Added first test that shows mentioned deficites

tests/tests_pytorch/test_cli.py

@@ -597,6 +597,44 @@ def add_arguments_to_parser(self, parser):
     assert cli.model.num_classes == 5
 
 
+def test_lightning_cli_link_arguments_init():
+    # Will not work without init_args ("--data.init_args.batch_size=12")
+    class MyLightningCLI(LightningCLI):
+        def add_arguments_to_parser(self, parser):
+            parser.link_arguments("data.batch_size", "model.init_args.batch_size")
+
+    cli_args = [
+        "--data=tests_pytorch.test_cli.BoringDataModuleBatchSizeAndClasses",
+        "--model=tests_pytorch.test_cli.BoringModelRequiredClasses",
+        "--data.init_args.batch_size=12",
+        "--model.init_args.num_classes=5",
+    ]
+
+    with mock.patch("sys.argv", ["any.py"] + cli_args):
+        cli = MyLightningCLI(run=False)
+
+    assert cli.datamodule.batch_size == 12
+
+    # Will work without init_args ("--data.batch_size=12")
+    class MyLightningCLI(LightningCLI):
+        def add_arguments_to_parser(self, parser):
+            pass
+
+    cli_args = [
+        "--data=tests_pytorch.test_cli.BoringDataModuleBatchSizeAndClasses",
+        "--model=tests_pytorch.test_cli.BoringModelRequiredClasses",
+        "--data.batch_size=12",
+        "--model.num_classes=12",
+    ]
+
+    with mock.patch("sys.argv", ["any.py"] + cli_args):
+        cli = MyLightningCLI(run=False)
+
+    print(cli.config)
+
+    assert cli.datamodule.batch_size == 12
+
+
 class EarlyExitTestModel(BoringModel):
     def on_fit_start(self):
         raise MisconfigurationException("Error on fit start")