diff --git a/exps/NATS-algos/README.md b/exps/NATS-algos/README.md
index 361ce4f..b4b2e39 100644
--- a/exps/NATS-algos/README.md
+++ b/exps/NATS-algos/README.md
@@ -11,7 +11,7 @@ The Python files in this folder are used to re-produce the results in ``NATS-Ben
 
 ## Requirements
 
-- `nats_bench`>=v1.1 : you can use `pip install nats_bench` to install or from [sources](https://github.com/D-X-Y/NATS-Bench)
+- `nats_bench`>=v1.2 : you can use `pip install nats_bench` to install or from [sources](https://github.com/D-X-Y/NATS-Bench)
 - `hpbandster` : if you want to run BOHB
 
 ## Citation
diff --git a/lib/spaces/__init__.py b/lib/spaces/__init__.py
index 5550320..7b4614f 100644
--- a/lib/spaces/__init__.py
+++ b/lib/spaces/__init__.py
@@ -5,3 +5,4 @@
 #####################################################
 
 from .basic_space import Categorical
+from .basic_space import Continuous
diff --git a/lib/spaces/basic_space.py b/lib/spaces/basic_space.py
index 3f04020..9db5723 100644
--- a/lib/spaces/basic_space.py
+++ b/lib/spaces/basic_space.py
@@ -3,12 +3,15 @@
 #####################################################
 
 import abc
+import math
 import random
 
+from typing import Optional
+
 
 class Space(metaclass=abc.ABCMeta):
     @abc.abstractmethod
-    def random(self):
+    def random(self, recursion=True):
         raise NotImplementedError
 
     @abc.abstractmethod
@@ -17,8 +20,12 @@ class Space(metaclass=abc.ABCMeta):
 
 
 class Categorical(Space):
-    def __init__(self, *data):
+    def __init__(self, *data, default: Optional[int] = None):
         self._candidates = [*data]
+        self._default = default
+        assert self._default is None or 0 <= self._default < len(self._candidates), "default >= {:}".format(
+            len(self._candidates)
+        )
 
     def __getitem__(self, index):
         return self._candidates[index]
@@ -27,7 +34,50 @@ class Categorical(Space):
         return len(self._candidates)
 
     def __repr__(self):
-        return "{name:}(candidates={cs:})".format(name=self.__class__.__name__, cs=self._candidates)
+        return "{name:}(candidates={cs:}, default_index={default:})".format(
+            name=self.__class__.__name__, cs=self._candidates, default=self._default
+        )
 
-    def random(self):
-        return random.choice(self._candidates)
+    def random(self, recursion=True):
+        sample = random.choice(self._candidates)
+        if recursion and isinstance(sample, Space):
+            return sample.random(recursion)
+        else:
+            return sample
+
+
+class Continuous(Space):
+    def __init__(self, lower: float, upper: float, default: Optional[float] = None, log: bool = False):
+        self._lower = lower
+        self._upper = upper
+        self._default = default
+        self._log_scale = log
+
+    @property
+    def lower(self):
+        return self._lower
+
+    @property
+    def upper(self):
+        return self._upper
+
+    @property
+    def default(self):
+        return self._default
+
+    def __repr__(self):
+        return "{name:}(lower={lower:}, upper={upper:}, default_value={default:}, log_scale={log:})".format(
+            name=self.__class__.__name__,
+            lower=self._lower,
+            upper=self._upper,
+            default=self._default,
+            log=self._log_scale,
+        )
+
+    def random(self, recursion=True):
+        del recursion
+        if self._log_scale:
+            sample = random.uniform(math.log(self._lower), math.log(self._upper))
+            return math.exp(sample)
+        else:
+            return random.uniform(self._lower, self._upper)
diff --git a/tests/test_basic.py b/tests/test_basic.py
index 6757e3a..637e282 100644
--- a/tests/test_basic.py
+++ b/tests/test_basic.py
@@ -12,6 +12,7 @@ if str(lib_dir) not in sys.path:
     sys.path.insert(0, str(lib_dir))
 
 from spaces import Categorical
+from spaces import Continuous
 
 
 class TestBasicSpace(unittest.TestCase):
@@ -19,4 +20,19 @@ class TestBasicSpace(unittest.TestCase):
         space = Categorical(1, 2, 3, 4)
         for i in range(4):
             self.assertEqual(space[i], i + 1)
-        self.assertEqual("Categorical(candidates=[1, 2, 3, 4])", str(space))
+        self.assertEqual("Categorical(candidates=[1, 2, 3, 4], default_index=None)", str(space))
+
+    def test_continuous(self):
+        space = Continuous(0, 1)
+        self.assertGreaterEqual(space.random(), 0)
+        self.assertGreaterEqual(1, space.random())
+
+        lower, upper = 1.5, 4.6
+        space = Continuous(lower, upper, log=False)
+        values = []
+        for i in range(100000):
+            x = space.random()
+            self.assertGreaterEqual(x, lower)
+            self.assertGreaterEqual(upper, x)
+            values.append(x)
+        self.assertAlmostEqual((lower + upper) / 2, sum(values) / len(values), places=2)