diff --git a/adaptive/runner.py b/adaptive/runner.py
index 9a8a9b1a5..73fd9ed94 100644
--- a/adaptive/runner.py
+++ b/adaptive/runner.py
@@ -1,7 +1,9 @@
 import abc
 import asyncio
 import concurrent.futures as concurrent
+import functools
 import inspect
+import itertools
 import pickle
 import sys
 import time
@@ -91,14 +93,14 @@ class BaseRunner(metaclass=abc.ABCMeta):
     log : list or None
         Record of the method calls made to the learner, in the format
         ``(method_name, *args)``.
-    to_retry : dict
-        Mapping of ``{point: n_fails, ...}``. When a point has failed
+    to_retry : list of tuples
+        List of ``(point, n_fails)``. When a point has failed
         ``runner.retries`` times it is removed but will be present
         in ``runner.tracebacks``.
-    tracebacks : dict
-        A mapping of point to the traceback if that point failed.
-    pending_points : dict
-        A mapping of `~concurrent.futures.Future`\s to points.
+    tracebacks : list of tuples
+        List of of ``(point, tb)`` for points that failed.
+    pending_points : list of tuples
+        A list of tuples with ``(concurrent.futures.Future, point)``.
 
     Methods
     -------
@@ -126,7 +128,7 @@ def __init__(
 
         self._max_tasks = ntasks
 
-        self.pending_points = {}
+        self._pending_tasks = {}  # mapping from concurrent.futures.Future → point id
 
         # if we instantiate our own executor, then we are also responsible
         # for calling 'shutdown'
@@ -143,14 +145,20 @@ def __init__(
         # Error handling attributes
         self.retries = retries
         self.raise_if_retries_exceeded = raise_if_retries_exceeded
-        self.to_retry = {}
-        self.tracebacks = {}
+        self._to_retry = {}
+        self._tracebacks = {}
+
+        self._id_to_point = {}
+        self._next_id = functools.partial(
+            next, itertools.count()
+        )  # some unique id to be associated with each point
 
     def _get_max_tasks(self):
         return self._max_tasks or _get_ncores(self.executor)
 
-    def _do_raise(self, e, x):
-        tb = self.tracebacks[x]
+    def _do_raise(self, e, i):
+        tb = self._tracebacks[i]
+        x = self._id_to_point[i]
         raise RuntimeError(
             "An error occured while evaluating "
             f'"learner.function({x})". '
@@ -162,15 +170,21 @@ def do_log(self):
         return self.log is not None
 
     def _ask(self, n):
-        points = [
-            p for p in self.to_retry.keys() if p not in self.pending_points.values()
-        ][:n]
-        loss_improvements = len(points) * [float("inf")]
-        if len(points) < n:
-            new_points, new_losses = self.learner.ask(n - len(points))
-            points += new_points
+        pending_ids = self._pending_tasks.values()
+        # using generator here because we only need until `n`
+        pids_gen = (pid for pid in self._to_retry.keys() if pid not in pending_ids)
+        pids = list(itertools.islice(pids_gen, n))
+
+        loss_improvements = len(pids) * [float("inf")]
+
+        if len(pids) < n:
+            new_points, new_losses = self.learner.ask(n - len(pids))
             loss_improvements += new_losses
-        return points, loss_improvements
+            for point in new_points:
+                pid = self._next_id()
+                self._id_to_point[pid] = point
+                pids.append(pid)
+        return pids, loss_improvements
 
     def overhead(self):
         """Overhead of using Adaptive and the executor in percent.
@@ -197,21 +211,22 @@ def overhead(self):
 
     def _process_futures(self, done_futs):
         for fut in done_futs:
-            x = self.pending_points.pop(fut)
+            pid = self._pending_tasks.pop(fut)
             try:
                 y = fut.result()
                 t = time.time() - fut.start_time  # total execution time
             except Exception as e:
-                self.tracebacks[x] = traceback.format_exc()
-                self.to_retry[x] = self.to_retry.get(x, 0) + 1
-                if self.to_retry[x] > self.retries:
-                    self.to_retry.pop(x)
+                self._tracebacks[pid] = traceback.format_exc()
+                self._to_retry[pid] = self._to_retry.get(pid, 0) + 1
+                if self._to_retry[pid] > self.retries:
+                    self._to_retry.pop(pid)
                     if self.raise_if_retries_exceeded:
-                        self._do_raise(e, x)
+                        self._do_raise(e, pid)
             else:
                 self._elapsed_function_time += t / self._get_max_tasks()
-                self.to_retry.pop(x, None)
-                self.tracebacks.pop(x, None)
+                self._to_retry.pop(pid, None)
+                self._tracebacks.pop(pid, None)
+                x = self._id_to_point.pop(pid)
                 if self.do_log:
                     self.log.append(("tell", x, y))
                 self.learner.tell(x, y)
@@ -220,28 +235,29 @@ def _get_futures(self):
         # Launch tasks to replace the ones that completed
         # on the last iteration, making sure to fill workers
         # that have started since the last iteration.
-        n_new_tasks = max(0, self._get_max_tasks() - len(self.pending_points))
+        n_new_tasks = max(0, self._get_max_tasks() - len(self._pending_tasks))
 
         if self.do_log:
             self.log.append(("ask", n_new_tasks))
 
-        points, _ = self._ask(n_new_tasks)
+        pids, _ = self._ask(n_new_tasks)
 
-        for x in points:
+        for pid in pids:
             start_time = time.time()  # so we can measure execution time
-            fut = self._submit(x)
+            point = self._id_to_point[pid]
+            fut = self._submit(point)
             fut.start_time = start_time
-            self.pending_points[fut] = x
+            self._pending_tasks[fut] = pid
 
         # Collect and results and add them to the learner
-        futures = list(self.pending_points.keys())
+        futures = list(self._pending_tasks.keys())
         return futures
 
     def _remove_unfinished(self):
         # remove points with 'None' values from the learner
         self.learner.remove_unfinished()
         # cancel any outstanding tasks
-        remaining = list(self.pending_points.keys())
+        remaining = list(self._pending_tasks.keys())
         for fut in remaining:
             fut.cancel()
         return remaining
@@ -260,7 +276,7 @@ def _cleanup(self):
     @property
     def failed(self):
         """Set of points that failed ``runner.retries`` times."""
-        return set(self.tracebacks) - set(self.to_retry)
+        return set(self._tracebacks) - set(self._to_retry)
 
     @abc.abstractmethod
     def elapsed_time(self):
@@ -276,6 +292,20 @@ def _submit(self, x):
         """Is called in `_get_futures`."""
         pass
 
+    @property
+    def tracebacks(self):
+        return [(self._id_to_point[pid], tb) for pid, tb in self._tracebacks.items()]
+
+    @property
+    def to_retry(self):
+        return [(self._id_to_point[pid], n) for pid, n in self._to_retry.items()]
+
+    @property
+    def pending_points(self):
+        return [
+            (fut, self._id_to_point[pid]) for fut, pid in self._pending_tasks.items()
+        ]
+
 
 class BlockingRunner(BaseRunner):
     """Run a learner synchronously in an executor.
@@ -315,14 +345,14 @@ class BlockingRunner(BaseRunner):
     log : list or None
         Record of the method calls made to the learner, in the format
         ``(method_name, *args)``.
-    to_retry : dict
-        Mapping of ``{point: n_fails, ...}``. When a point has failed
+    to_retry : list of tuples
+        List of ``(point, n_fails)``. When a point has failed
         ``runner.retries`` times it is removed but will be present
         in ``runner.tracebacks``.
-    tracebacks : dict
-        A mapping of point to the traceback if that point failed.
-    pending_points : dict
-        A mapping of `~concurrent.futures.Future`\to points.
+    tracebacks : list of tuples
+        List of of ``(point, tb)`` for points that failed.
+    pending_points : list of tuples
+        A list of tuples with ``(concurrent.futures.Future, point)``.
 
     Methods
     -------
@@ -438,14 +468,14 @@ class AsyncRunner(BaseRunner):
     log : list or None
         Record of the method calls made to the learner, in the format
         ``(method_name, *args)``.
-    to_retry : dict
-        Mapping of ``{point: n_fails, ...}``. When a point has failed
+    to_retry : list of tuples
+        List of ``(point, n_fails)``. When a point has failed
         ``runner.retries`` times it is removed but will be present
         in ``runner.tracebacks``.
-    tracebacks : dict
-        A mapping of point to the traceback if that point failed.
-    pending_points : dict
-        A mapping of `~concurrent.futures.Future`\s to points.
+    tracebacks : list of tuples
+        List of of ``(point, tb)`` for points that failed.
+    pending_points : list of tuples
+        A list of tuples with ``(concurrent.futures.Future, point)``.
 
     Methods
     -------
diff --git a/docs/source/tutorial/tutorial.advanced-topics.rst b/docs/source/tutorial/tutorial.advanced-topics.rst
index 84487a9cb..1156979c8 100644
--- a/docs/source/tutorial/tutorial.advanced-topics.rst
+++ b/docs/source/tutorial/tutorial.advanced-topics.rst
@@ -297,12 +297,12 @@ raise the exception with the stack trace:
     runner.task.result()
 
 
-You can also check ``runner.tracebacks`` which is a mapping from
-point → traceback.
+You can also check ``runner.tracebacks`` which is a list of tuples with
+(point, traceback).
 
 .. jupyter-execute::
 
-    for point, tb in runner.tracebacks.items():
+    for point, tb in runner.tracebacks:
         print(f'point: {point}:\n {tb}')
 
 Logging runners