diff --git a/python/ray/tune/examples/mnist_pytorch.py b/python/ray/tune/examples/mnist_pytorch.py
index b6858cea2..f05db73e5 100644
--- a/python/ray/tune/examples/mnist_pytorch.py
+++ b/python/ray/tune/examples/mnist_pytorch.py
@@ -117,6 +117,8 @@ if __name__ == "__main__":
     args = parser.parse_args()
     if args.ray_address:
         ray.init(address=args.ray_address)
+    else:
+        ray.init(num_cpus=2 if args.smoke_test else None)
     sched = AsyncHyperBandScheduler(
         time_attr="training_iteration", metric="mean_accuracy")
     analysis = tune.run(
diff --git a/python/ray/tune/examples/mnist_pytorch_trainable.py b/python/ray/tune/examples/mnist_pytorch_trainable.py
index f006848f0..43f51cc7b 100644
--- a/python/ray/tune/examples/mnist_pytorch_trainable.py
+++ b/python/ray/tune/examples/mnist_pytorch_trainable.py
@@ -64,7 +64,7 @@ class TrainMNIST(tune.Trainable):
 
 if __name__ == "__main__":
     args = parser.parse_args()
-    ray.init(address=args.ray_address)
+    ray.init(address=args.ray_address, num_cpus=6 if args.smoke_test else None)
     sched = ASHAScheduler(metric="mean_accuracy")
     analysis = tune.run(
         TrainMNIST,
diff --git a/python/ray/tune/examples/tune_mnist_keras.py b/python/ray/tune/examples/tune_mnist_keras.py
index c2ac39486..1d043c74f 100644
--- a/python/ray/tune/examples/tune_mnist_keras.py
+++ b/python/ray/tune/examples/tune_mnist_keras.py
@@ -48,7 +48,7 @@ if __name__ == "__main__":
     from ray.tune.schedulers import AsyncHyperBandScheduler
     mnist.load_data()  # we do this on the driver because it's not threadsafe
 
-    ray.init()
+    ray.init(num_cpus=2 if args.smoke_test else None)
     sched = AsyncHyperBandScheduler(
         time_attr="training_iteration",
         metric="mean_accuracy",
diff --git a/python/ray/tune/schedulers/pbt.py b/python/ray/tune/schedulers/pbt.py
index 344db3b2b..d868b8289 100644
--- a/python/ray/tune/schedulers/pbt.py
+++ b/python/ray/tune/schedulers/pbt.py
@@ -179,9 +179,9 @@ class PopulationBasedTraining(FIFOScheduler):
                  custom_explore_fn=None,
                  log_config=True):
         for value in hyperparam_mutations.values():
-            if not (isinstance(value, list) or callable(value)):
+            if not (isinstance(value, (list, dict)) or callable(value)):
                 raise TypeError("`hyperparam_mutation` values must be either "
-                                "a List or callable.")
+                                "a List, Dict, or callable.")
 
         if not hyperparam_mutations and not custom_explore_fn:
             raise TuneError(
diff --git a/python/ray/tune/tests/test_trial_scheduler.py b/python/ray/tune/tests/test_trial_scheduler.py
index b8c12cbfb..f8e102220 100644
--- a/python/ray/tune/tests/test_trial_scheduler.py
+++ b/python/ray/tune/tests/test_trial_scheduler.py
@@ -711,28 +711,31 @@ class PopulationBasedTestingSuite(unittest.TestCase):
                    explore=None,
                    perturbation_interval=10,
                    log_config=False,
+                   hyperparams=None,
+                   hyperparam_mutations=None,
                    step_once=True):
+        hyperparam_mutations = hyperparam_mutations or {
+            "float_factor": lambda: 100.0,
+            "int_factor": lambda: 10,
+            "id_factor": [100]
+        }
         pbt = PopulationBasedTraining(
             time_attr="training_iteration",
             perturbation_interval=perturbation_interval,
             resample_probability=resample_prob,
             quantile_fraction=0.25,
-            hyperparam_mutations={
-                "id_factor": [100],
-                "float_factor": lambda: 100.0,
-                "int_factor": lambda: 10,
-            },
+            hyperparam_mutations=hyperparam_mutations,
             custom_explore_fn=explore,
             log_config=log_config)
         runner = _MockTrialRunner(pbt)
         for i in range(5):
-            trial = _MockTrial(
-                i, {
-                    "id_factor": i,
-                    "float_factor": 2.0,
-                    "const_factor": 3,
-                    "int_factor": 10
-                })
+            trial_hyperparams = hyperparams or {
+                "float_factor": 2.0,
+                "const_factor": 3,
+                "int_factor": 10,
+                "id_factor": i
+            }
+            trial = _MockTrial(i, trial_hyperparams)
             runner.add_trial(trial)
             trial.status = Trial.RUNNING
             if step_once:
@@ -958,6 +961,37 @@ class PopulationBasedTestingSuite(unittest.TestCase):
         # Expect call count to be 100 because we call explore 100 times
         self.assertEqual(custom_explore_fn.call_count, 100)
 
+    def testDictPerturbation(self):
+        pbt, runner = self.basicSetup(
+            resample_prob=1.0,
+            hyperparams={
+                "float_factor": 2.0,
+                "nest": {
+                    "nest_float": 3.0
+                },
+                "int_factor": 10,
+                "const_factor": 3
+            },
+            hyperparam_mutations={
+                "float_factor": lambda: 100.0,
+                "nest": {
+                    "nest_float": lambda: 101.0
+                },
+                "int_factor": lambda: 10,
+            })
+        trials = runner.get_trials()
+        self.assertEqual(
+            pbt.on_trial_result(runner, trials[0], result(20, -100)),
+            TrialScheduler.CONTINUE)
+        self.assertIn(trials[0].restored_checkpoint, ["trial_3", "trial_4"])
+        self.assertEqual(trials[0].config["float_factor"], 100.0)
+        self.assertIsInstance(trials[0].config["float_factor"], float)
+        self.assertEqual(trials[0].config["int_factor"], 10)
+        self.assertIsInstance(trials[0].config["int_factor"], int)
+        self.assertEqual(trials[0].config["const_factor"], 3)
+        self.assertEqual(trials[0].config["nest"]["nest_float"], 101.0)
+        self.assertIsInstance(trials[0].config["nest"]["nest_float"], float)
+
     def testYieldsTimeToOtherTrials(self):
         pbt, runner = self.basicSetup()
         trials = runner.get_trials()