[doc] Fix closure in manual optimization (#6374)

* Fix manual optimization docs

* Fix typo. Thanks @import-antigravity

Author: akihironitta

docs/source/common/optimizers.rst

@@ -40,10 +40,9 @@ to manually manage the optimization process. To do so, do the following:
             loss = self.compute_loss(batch)
             self.manual_backward(loss)
 
-
 .. note:: This is only recommended for experts who need ultimate flexibility. Lightning will handle only precision and accelerators logic. The users are left with ``optimizer.zero_grad()``, gradient accumulation, model toggling, etc..
 
-.. warning:: Before 1.2, ``optimzer.step`` was calling ``optimizer.zero_grad()`` internally. From 1.2, it is left to the users expertize.
+.. warning:: Before 1.2, ``optimzer.step`` was calling ``optimizer.zero_grad()`` internally. From 1.2, it is left to the users expertise.
 
 .. tip:: To perform ``accumulate_grad_batches`` with one optimizer, you can do as such.
 
@@ -65,8 +64,7 @@ to manually manage the optimization process. To do so, do the following:
             opt.step()
             opt.zero_grad()
 
-
-.. tip:: It is a good practice to provide the optimizer with a ``closure`` function that performs a ``forward`` and ``backward`` pass of your model. It is optional for most optimizers, but makes your code compatible if you switch to an optimizer which requires a closure. See also `the PyTorch docs <https://pytorch.org/docs/stable/optim.html#optimizer-step-closure>`_.
+.. tip:: It is a good practice to provide the optimizer with a ``closure`` function that performs a ``forward``, ``zero_grad`` and ``backward`` of your model. It is optional for most optimizers, but makes your code compatible if you switch to an optimizer which requires a closure. See also `the PyTorch docs <https://pytorch.org/docs/stable/optim.html#optimizer-step-closure>`_.
 
 Here is the same example as above using a ``closure``.
 
@@ -78,20 +76,20 @@ Here is the same example as above using a ``closure``.
     def training_step(self, batch, batch_idx):
         opt = self.optimizers()
 
-        def forward_and_backward():
+        def closure():
+            # Only zero_grad on the first batch to accumulate gradients
+            is_first_batch_to_accumulate = batch_idx % 2 == 0
+            if is_first_batch_to_accumulate:
+                opt.zero_grad()
+
             loss = self.compute_loss(batch)
             self.manual_backward(loss)
+            return loss
 
-        opt.step(closure=forward_and_backward)
-
-        # accumulate gradient batches
-        if batch_idx % 2 == 0:
-            opt.zero_grad()
-
+        opt.step(closure=closure)
 
 .. tip:: Be careful where you call ``zero_grad`` or your model won't converge. It is good pratice to call ``zero_grad`` before ``manual_backward``.
 
-
 .. testcode:: python
 
     import torch
@@ -174,10 +172,8 @@ Setting ``sync_grad`` to ``False`` will block this synchronization and improve y
 
 Here is an example for advanced use-case.
 
-
 .. testcode:: python
 
-
     # Scenario for a GAN with gradient accumulation every 2 batches and optimized for multiple gpus.
 
     class SimpleGAN(LightningModule):