Push running checkpoint to remote

Fix iterative#6182

dvc/repo/experiments/executor/base.py

@@ -18,6 +18,7 @@
 
 from dvc.exceptions import DvcException
 from dvc.path_info import PathInfo
+from dvc.repo import Repo
 from dvc.repo.experiments.base import (
     EXEC_BASELINE,
     EXEC_BRANCH,
@@ -331,6 +332,7 @@ def filter_pipeline(stages):
 
             checkpoint_func = partial(
                 cls.checkpoint_callback,
+                dvc,
                 dvc.scm,
                 name,
                 repro_force or checkpoint_reset,
@@ -393,7 +395,6 @@ def _repro_dvc(
         git_url: Optional[str] = None,
         **kwargs,
     ):
-        from dvc.repo import Repo
         from dvc.utils.serialize import modify_yaml
 
         dvc = Repo(dvc_dir)
@@ -453,6 +454,7 @@ def _repro_args(cls, dvc):
     @classmethod
     def checkpoint_callback(
         cls,
+        dvc: "Repo",
         scm: "Git",
         name: Optional[str],
         force: bool,
@@ -464,6 +466,23 @@ def checkpoint_callback(
             exp_rev = cls.commit(
                 scm, exp_hash, exp_name=name, force=force, checkpoint=True
             )
+
+            git_remote = os.environ.get("DVC_EXP_AUTO_PUSH", None)
+            if git_remote:
+                from dvc.repo.experiments.push import push
+
+                branch = dvc.experiments.get_branch_by_rev(
+                    exp_rev, allow_multiple=None
+                )
+                branch_name = ExpRefInfo.from_ref(branch).name
+                push(
+                    dvc,
+                    git_remote,
+                    branch_name,
+                    push_cache=True,
+                    run_cache=True,
+                )
+                logger.info({"pushed": branch_name})
             logger.info("Checkpoint experiment iteration '%s'.", exp_rev[:7])
         except UnchangedExperimentError:
             pass