Fix action_name usage in XLAProfiler (#15886)

* Fix `action_name` usage in `XLAProfiler`
* add changelog
* Update src/pytorch_ligh
* Update xla.py

Co-authored-by: awaelchli <aedu.waelchli@gmail.com>
Co-authored-by: Jirka Borovec <6035284+Borda@users.noreply.github.com>

src/pytorch_lightning/CHANGELOG.md

@@ -86,6 +86,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Enhanced `reduce_boolean_decision` to accommodate `any`-analogous semantics expected by the `EarlyStopping` callback ([#15253](https://github.com/Lightning-AI/lightning/pull/15253))
 
 
+- Fixed the `XLAProfiler` not recording anything due to mismatching of action names ([#15885](https://github.com/Lightning-AI/lightning/pull/15885))
+
+
 ## [1.8.4] - 2022-12-08
 
 ### Changed

src/pytorch_lightning/profilers/xla.py

@@ -50,12 +50,14 @@ def __init__(self, port: int = 9012) -> None:
     def start(self, action_name: str) -> None:
         import torch_xla.debug.profiler as xp
 
-        if action_name in self.RECORD_FUNCTIONS:
+        # The action name is formatted as '[TYPE]{class name}.{hook name}'
+        # Example: [LightningModule]BoringModel.training_step
+        if action_name.split(".")[-1] in self.RECORD_FUNCTIONS:
             if not self._start_trace:
                 self.server = xp.start_server(self.port)
                 self._start_trace = True
 
-            if action_name in self.STEP_FUNCTIONS:
+            if action_name.split(".")[-1] in self.STEP_FUNCTIONS:
                 step = self._get_step_num(action_name)
                 recording = xp.StepTrace(action_name, step_num=step)
             else: