diff --git a/.github/workflows/regression_tests_docker.yml b/.github/workflows/regression_tests_docker.yml
index 0cf5a868b0..ca4aa1d749 100644
--- a/.github/workflows/regression_tests_docker.yml
+++ b/.github/workflows/regression_tests_docker.yml
@@ -1,6 +1,9 @@
 name: Run Regression Tests on Docker
 
 on:
+  push:
+    tags:
+      - docker
   workflow_dispatch:
   # run every day at 5:15am
   schedule:
diff --git a/test/pytest/test_torch_export.py b/test/pytest/test_torch_export.py
index dbd16fd3df..005b059a5b 100644
--- a/test/pytest/test_torch_export.py
+++ b/test/pytest/test_torch_export.py
@@ -49,6 +49,10 @@ def custom_working_directory(tmp_path):
     os.chdir(tmp_path)
 
 
+@pytest.mark.skipif(
+    os.environ.get("TS_RUN_IN_DOCKER", False),
+    reason="Test to be run outside docker",
+)
 @pytest.mark.skipif(PT_230_AVAILABLE == False, reason="torch version is < 2.3.0")
 def test_torch_export_aot_compile(custom_working_directory):
     # Get the path to the custom working directory
@@ -90,6 +94,10 @@ def test_torch_export_aot_compile(custom_working_directory):
     assert labels == EXPECTED_RESULTS
 
 
+@pytest.mark.skipif(
+    os.environ.get("TS_RUN_IN_DOCKER", False),
+    reason="Test to be run outside docker",
+)
 @pytest.mark.skipif(PT_230_AVAILABLE == False, reason="torch version is < 2.3.0")
 def test_torch_export_aot_compile_dynamic_batching(custom_working_directory):
     # Get the path to the custom working directory