diff --git a/jumanji/environments/routing/connector/env.py b/jumanji/environments/routing/connector/env.py
index dae55c0fc..2aa71fe6c 100644
--- a/jumanji/environments/routing/connector/env.py
+++ b/jumanji/environments/routing/connector/env.py
@@ -70,9 +70,10 @@ class Connector(Environment[State, specs.MultiDiscreteArray, Observation]):
         - can take the values [0,1,2,3,4] which correspond to [No Op, Up, Right, Down, Left].
         - each value in the array corresponds to an agent's action.
 
-    - reward: jax array (float) of shape ():
-        - dense: reward is 1 for each successful connection on that step. Additionally,
-            each pair of points that have not connected receives a penalty reward of -0.03.
+    - reward: jax array (float) of shape (num_agents,):
+        - dense: for each agent the reward is 1 for each successful connection on that step.
+                Additionally, each pair of points that have not connected receives a
+                penalty reward of -0.03.
 
     - episode termination:
         - all agents either can't move (no available actions) or have connected to their target.
@@ -142,7 +143,7 @@ def reset(self, key: chex.PRNGKey) -> Tuple[State, TimeStep[Observation]]:
             step_count=state.step_count,
         )
         extras = self._get_extras(state)
-        timestep = restart(observation=observation, extras=extras)
+        timestep = restart(observation=observation, extras=extras, shape=(self.num_agents,))
         return state, timestep
 
     def step(self, state: State, action: chex.Array) -> Tuple[State, TimeStep[Observation]]:
@@ -171,19 +172,23 @@ def step(self, state: State, action: chex.Array) -> Tuple[State, TimeStep[Observ
             grid=grid, action_mask=action_mask, step_count=new_state.step_count
         )
 
-        done = jnp.all(jax.vmap(connected_or_blocked)(agents, action_mask))
+        done = jax.vmap(connected_or_blocked)(agents, action_mask)
+        discount = (1 - done).astype(float)
         extras = self._get_extras(new_state)
         timestep = jax.lax.cond(
-            done | (new_state.step_count >= self.time_limit),
+            jnp.all(done) | (new_state.step_count >= self.time_limit),
             lambda: termination(
                 reward=reward,
                 observation=observation,
                 extras=extras,
+                shape=(self.num_agents,),
             ),
             lambda: transition(
                 reward=reward,
                 observation=observation,
                 extras=extras,
+                discount=discount,
+                shape=(self.num_agents,),
             ),
         )
 
@@ -362,3 +367,19 @@ def action_spec(self) -> specs.MultiDiscreteArray:
             dtype=jnp.int32,
             name="action",
         )
+
+    @cached_property
+    def reward_spec(self) -> specs.Array:
+        """Returns: a reward per agent."""
+        return specs.Array(shape=(self.num_agents,), dtype=float, name="reward")
+
+    @cached_property
+    def discount_spec(self) -> specs.BoundedArray:
+        """Returns: discount per agent."""
+        return specs.BoundedArray(
+            shape=(self.num_agents,),
+            dtype=float,
+            minimum=0.0,
+            maximum=1.0,
+            name="discount",
+        )
diff --git a/jumanji/environments/routing/connector/env_test.py b/jumanji/environments/routing/connector/env_test.py
index 5abe0dbbe..9e31bf364 100644
--- a/jumanji/environments/routing/connector/env_test.py
+++ b/jumanji/environments/routing/connector/env_test.py
@@ -57,8 +57,8 @@ def test_connector__reset(connector: Connector, key: jax.random.PRNGKey) -> None
     assert all(is_head_on_grid(state.agents, state.grid))
     assert all(is_target_on_grid(state.agents, state.grid))
 
-    assert timestep.discount == 1.0
-    assert timestep.reward == 0.0
+    assert jnp.allclose(timestep.discount, jnp.ones((connector.num_agents,)))
+    assert jnp.allclose(timestep.reward, jnp.zeros((connector.num_agents,)))
     assert timestep.step_type == StepType.FIRST
 
 
@@ -94,7 +94,7 @@ def test_connector__step_connected(
     chex.assert_trees_all_equal(real_state2, state2)
 
     assert timestep.step_type == StepType.LAST
-    assert jnp.array_equal(timestep.discount, jnp.asarray(0))
+    assert jnp.array_equal(timestep.discount, jnp.zeros(connector.num_agents))
     reward = connector._reward_fn(real_state1, action2, real_state2)
     assert jnp.array_equal(timestep.reward, reward)
 
@@ -146,7 +146,7 @@ def test_connector__step_blocked(
 
     assert jnp.array_equal(state.grid, expected_grid)
     assert timestep.step_type == StepType.LAST
-    assert jnp.array_equal(timestep.discount, jnp.asarray(0))
+    assert jnp.array_equal(timestep.discount, jnp.zeros(connector.num_agents))
 
     assert all(is_head_on_grid(state.agents, state.grid))
     assert all(is_target_on_grid(state.agents, state.grid))
@@ -165,12 +165,12 @@ def test_connector__step_horizon(connector: Connector, state: State) -> None:
         state, timestep = step_fn(state, actions)
 
         assert timestep.step_type != StepType.LAST
-        assert jnp.array_equal(timestep.discount, jnp.asarray(1))
+        assert jnp.array_equal(timestep.discount, jnp.ones(connector.num_agents))
 
     # step 5
     state, timestep = step_fn(state, actions)
     assert timestep.step_type == StepType.LAST
-    assert jnp.array_equal(timestep.discount, jnp.asarray(0))
+    assert jnp.array_equal(timestep.discount, jnp.zeros(connector.num_agents))
 
 
 def test_connector__step_agents_collision(
diff --git a/jumanji/environments/routing/connector/reward.py b/jumanji/environments/routing/connector/reward.py
index f29dbf2d5..8d176f74c 100644
--- a/jumanji/environments/routing/connector/reward.py
+++ b/jumanji/environments/routing/connector/reward.py
@@ -71,4 +71,4 @@ def __call__(
             ~state.agents.connected & next_state.agents.connected, float
         )
         timestep_rewards = self.timestep_reward * jnp.asarray(~state.agents.connected, float)
-        return jnp.sum(connected_rewards + timestep_rewards)
+        return connected_rewards + timestep_rewards
diff --git a/jumanji/environments/routing/connector/reward_test.py b/jumanji/environments/routing/connector/reward_test.py
index 226a42ed1..205b61689 100644
--- a/jumanji/environments/routing/connector/reward_test.py
+++ b/jumanji/environments/routing/connector/reward_test.py
@@ -35,26 +35,27 @@ def test_dense_reward(
 
     # Reward of moving between the same states should be 0.
     reward = dense_reward_fn(state, jnp.array([0, 0, 0]), state)
-    chex.assert_rank(reward, 0)
-    assert jnp.isclose(reward, jnp.asarray(timestep_reward * 3))
+    chex.assert_rank(reward, 1)
+    assert jnp.allclose(reward, jnp.array([timestep_reward] * 3))
 
     # Reward for no agents finished to 2 agents finished.
     reward = dense_reward_fn(state, action1, state1)
-    chex.assert_rank(reward, 0)
-    expected_reward = connected_reward * 2 + timestep_reward * 3
-    assert jnp.isclose(reward, expected_reward)
+    chex.assert_rank(reward, 1)
+    expected_reward = jnp.array([connected_reward, 0, connected_reward]) + timestep_reward
+    assert jnp.allclose(reward, expected_reward)
 
     # Reward for some agents finished to all agents finished.
     reward = dense_reward_fn(state1, action2, state2)
-    chex.assert_rank(reward, 0)
-    assert jnp.isclose(reward, jnp.array(connected_reward + timestep_reward))
+    chex.assert_rank(reward, 1)
+    expected_reward = jnp.array([0, connected_reward + timestep_reward, 0])
+    assert jnp.allclose(reward, expected_reward)
 
     # Reward for none finished to all finished
     reward = dense_reward_fn(state, action1, state2)
-    chex.assert_rank(reward, 0)
-    assert jnp.isclose(reward, jnp.array((connected_reward + timestep_reward) * 3))
+    chex.assert_rank(reward, 1)
+    assert jnp.allclose(reward, jnp.array([connected_reward + timestep_reward] * 3))
 
     # Reward of all finished to all finished.
     reward = dense_reward_fn(state2, jnp.zeros(3), state2)
-    chex.assert_rank(reward, 0)
-    assert jnp.isclose(reward, jnp.zeros(1))
+    chex.assert_rank(reward, 1)
+    assert jnp.allclose(reward, jnp.zeros(1))
diff --git a/jumanji/training/setup_train.py b/jumanji/training/setup_train.py
index d8612bed9..7daa0201d 100644
--- a/jumanji/training/setup_train.py
+++ b/jumanji/training/setup_train.py
@@ -90,7 +90,7 @@ def setup_logger(cfg: DictConfig) -> Logger:
 
 def _make_raw_env(cfg: DictConfig) -> Environment:
     env = jumanji.make(cfg.env.registered_version)
-    if cfg.env.name in {"lbf"}:
+    if cfg.env.name in {"lbf", "connector"}:
         # Convert a multi-agent environment to a single-agent environment
         env = MultiToSingleWrapper(env)
     return env
diff --git a/jumanji/types.py b/jumanji/types.py
index ecbb069a7..249851846 100644
--- a/jumanji/types.py
+++ b/jumanji/types.py
@@ -95,6 +95,7 @@ def restart(
     observation: Observation,
     extras: Optional[Dict] = None,
     shape: Union[int, Sequence[int]] = (),
+    dtype: Union[jnp.dtype, type] = float,
 ) -> TimeStep:
     """Returns a `TimeStep` with `step_type` set to `StepType.FIRST`.
 
@@ -107,6 +108,8 @@ def restart(
         shape: optional parameter to specify the shape of the rewards and discounts.
             Allows multi-agent environment compatibility. Defaults to () for
             scalar reward and discount.
+        dtype: Optional parameter to specify the data type of the rewards and discounts.
+            Defaults to `float`.
 
     Returns:
         TimeStep identified as a reset.
@@ -114,8 +117,8 @@ def restart(
     extras = extras or {}
     return TimeStep(
         step_type=StepType.FIRST,
-        reward=jnp.zeros(shape, dtype=float),
-        discount=jnp.ones(shape, dtype=float),
+        reward=jnp.zeros(shape, dtype=dtype),
+        discount=jnp.ones(shape, dtype=dtype),
         observation=observation,
         extras=extras,
     )
@@ -127,6 +130,7 @@ def transition(
     discount: Optional[Array] = None,
     extras: Optional[Dict] = None,
     shape: Union[int, Sequence[int]] = (),
+    dtype: Union[jnp.dtype, type] = float,
 ) -> TimeStep:
     """Returns a `TimeStep` with `step_type` set to `StepType.MID`.
 
@@ -141,11 +145,13 @@ def transition(
         shape: optional parameter to specify the shape of the rewards and discounts.
             Allows multi-agent environment compatibility. Defaults to () for
             scalar reward and discount.
+        dtype: Optional parameter to specify the data type of the discounts. Defaults
+            to `float`.
 
     Returns:
         TimeStep identified as a transition.
     """
-    discount = discount if discount is not None else jnp.ones(shape, dtype=float)
+    discount = discount if discount is not None else jnp.ones(shape, dtype=dtype)
     extras = extras or {}
     return TimeStep(
         step_type=StepType.MID,
@@ -161,6 +167,7 @@ def termination(
     observation: Observation,
     extras: Optional[Dict] = None,
     shape: Union[int, Sequence[int]] = (),
+    dtype: Union[jnp.dtype, type] = float,
 ) -> TimeStep:
     """Returns a `TimeStep` with `step_type` set to `StepType.LAST`.
 
@@ -174,6 +181,8 @@ def termination(
         shape: optional parameter to specify the shape of the rewards and discounts.
             Allows multi-agent environment compatibility. Defaults to () for
             scalar reward and discount.
+        dtype: Optional parameter to specify the data type of the discounts. Defaults
+            to `float`.
 
     Returns:
         TimeStep identified as the termination of an episode.
@@ -182,7 +191,7 @@ def termination(
     return TimeStep(
         step_type=StepType.LAST,
         reward=reward,
-        discount=jnp.zeros(shape, dtype=float),
+        discount=jnp.zeros(shape, dtype=dtype),
         observation=observation,
         extras=extras,
     )
@@ -194,6 +203,7 @@ def truncation(
     discount: Optional[Array] = None,
     extras: Optional[Dict] = None,
     shape: Union[int, Sequence[int]] = (),
+    dtype: Union[jnp.dtype, type] = float,
 ) -> TimeStep:
     """Returns a `TimeStep` with `step_type` set to `StepType.LAST`.
 
@@ -208,10 +218,13 @@ def truncation(
         shape: optional parameter to specify the shape of the rewards and discounts.
             Allows multi-agent environment compatibility. Defaults to () for
             scalar reward and discount.
+        dtype: Optional parameter to specify the data type of the discounts. Defaults
+            to `float`.
+
     Returns:
         TimeStep identified as the truncation of an episode.
     """
-    discount = discount if discount is not None else jnp.ones(shape, dtype=float)
+    discount = discount if discount is not None else jnp.ones(shape, dtype=dtype)
     extras = extras or {}
     return TimeStep(
         step_type=StepType.LAST,