buffer
+    assert os.path.exists(args.load_buffer_name), \
+        "Please run test_dqn.py first to get expert's data buffer."
+    buffer = pickle.load(open(args.load_buffer_name, "rb"))
+
+    # collector
+    test_collector = Collector(policy, test_envs)
+
+    log_path = os.path.join(args.logdir, args.task, 'discrete_bcq')
+    writer = SummaryWriter(log_path)
+
+    def save_fn(policy):
+        torch.save(policy.state_dict(), os.path.join(log_path, 'policy.pth'))
+
+    def stop_fn(mean_rewards):
+        return mean_rewards >= env.spec.reward_threshold
+
+    result = offline_trainer(
+        policy, buffer, test_collector,
+        args.epoch, args.step_per_epoch, args.test_num, args.batch_size,
+        stop_fn=stop_fn, save_fn=save_fn, writer=writer)
+
+    assert stop_fn(result['best_reward'])
+
+    if __name__ == '__main__':
+        pprint.pprint(result)
+        # Let's watch its performance!
+        env = gym.make(args.task)
+        policy.eval()
+        policy.set_eps(args.eps_test)
+        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_bcq(get_args())
diff --git a/tianshou/__init__.py b/tianshou/__init__.py
index cc37f27..0f7a59c 100644
--- a/tianshou/__init__.py
+++ b/tianshou/__init__.py
@@ -1,7 +1,7 @@
 from tianshou import data, env, utils, policy, trainer, exploration
 
 
-__version__ = "0.3.0"
+__version__ = "0.3.1"
 
 __all__ = [
     "env",
diff --git a/tianshou/policy/__init__.py b/tianshou/policy/__init__.py
index 9626d97..968aaf6 100644
--- a/tianshou/policy/__init__.py
+++ b/tianshou/policy/__init__.py
@@ -10,6 +10,7 @@ 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.imitation.discrete_bcq import DiscreteBCQPolicy
 from tianshou.policy.modelbase.psrl import PSRLPolicy
 from tianshou.policy.multiagent.mapolicy import MultiAgentPolicyManager
 
@@ -27,6 +28,7 @@ __all__ = [
     "TD3Policy",
     "SACPolicy",
     "DiscreteSACPolicy",
+    "DiscreteBCQPolicy",
     "PSRLPolicy",
     "MultiAgentPolicyManager",
 ]
diff --git a/tianshou/policy/imitation/base.py b/tianshou/policy/imitation/base.py
index d65cbc8..954bc81 100644
--- a/tianshou/policy/imitation/base.py
+++ b/tianshou/policy/imitation/base.py
@@ -57,7 +57,7 @@ class ImitationPolicy(BasePolicy):
             a_ = to_torch(batch.act, dtype=torch.float32, device=a.device)
             loss = F.mse_loss(a, a_)  # type: ignore
         elif self.mode == "discrete":  # classification
-            a = self(batch).logits
+            a = F.log_softmax(self(batch).logits, dim=-1)
             a_ = to_torch(batch.act, dtype=torch.long, device=a.device)
             loss = F.nll_loss(a, a_)  # type: ignore
         loss.backward()
diff --git a/tianshou/policy/imitation/discrete_bcq.py b/tianshou/policy/imitation/discrete_bcq.py
new file mode 100644
index 0000000..faae34a
--- /dev/null
+++ b/tianshou/policy/imitation/discrete_bcq.py
@@ -0,0 +1,139 @@
+import math
+import torch
+import numpy as np
+import torch.nn.functional as F
+from typing import Any, Dict, Union, Optional
+
+from tianshou.policy import DQNPolicy
+from tianshou.data import Batch, ReplayBuffer, to_torch
+
+
+class DiscreteBCQPolicy(DQNPolicy):
+    """Implementation of discrete BCQ algorithm. arXiv:1910.01708.
+
+    :param torch.nn.Module model: a model following the rules in
+        :class:`~tianshou.policy.BasePolicy`. (s -> q_value)
+    :param torch.nn.Module imitator: a model following the rules in
+        :class:`~tianshou.policy.BasePolicy`. (s -> imtation_logits)
+    :param torch.optim.Optimizer optim: a torch.optim for optimizing the model.
+    :param float discount_factor: in [0, 1].
+    :param int estimation_step: greater than 1, the number of steps to look
+        ahead.
+    :param int target_update_freq: the target network update frequency.
+    :param float eval_eps: the epsilon-greedy noise added in evaluation.
+    :param float unlikely_action_threshold: the threshold (tau) for unlikely
+        actions, as shown in Equ. (17) in the paper, defaults to 0.3.
+    :param float imitation_logits_penalty: reguralization weight for imitation
+        logits, defaults to 1e-2.
+    :param bool reward_normalization: normalize the reward to Normal(0, 1),
+        defaults to False.
+
+    .. seealso::
+
+        Please refer to :class:`~tianshou.policy.BasePolicy` for more detailed
+        explanation.
+    """
+
+    def __init__(
+        self,
+        model: torch.nn.Module,
+        imitator: torch.nn.Module,
+        optim: torch.optim.Optimizer,
+        discount_factor: float = 0.99,
+        estimation_step: int = 1,
+        target_update_freq: int = 8000,
+        eval_eps: float = 1e-3,
+        unlikely_action_threshold: float = 0.3,
+        imitation_logits_penalty: float = 1e-2,
+        reward_normalization: bool = False,
+        **kwargs: Any,
+    ) -> None:
+        super().__init__(model, optim, discount_factor, estimation_step,
+                         target_update_freq, reward_normalization, **kwargs)
+        assert target_update_freq > 0, "BCQ needs target network setting."
+        self.imitator = imitator
+        assert (
+            0.0 <= unlikely_action_threshold < 1.0
+        ), "unlikely_action_threshold should be in [0, 1)"
+        if unlikely_action_threshold > 0:
+            self._log_tau = math.log(unlikely_action_threshold)
+        else:
+            self._log_tau = -np.inf
+        assert 0.0 <= eval_eps < 1.0
+        self._eps = eval_eps
+        self._weight_reg = imitation_logits_penalty
+
+    def train(self, mode: bool = True) -> "DiscreteBCQPolicy":
+        self.training = mode
+        self.model.train(mode)
+        self.imitator.train(mode)
+        return self
+
+    def _target_q(
+        self, buffer: ReplayBuffer, indice: np.ndarray
+    ) -> torch.Tensor:
+        batch = buffer[indice]  # batch.obs_next: s_{t+n}
+        # target_Q = Q_old(s_, argmax(Q_new(s_, *)))
+        with torch.no_grad():
+            act = self(batch, input="obs_next", eps=0.0).act
+            target_q, _ = self.model_old(batch.obs_next)
+            target_q = target_q[np.arange(len(act)), act]
+        return target_q
+
+    def forward(  # type: ignore
+        self,
+        batch: Batch,
+        state: Optional[Union[dict, Batch, np.ndarray]] = None,
+        input: str = "obs",
+        eps: Optional[float] = None,
+        **kwargs: Any,
+    ) -> Batch:
+        if eps is None:
+            eps = self._eps
+        obs = batch[input]
+        q_value, state = self.model(obs, state=state, info=batch.info)
+        imitation_logits, _ = self.imitator(obs, state=state, info=batch.info)
+
+        # mask actions for argmax
+        ratio = imitation_logits - imitation_logits.max(
+            dim=-1, keepdim=True).values
+        mask = (ratio < self._log_tau).float()
+        action = (q_value - np.inf * mask).argmax(dim=-1)
+
+        # add eps to act
+        if not np.isclose(eps, 0.0):
+            bsz, action_num = q_value.shape
+            mask = np.random.rand(bsz) < eps
+            action_rand = torch.randint(
+                action_num, size=[bsz], device=action.device)
+            action[mask] = action_rand[mask]
+
+        return Batch(act=action, state=state, q_value=q_value,
+                     imitation_logits=imitation_logits)
+
+    def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
+        if self._iter % self._freq == 0:
+            self.sync_weight()
+        self._iter += 1
+
+        target_q = batch.returns.flatten()
+        result = self(batch, eps=0.0)
+        imitation_logits = result.imitation_logits
+        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
+        reg_loss = imitation_logits.pow(2).mean()
+        loss = q_loss + i_loss + self._weight_reg * reg_loss
+
+        self.optim.zero_grad()
+        loss.backward()
+        self.optim.step()
+
+        return {
+            "loss": loss.item(),
+            "q_loss": q_loss.item(),
+            "i_loss": i_loss.item(),
+            "reg_loss": reg_loss.item(),
+        }
diff --git a/tianshou/policy/modelfree/a2c.py b/tianshou/policy/modelfree/a2c.py
index df34e01..e215c6b 100644
--- a/tianshou/policy/modelfree/a2c.py
+++ b/tianshou/policy/modelfree/a2c.py
@@ -58,8 +58,8 @@ class A2CPolicy(PGPolicy):
         self.critic = critic
         assert 0.0 <= gae_lambda <= 1.0, "GAE lambda should be in [0, 1]."
         self._lambda = gae_lambda
-        self._w_vf = vf_coef
-        self._w_ent = ent_coef
+        self._weight_vf = vf_coef
+        self._weight_ent = ent_coef
         self._grad_norm = max_grad_norm
         self._batch = max_batchsize
         self._rew_norm = reward_normalization
@@ -122,7 +122,8 @@ class A2CPolicy(PGPolicy):
                 a_loss = -(log_prob * (r - v).detach()).mean()
                 vf_loss = F.mse_loss(r, v)  # type: ignore
                 ent_loss = dist.entropy().mean()
-                loss = a_loss + self._w_vf * vf_loss - self._w_ent * ent_loss
+                loss = a_loss + self._weight_vf * vf_loss - \
+                    self._weight_ent * ent_loss
                 loss.backward()
                 if self._grad_norm is not None:
                     nn.utils.clip_grad_norm_(
diff --git a/tianshou/policy/modelfree/c51.py b/tianshou/policy/modelfree/c51.py
index 96cc680..706872e 100644
--- a/tianshou/policy/modelfree/c51.py
+++ b/tianshou/policy/modelfree/c51.py
@@ -124,7 +124,7 @@ class C51Policy(DQNPolicy):
         return target_dist.sum(-1)
 
     def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
-        if self._target and self._cnt % self._freq == 0:
+        if self._target and self._iter % self._freq == 0:
             self.sync_weight()
         self.optim.zero_grad()
         with torch.no_grad():
@@ -139,5 +139,5 @@ class C51Policy(DQNPolicy):
         batch.weight = cross_entropy.detach()  # prio-buffer
         loss.backward()
         self.optim.step()
-        self._cnt += 1
+        self._iter += 1
         return {"loss": loss.item()}
diff --git a/tianshou/policy/modelfree/dqn.py b/tianshou/policy/modelfree/dqn.py
index 91cca61..a8f705b 100644
--- a/tianshou/policy/modelfree/dqn.py
+++ b/tianshou/policy/modelfree/dqn.py
@@ -54,7 +54,7 @@ class DQNPolicy(BasePolicy):
         self._n_step = estimation_step
         self._target = target_update_freq > 0
         self._freq = target_update_freq
-        self._cnt = 0
+        self._iter = 0
         if self._target:
             self.model_old = deepcopy(self.model)
             self.model_old.eval()
@@ -78,16 +78,15 @@ class DQNPolicy(BasePolicy):
         self, buffer: ReplayBuffer, indice: np.ndarray
     ) -> torch.Tensor:
         batch = buffer[indice]  # batch.obs_next: s_{t+n}
-        if self._target:
-            # target_Q = Q_old(s_, argmax(Q_new(s_, *)))
-            a = self(batch, input="obs_next").act
-            with torch.no_grad():
+        # target_Q = Q_old(s_, argmax(Q_new(s_, *)))
+        with torch.no_grad():
+            if self._target:
+                a = self(batch, input="obs_next").act
                 target_q = self(
                     batch, model="model_old", input="obs_next"
                 ).logits
-            target_q = target_q[np.arange(len(a)), a]
-        else:
-            with torch.no_grad():
+                target_q = target_q[np.arange(len(a)), a]
+            else:
                 target_q = self(batch, input="obs_next").logits.max(dim=1)[0]
         return target_q
 
@@ -162,7 +161,7 @@ class DQNPolicy(BasePolicy):
         return Batch(logits=q, act=act, state=h)
 
     def learn(self, batch: Batch, **kwargs: Any) -> Dict[str, float]:
-        if self._target and self._cnt % self._freq == 0:
+        if self._target and self._iter % self._freq == 0:
             self.sync_weight()
         self.optim.zero_grad()
         weight = batch.pop("weight", 1.0)
@@ -174,5 +173,5 @@ class DQNPolicy(BasePolicy):
         batch.weight = td  # prio-buffer
         loss.backward()
         self.optim.step()
-        self._cnt += 1
+        self._iter += 1
         return {"loss": loss.item()}
diff --git a/tianshou/policy/modelfree/ppo.py b/tianshou/policy/modelfree/ppo.py
index 5a04ec6..4cf9f90 100644
--- a/tianshou/policy/modelfree/ppo.py
+++ b/tianshou/policy/modelfree/ppo.py
@@ -68,8 +68,8 @@ class PPOPolicy(PGPolicy):
         super().__init__(None, optim, dist_fn, discount_factor, **kwargs)
         self._max_grad_norm = max_grad_norm
         self._eps_clip = eps_clip
-        self._w_vf = vf_coef
-        self._w_ent = ent_coef
+        self._weight_vf = vf_coef
+        self._weight_ent = ent_coef
         self._range = action_range
         self.actor = actor
         self.critic = critic
@@ -174,7 +174,8 @@ class PPOPolicy(PGPolicy):
                 vf_losses.append(vf_loss.item())
                 e_loss = dist.entropy().mean()
                 ent_losses.append(e_loss.item())
-                loss = clip_loss + self._w_vf * vf_loss - self._w_ent * e_loss
+                loss = clip_loss + self._weight_vf * vf_loss - \
+                    self._weight_ent * e_loss
                 losses.append(loss.item())
                 self.optim.zero_grad()
                 loss.backward()
diff --git a/tianshou/policy/modelfree/sac.py b/tianshou/policy/modelfree/sac.py
index 014fbe6..983df71 100644
--- a/tianshou/policy/modelfree/sac.py
+++ b/tianshou/policy/modelfree/sac.py
@@ -143,7 +143,6 @@ class SACPolicy(DDPGPolicy):
         with torch.no_grad():
             obs_next_result = self(batch, input='obs_next')
             a_ = obs_next_result.act
-            batch.act = to_torch_as(batch.act, a_)
             target_q = torch.min(
                 self.critic1_old(batch.obs_next, a_),
                 self.critic2_old(batch.obs_next, a_),
diff --git a/tianshou/trainer/__init__.py b/tianshou/trainer/__init__.py
index 36a8ed4..22fc1ee 100644
--- a/tianshou/trainer/__init__.py
+++ b/tianshou/trainer/__init__.py
@@ -1,10 +1,12 @@
 from tianshou.trainer.utils import test_episode, gather_info
 from tianshou.trainer.onpolicy import onpolicy_trainer
 from tianshou.trainer.offpolicy import offpolicy_trainer
+from tianshou.trainer.offline import offline_trainer
 
 __all__ = [
     "gather_info",
     "test_episode",
     "onpolicy_trainer",
     "offpolicy_trainer",
+    "offline_trainer",
 ]
diff --git a/tianshou/trainer/offline.py b/tianshou/trainer/offline.py
new file mode 100644
index 0000000..e693641
--- /dev/null
+++ b/tianshou/trainer/offline.py
@@ -0,0 +1,97 @@
+import time
+import tqdm
+from collections import defaultdict
+from torch.utils.tensorboard import SummaryWriter
+from typing import Dict, List, Union, Callable, Optional
+
+from tianshou.policy import BasePolicy
+from tianshou.utils import tqdm_config, MovAvg
+from tianshou.data import Collector, ReplayBuffer
+from tianshou.trainer import test_episode, gather_info
+
+
+def offline_trainer(
+    policy: BasePolicy,
+    buffer: ReplayBuffer,
+    test_collector: Collector,
+    max_epoch: int,
+    step_per_epoch: int,
+    episode_per_test: Union[int, List[int]],
+    batch_size: int,
+    test_fn: Optional[Callable[[int, Optional[int]], None]] = None,
+    stop_fn: Optional[Callable[[float], bool]] = None,
+    save_fn: Optional[Callable[[BasePolicy], None]] = None,
+    writer: Optional[SummaryWriter] = None,
+    log_interval: int = 1,
+    verbose: bool = True,
+) -> Dict[str, Union[float, str]]:
+    """A wrapper for offline trainer procedure.
+
+    The "step" in trainer means a policy network update.
+
+    :param policy: an instance of the :class:`~tianshou.policy.BasePolicy`
+        class.
+    :param test_collector: the collector used for testing.
+    :type test_collector: :class:`~tianshou.data.Collector`
+    :param int max_epoch: the maximum number of epochs for training. The
+        training process might be finished before reaching the ``max_epoch``.
+    :param int step_per_epoch: the number of policy network updates, so-called
+        gradient steps, per epoch.
+    :param episode_per_test: the number of episodes for one policy evaluation.
+    :param int batch_size: the batch size of sample data, which is going to
+        feed in the policy network.
+    :param function test_fn: a hook called at the beginning of testing in each
+        epoch. It can be used to perform custom additional operations, with the
+        signature ``f(num_epoch: int, step_idx: int) -> None``.
+    :param function save_fn: a hook called when the undiscounted average mean
+        reward in evaluation phase gets better, with the signature ``f(policy:
+        BasePolicy) -> None``.
+    :param function stop_fn: a function with signature ``f(mean_rewards: float)
+        -> bool``, receives the average undiscounted returns of the testing
+        result, returns a boolean which indicates whether reaching the goal.
+    :param torch.utils.tensorboard.SummaryWriter writer: a TensorBoard
+        SummaryWriter; if None is given, it will not write logs to TensorBoard.
+    :param int log_interval: the log interval of the writer.
+    :param bool verbose: whether to print the information.
+
+    :return: See :func:`~tianshou.trainer.gather_info`.
+    """
+    gradient_step = 0
+    best_epoch, best_reward, best_reward_std = -1, -1.0, 0.0
+    stat: Dict[str, MovAvg] = defaultdict(MovAvg)
+    start_time = time.time()
+    test_collector.reset_stat()
+
+    for epoch in range(1, 1 + max_epoch):
+        policy.train()
+        with tqdm.trange(
+            step_per_epoch, desc=f"Epoch #{epoch}", **tqdm_config
+        ) as t:
+            for i in t:
+                gradient_step += 1
+                losses = policy.update(batch_size, buffer)
+                data = {"gradient_step": str(gradient_step)}
+                for k in losses.keys():
+                    stat[k].add(losses[k])
+                    data[k] = f"{stat[k].get():.6f}"
+                    if writer and gradient_step % log_interval == 0:
+                        writer.add_scalar(
+                            "train/" + k, stat[k].get(),
+                            global_step=gradient_step)
+                t.set_postfix(**data)
+        # test
+        result = test_episode(policy, test_collector, test_fn, epoch,
+                              episode_per_test, writer, gradient_step)
+        if best_epoch == -1 or best_reward < result["rew"]:
+            best_reward, best_reward_std = result["rew"], result["rew_std"]
+            best_epoch = epoch
+            if save_fn:
+                save_fn(policy)
+        if verbose:
+            print(f"Epoch #{epoch}: test_reward: {result['rew']:.6f} ± "
+                  f"{result['rew_std']:.6f}, best_reward: {best_reward:.6f} ± "
+                  f"{best_reward_std:.6f} in #{best_epoch}")
+        if stop_fn and stop_fn(best_reward):
+            break
+    return gather_info(start_time, None, test_collector,
+                       best_reward, best_reward_std)
diff --git a/tianshou/trainer/offpolicy.py b/tianshou/trainer/offpolicy.py
index fb4b6f4..f34f5b2 100644
--- a/tianshou/trainer/offpolicy.py
+++ b/tianshou/trainer/offpolicy.py
@@ -1,5 +1,6 @@
 import time
 import tqdm
+from collections import defaultdict
 from torch.utils.tensorboard import SummaryWriter
 from typing import Dict, List, Union, Callable, Optional
 
@@ -38,10 +39,10 @@ def offpolicy_trainer(
     :type train_collector: :class:`~tianshou.data.Collector`
     :param test_collector: the collector used for testing.
     :type test_collector: :class:`~tianshou.data.Collector`
-    :param int max_epoch: the maximum of epochs for training. The training
-        process might be finished before reaching the ``max_epoch``.
-    :param int step_per_epoch: the number of step for updating policy network
-        in one epoch.
+    :param int max_epoch: the maximum number of epochs for training. The
+        training process might be finished before reaching the ``max_epoch``.
+    :param int step_per_epoch: the number of policy network updates, so-called
+        gradient steps, per epoch.
     :param int collect_per_step: the number of frames the collector would
         collect before the network update. In other words, collect some frames
         and do some policy network update.
@@ -52,19 +53,20 @@ def offpolicy_trainer(
         be updated after frames are collected, for example, set it to 256 means
         it updates policy 256 times once after ``collect_per_step`` frames are
         collected.
-    :param function train_fn: a function receives the current number of epoch
-        and step index, and performs some operations at the beginning of
-        training in this epoch.
-    :param function test_fn: a function receives the current number of epoch
-        and step index, and performs some operations at the beginning of
-        testing in this epoch.
-    :param function save_fn: a function for saving policy when the undiscounted
-        average mean reward in evaluation phase gets better.
-    :param function stop_fn: a function receives the average undiscounted
-        returns of the testing result, return a boolean which indicates whether
-        reaching the goal.
+    :param function train_fn: a hook called at the beginning of training in
+        each epoch. It can be used to perform custom additional operations,
+        with the signature ``f(num_epoch: int, step_idx: int) -> None``.
+    :param function test_fn: a hook called at the beginning of testing in each
+        epoch. It can be used to perform custom additional operations, with the
+        signature ``f(num_epoch: int, step_idx: int) -> None``.
+    :param function save_fn: a hook called when the undiscounted average mean
+        reward in evaluation phase gets better, with the signature ``f(policy:
+        BasePolicy) -> None``.
+    :param function stop_fn: a function with signature ``f(mean_rewards: float)
+        -> bool``, receives the average undiscounted returns of the testing
+        result, returns a boolean which indicates whether reaching the goal.
     :param torch.utils.tensorboard.SummaryWriter writer: a TensorBoard
-        SummaryWriter.
+        SummaryWriter; if None is given, it will not write logs to TensorBoard.
     :param int log_interval: the log interval of the writer.
     :param bool verbose: whether to print the information.
     :param bool test_in_train: whether to test in the training phase.
@@ -73,7 +75,7 @@ def offpolicy_trainer(
     """
     env_step, gradient_step = 0, 0
     best_epoch, best_reward, best_reward_std = -1, -1.0, 0.0
-    stat: Dict[str, MovAvg] = {}
+    stat: Dict[str, MovAvg] = defaultdict(MovAvg)
     start_time = time.time()
     train_collector.reset_stat()
     test_collector.reset_stat()
@@ -122,8 +124,6 @@ def offpolicy_trainer(
                     gradient_step += 1
                     losses = policy.update(batch_size, train_collector.buffer)
                     for k in losses.keys():
-                        if stat.get(k) is None:
-                            stat[k] = MovAvg()
                         stat[k].add(losses[k])
                         data[k] = f"{stat[k].get():.6f}"
                         if writer and gradient_step % log_interval == 0:
diff --git a/tianshou/trainer/onpolicy.py b/tianshou/trainer/onpolicy.py
index 5aff68b..f094ddd 100644
--- a/tianshou/trainer/onpolicy.py
+++ b/tianshou/trainer/onpolicy.py
@@ -1,5 +1,6 @@
 import time
 import tqdm
+from collections import defaultdict
 from torch.utils.tensorboard import SummaryWriter
 from typing import Dict, List, Union, Callable, Optional
 
@@ -38,10 +39,10 @@ def onpolicy_trainer(
     :type train_collector: :class:`~tianshou.data.Collector`
     :param test_collector: the collector used for testing.
     :type test_collector: :class:`~tianshou.data.Collector`
-    :param int max_epoch: the maximum of epochs for training. The training
-        process might be finished before reaching the ``max_epoch``.
-    :param int step_per_epoch: the number of step for updating policy network
-        in one epoch.
+    :param int max_epoch: the maximum number of epochs for training. The
+        training process might be finished before reaching the ``max_epoch``.
+    :param int step_per_epoch: the number of policy network updates, so-called
+        gradient steps, per epoch.
     :param int collect_per_step: the number of episodes the collector would
         collect before the network update. In other words, collect some
         episodes and do one policy network update.
@@ -52,19 +53,20 @@ def onpolicy_trainer(
     :type episode_per_test: int or list of ints
     :param int batch_size: the batch size of sample data, which is going to
         feed in the policy network.
-    :param function train_fn: a function receives the current number of epoch
-        and step index, and performs some operations at the beginning of
-        training in this poch.
-    :param function test_fn: a function receives the current number of epoch
-        and step index, and performs some operations at the beginning of
-        testing in this epoch.
-    :param function save_fn: a function for saving policy when the undiscounted
-        average mean reward in evaluation phase gets better.
-    :param function stop_fn: a function receives the average undiscounted
-        returns of the testing result, return a boolean which indicates whether
-        reaching the goal.
+    :param function train_fn: a hook called at the beginning of training in
+        each epoch. It can be used to perform custom additional operations,
+        with the signature ``f(num_epoch: int, step_idx: int) -> None``.
+    :param function test_fn: a hook called at the beginning of testing in each
+        epoch. It can be used to perform custom additional operations, with the
+        signature ``f(num_epoch: int, step_idx: int) -> None``.
+    :param function save_fn: a hook called when the undiscounted average mean
+        reward in evaluation phase gets better, with the signature ``f(policy:
+        BasePolicy) -> None``.
+    :param function stop_fn: a function with signature ``f(mean_rewards: float)
+        -> bool``, receives the average undiscounted returns of the testing
+        result, returns a boolean which indicates whether reaching the goal.
     :param torch.utils.tensorboard.SummaryWriter writer: a TensorBoard
-        SummaryWriter.
+        SummaryWriter; if None is given, it will not write logs to TensorBoard.
     :param int log_interval: the log interval of the writer.
     :param bool verbose: whether to print the information.
     :param bool test_in_train: whether to test in the training phase.
@@ -73,7 +75,7 @@ def onpolicy_trainer(
     """
     env_step, gradient_step = 0, 0
     best_epoch, best_reward, best_reward_std = -1, -1.0, 0.0
-    stat: Dict[str, MovAvg] = {}
+    stat: Dict[str, MovAvg] = defaultdict(MovAvg)
     start_time = time.time()
     train_collector.reset_stat()
     test_collector.reset_stat()
@@ -125,8 +127,6 @@ def onpolicy_trainer(
                     len(v) for v in losses.values() if isinstance(v, list)])
                 gradient_step += step
                 for k in losses.keys():
-                    if stat.get(k) is None:
-                        stat[k] = MovAvg()
                     stat[k].add(losses[k])
                     data[k] = f"{stat[k].get():.6f}"
                     if writer and gradient_step % log_interval == 0:
diff --git a/tianshou/trainer/utils.py b/tianshou/trainer/utils.py
index da9dea8..dfffd71 100644
--- a/tianshou/trainer/utils.py
+++ b/tianshou/trainer/utils.py
@@ -36,7 +36,7 @@ def test_episode(
 
 def gather_info(
     start_time: float,
-    train_c: Collector,
+    train_c: Optional[Collector],
     test_c: Collector,
     best_reward: float,
     best_reward_std: float,
@@ -59,15 +59,9 @@ def gather_info(
         * ``duration`` the total elapsed time.
     """
     duration = time.time() - start_time
-    model_time = duration - train_c.collect_time - test_c.collect_time
-    train_speed = train_c.collect_step / (duration - test_c.collect_time)
+    model_time = duration - test_c.collect_time
     test_speed = test_c.collect_step / test_c.collect_time
-    return {
-        "train_step": train_c.collect_step,
-        "train_episode": train_c.collect_episode,
-        "train_time/collector": f"{train_c.collect_time:.2f}s",
-        "train_time/model": f"{model_time:.2f}s",
-        "train_speed": f"{train_speed:.2f} step/s",
+    result: Dict[str, Union[float, str]] = {
         "test_step": test_c.collect_step,
         "test_episode": test_c.collect_episode,
         "test_time": f"{test_c.collect_time:.2f}s",
@@ -75,4 +69,16 @@ def gather_info(
         "best_reward": best_reward,
         "best_result": f"{best_reward:.2f} ± {best_reward_std:.2f}",
         "duration": f"{duration:.2f}s",
+        "train_time/model": f"{model_time:.2f}s",
     }
+    if train_c is not None:
+        model_time -= train_c.collect_time
+        train_speed = train_c.collect_step / (duration - test_c.collect_time)
+        result.update({
+            "train_step": train_c.collect_step,
+            "train_episode": train_c.collect_episode,
+            "train_time/collector": f"{train_c.collect_time:.2f}s",
+            "train_time/model": f"{model_time:.2f}s",
+            "train_speed": f"{train_speed:.2f} step/s",
+        })
+    return result