diff --git a/python/ray/tune/analysis/experiment_analysis.py b/python/ray/tune/analysis/experiment_analysis.py
index 5ed038aa7..12023a377 100644
--- a/python/ray/tune/analysis/experiment_analysis.py
+++ b/python/ray/tune/analysis/experiment_analysis.py
@@ -220,34 +220,35 @@ class ExperimentAnalysis(Analysis):
         Args:
             metric (str): Key for trial info to order on.
             mode (str): One of [min, max].
-            scope (str): One of [all, last, avg]. If `scope=last`, only look at
-                each trial's final step for `metric`, and compare across
-                trials based on `mode=[min,max]`. If `scope=avg`, consider the
-                simple average over all steps for `metric` and compare across
-                trials based on `mode=[min,max]`. If `scope=all`, find each
-                trial's min/max score for `metric` based on `mode`, and
-                compare trials based on `mode=[min,max]`.
+            scope (str): One of [all, last, avg, last-5-avg, last-10-avg].
+                If `scope=last`, only look at each trial's final step for
+                `metric`, and compare across trials based on `mode=[min,max]`.
+                If `scope=avg`, consider the simple average over all steps
+                for `metric` and compare across trials based on
+                `mode=[min,max]`. If `scope=last-5-avg` or `scope=last-10-avg`,
+                consider the simple average over the last 5 or 10 steps for
+                `metric` and compare across trials based on `mode=[min,max]`.
+                If `scope=all`, find each trial's min/max score for `metric`
+                based on `mode`, and compare trials based on `mode=[min,max]`.
         """
         if mode not in ["max", "min"]:
             raise ValueError(
                 "ExperimentAnalysis: attempting to get best trial for "
                 "metric {} for mode {} not in [\"max\", \"min\"]".format(
                     metric, mode))
-        if scope not in ["all", "last", "avg"]:
+        if scope not in ["all", "last", "avg", "last-5-avg", "last-10-avg"]:
             raise ValueError(
                 "ExperimentAnalysis: attempting to get best trial for "
-                "metric {} for scope {} not in [\"all\", \"last\", \"avg\"]".
-                format(metric, scope))
+                "metric {} for scope {} not in [\"all\", \"last\", \"avg\", "
+                "\"last-5-avg\", \"last-10-avg\"]".format(metric, scope))
         best_trial = None
         best_metric_score = None
         for trial in self.trials:
             if metric not in trial.metric_analysis:
                 continue
 
-            if scope == "last":
-                metric_score = trial.metric_analysis[metric]["last"]
-            elif scope == "avg":
-                metric_score = trial.metric_analysis[metric]["avg"]
+            if scope in ["last", "avg", "last-5-avg", "last-10-avg"]:
+                metric_score = trial.metric_analysis[metric][scope]
             else:
                 metric_score = trial.metric_analysis[metric][mode]
 
@@ -273,13 +274,16 @@ class ExperimentAnalysis(Analysis):
         Args:
             metric (str): Key for trial info to order on.
             mode (str): One of [min, max].
-            scope (str): One of [all, last, avg]. If `scope=last`, only look at
-                each trial's final step for `metric`, and compare across
-                trials based on `mode=[min,max]`. If `scope=avg`, consider the
-                simple average over all steps for `metric` and compare across
-                trials based on `mode=[min,max]`. If `scope=all`, find each
-                trial's min/max score for `metric` based on `mode`, and
-                compare trials based on `mode=[min,max]`.
+            scope (str): One of [all, last, avg, last-5-avg, last-10-avg].
+                If `scope=last`, only look at each trial's final step for
+                `metric`, and compare across trials based on `mode=[min,max]`.
+                If `scope=avg`, consider the simple average over all steps
+                for `metric` and compare across trials based on
+                `mode=[min,max]`. If `scope=last-5-avg` or `scope=last-10-avg`,
+                consider the simple average over the last 5 or 10 steps for
+                `metric` and compare across trials based on `mode=[min,max]`.
+                If `scope=all`, find each trial's min/max score for `metric`
+                based on `mode`, and compare trials based on `mode=[min,max]`.
         """
         best_trial = self.get_best_trial(metric, mode, scope)
         return best_trial.config if best_trial else None
@@ -292,13 +296,16 @@ class ExperimentAnalysis(Analysis):
         Args:
             metric (str): Key for trial info to order on.
             mode (str): One of [min, max].
-            scope (str): One of [all, last, avg]. If `scope=last`, only look at
-                each trial's final step for `metric`, and compare across
-                trials based on `mode=[min,max]`. If `scope=avg`, consider the
-                simple average over all steps for `metric` and compare across
-                trials based on `mode=[min,max]`. If `scope=all`, find each
-                trial's min/max score for `metric` based on `mode`, and
-                compare trials based on `mode=[min,max]`.
+            scope (str): One of [all, last, avg, last-5-avg, last-10-avg].
+                If `scope=last`, only look at each trial's final step for
+                `metric`, and compare across trials based on `mode=[min,max]`.
+                If `scope=avg`, consider the simple average over all steps
+                for `metric` and compare across trials based on
+                `mode=[min,max]`. If `scope=last-5-avg` or `scope=last-10-avg`,
+                consider the simple average over the last 5 or 10 steps for
+                `metric` and compare across trials based on `mode=[min,max]`.
+                If `scope=all`, find each trial's min/max score for `metric`
+                based on `mode`, and compare trials based on `mode=[min,max]`.
         """
         best_trial = self.get_best_trial(metric, mode, scope)
         return best_trial.logdir if best_trial else None
diff --git a/python/ray/tune/tests/test_experiment_analysis_mem.py b/python/ray/tune/tests/test_experiment_analysis_mem.py
index 319c97bab..4667c87aa 100644
--- a/python/ray/tune/tests/test_experiment_analysis_mem.py
+++ b/python/ray/tune/tests/test_experiment_analysis_mem.py
@@ -14,11 +14,11 @@ class ExperimentAnalysisInMemorySuite(unittest.TestCase):
     def setUp(self):
         class MockTrainable(Trainable):
             scores_dict = {
-                0: [5, 4, 0],
-                1: [4, 3, 1],
-                2: [2, 1, 8],
-                3: [9, 7, 6],
-                4: [7, 5, 3]
+                0: [5, 4, 4, 4, 4, 4, 4, 4, 0],
+                1: [4, 3, 3, 3, 3, 3, 3, 3, 1],
+                2: [2, 1, 1, 1, 1, 1, 1, 1, 8],
+                3: [9, 7, 7, 7, 7, 7, 7, 7, 6],
+                4: [7, 5, 5, 5, 5, 5, 5, 5, 3]
             }
 
             def _setup(self, config):
@@ -53,7 +53,7 @@ class ExperimentAnalysisInMemorySuite(unittest.TestCase):
             self.MockTrainable,
             name="analysis_exp",
             local_dir=self.test_dir,
-            stop={"training_iteration": 3},
+            stop={"training_iteration": len(scores[0])},
             num_samples=1,
             config={"id": grid_search(list(range(5)))})
 
@@ -67,12 +67,33 @@ class ExperimentAnalysisInMemorySuite(unittest.TestCase):
                                     "avg").metric_analysis["score"]["avg"]
         min_avg = ea.get_best_trial("score", "min",
                                     "avg").metric_analysis["score"]["avg"]
+        max_avg_5 = ea.get_best_trial(
+            "score", "max",
+            "last-5-avg").metric_analysis["score"]["last-5-avg"]
+        min_avg_5 = ea.get_best_trial(
+            "score", "min",
+            "last-5-avg").metric_analysis["score"]["last-5-avg"]
+        max_avg_10 = ea.get_best_trial(
+            "score", "max",
+            "last-10-avg").metric_analysis["score"]["last-10-avg"]
+        min_avg_10 = ea.get_best_trial(
+            "score", "min",
+            "last-10-avg").metric_analysis["score"]["last-10-avg"]
         self.assertEqual(max_all, max(scores_all))
         self.assertEqual(min_all, min(scores_all))
         self.assertEqual(max_last, max(scores_last))
+        self.assertNotEqual(max_last, max(scores_all))
+
         self.assertAlmostEqual(max_avg, max(np.mean(scores, axis=1)))
         self.assertAlmostEqual(min_avg, min(np.mean(scores, axis=1)))
-        self.assertNotEqual(max_last, max(scores_all))
+
+        self.assertAlmostEqual(max_avg_5, max(np.mean(scores[:, -5:], axis=1)))
+        self.assertAlmostEqual(min_avg_5, min(np.mean(scores[:, -5:], axis=1)))
+
+        self.assertAlmostEqual(max_avg_10, max(
+            np.mean(scores[:, -10:], axis=1)))
+        self.assertAlmostEqual(min_avg_10, min(
+            np.mean(scores[:, -10:], axis=1)))
 
 
 class AnalysisSuite(unittest.TestCase):
diff --git a/python/ray/tune/trial.py b/python/ray/tune/trial.py
index e0e352a57..ca273c155 100644
--- a/python/ray/tune/trial.py
+++ b/python/ray/tune/trial.py
@@ -1,4 +1,5 @@
 import ray.cloudpickle as cloudpickle
+from collections import deque
 import copy
 from datetime import datetime
 import logging
@@ -214,9 +215,14 @@ class Trial:
         self.last_result = {}
         self.last_update_time = -float("inf")
 
-        # stores in memory max/min/avg/last result for each metric by trial
+        # stores in memory max/min/avg/last-n-avg/last result for each
+        # metric by trial
         self.metric_analysis = {}
 
+        # keep a moving average over these last n steps
+        self.n_steps = [5, 10]
+        self.metric_n_steps = {}
+
         self.export_formats = export_formats
         self.status = Trial.PENDING
         self.start_time = None
@@ -470,6 +476,7 @@ class Trial:
         self.last_result = result
         self.last_update_time = time.time()
         self.result_logger.on_result(self.last_result)
+
         for metric, value in flatten_dict(result).items():
             if isinstance(value, Number):
                 if metric not in self.metric_analysis:
@@ -479,6 +486,13 @@ class Trial:
                         "avg": value,
                         "last": value
                     }
+                    self.metric_n_steps[metric] = {}
+                    for n in self.n_steps:
+                        key = "last-{:d}-avg".format(n)
+                        self.metric_analysis[metric][key] = value
+                        # Store n as string for correct restore.
+                        self.metric_n_steps[metric][str(n)] = deque(
+                            [value], maxlen=n)
                 else:
                     step = result["training_iteration"] or 1
                     self.metric_analysis[metric]["max"] = max(
@@ -490,6 +504,13 @@ class Trial:
                         (step - 1) * self.metric_analysis[metric]["avg"])
                     self.metric_analysis[metric]["last"] = value
 
+                    for n in self.n_steps:
+                        key = "last-{:d}-avg".format(n)
+                        self.metric_n_steps[metric][str(n)].append(value)
+                        self.metric_analysis[metric][key] = sum(
+                            self.metric_n_steps[metric][str(n)]) / len(
+                                self.metric_n_steps[metric][str(n)])
+
     def get_trainable_cls(self):
         return get_trainable_cls(self.trainable_name)