diff --git a/python/ray/rllib/optimizers/async_replay_optimizer.py b/python/ray/rllib/optimizers/async_replay_optimizer.py
index bacec3675..70779f9e9 100644
--- a/python/ray/rllib/optimizers/async_replay_optimizer.py
+++ b/python/ray/rllib/optimizers/async_replay_optimizer.py
@@ -203,11 +203,12 @@ class AsyncReplayOptimizer(PolicyOptimizer):
         self.timers = {
             k: TimerStat()
             for k in [
-                "put_weights", "get_samples", "enqueue", "sample_processing",
+                "put_weights", "get_samples", "sample_processing",
                 "replay_processing", "update_priorities", "train", "sample"
             ]
         }
         self.num_weight_syncs = 0
+        self.num_samples_dropped = 0
         self.learning_started = False
 
         # Number of worker steps since the last weight update
@@ -283,9 +284,11 @@ class AsyncReplayOptimizer(PolicyOptimizer):
         with self.timers["replay_processing"]:
             for ra, replay in self.replay_tasks.completed():
                 self.replay_tasks.add(ra, ra.replay.remote())
-                with self.timers["get_samples"]:
-                    samples = ray.get(replay)
-                with self.timers["enqueue"]:
+                if self.learner.inqueue.full():
+                    self.num_samples_dropped += 1
+                else:
+                    with self.timers["get_samples"]:
+                        samples = ray.get(replay)
                     self.learner.inqueue.put((ra, samples))
 
         with self.timers["update_priorities"]:
@@ -311,6 +314,7 @@ class AsyncReplayOptimizer(PolicyOptimizer):
                                        3),
             "train_throughput": round(self.timers["train"].mean_throughput, 3),
             "num_weight_syncs": self.num_weight_syncs,
+            "num_samples_dropped": self.num_samples_dropped,
             "learner_queue": self.learner.learner_queue_size.stats(),
             "replay_shard_0": replay_stats,
         }