diff --git a/tianshou/data/collector.py b/tianshou/data/collector.py
index 213b49d..592f091 100644
--- a/tianshou/data/collector.py
+++ b/tianshou/data/collector.py
@@ -226,6 +226,7 @@ class Collector(object):
                     ]
                 except TypeError:  # envpool's action space is not for per-env
                     act_sample = [self._action_space.sample() for _ in ready_env_ids]
+                act_sample = self.policy.map_action_inverse(act_sample)  # type: ignore
                 self.data.update(act=act_sample)
             else:
                 if no_grad:
@@ -451,6 +452,7 @@ class AsyncCollector(Collector):
                     ]
                 except TypeError:  # envpool's action space is not for per-env
                     act_sample = [self._action_space.sample() for _ in ready_env_ids]
+                act_sample = self.policy.map_action_inverse(act_sample)  # type: ignore
                 self.data.update(act=act_sample)
             else:
                 if no_grad:
diff --git a/tianshou/policy/base.py b/tianshou/policy/base.py
index 3572e83..fd055ab 100644
--- a/tianshou/policy/base.py
+++ b/tianshou/policy/base.py
@@ -1,5 +1,5 @@
 from abc import ABC, abstractmethod
-from typing import Any, Callable, Dict, Optional, Tuple, Union
+from typing import Any, Callable, Dict, List, Optional, Tuple, Union
 
 import gym
 import numpy as np
@@ -178,6 +178,33 @@ class BasePolicy(ABC, nn.Module):
                 act = low + (high - low) * (act + 1.0) / 2.0  # type: ignore
         return act
 
+    def map_action_inverse(
+        self, act: Union[Batch, List, np.ndarray]
+    ) -> Union[Batch, List, np.ndarray]:
+        """Inverse operation to :meth:`~tianshou.policy.BasePolicy.map_action`.
+
+        This function is called in :meth:`~tianshou.data.Collector.collect` for
+        random initial steps. It scales [action_space.low, action_space.high] to
+        the value ranges of policy.forward.
+
+        :param act: a data batch, list or numpy.ndarray which is the action taken
+            by gym.spaces.Box.sample().
+
+        :return: action remapped.
+        """
+        if isinstance(self.action_space, gym.spaces.Box):
+            act = to_numpy(act)
+            if isinstance(act, np.ndarray):
+                if self.action_scaling:
+                    low, high = self.action_space.low, self.action_space.high
+                    scale = high - low
+                    eps = np.finfo(np.float32).eps.item()
+                    scale[scale < eps] += eps
+                    act = (act - low) * 2.0 / scale - 1.0
+                if self.action_bound_method == "tanh":
+                    act = (np.log(1.0 + act) - np.log(1.0 - act)) / 2.0  # type: ignore
+        return act
+
     def process_fn(
         self, batch: Batch, buffer: ReplayBuffer, indices: np.ndarray
     ) -> Batch: