diff --git a/flaml/automl.py b/flaml/automl.py
index ed72ec77d..7190cda6b 100644
--- a/flaml/automl.py
+++ b/flaml/automl.py
@@ -542,7 +542,7 @@ class AutoML(BaseEstimator):
         new_automl.fit(X_train, y_train, starting_points=starting_points)
         ```
 
-            seed: int or None, default=None | The random seed for np.random.
+            seed: int or None, default=None | The random seed for hpo.
             n_concurrent_trials: [Experimental] int, default=1 | The number of
                 concurrent trials. For n_concurrent_trials > 1, installation of
                 ray is required: `pip install flaml[ray]`.
@@ -1845,7 +1845,7 @@ class AutoML(BaseEstimator):
         new_automl.fit(X_train, y_train, starting_points=starting_points)
         ```
 
-            seed: int or None, default=None | The random seed for np.random.
+            seed: int or None, default=None | The random seed for hpo.
             n_concurrent_trials: [Experimental] int, default=1 | The number of
                 concurrent trials. For n_concurrent_trials > 1, installation of
                 ray is required: `pip install flaml[ray]`.
@@ -1949,13 +1949,10 @@ class AutoML(BaseEstimator):
         )
         self._search_states = {}  # key: estimator name; value: SearchState
         self._random = np.random.RandomState(RANDOM_SEED)
-        if seed is not None:
-            np.random.seed(seed)
-        self._seed = seed + 19823 if seed is not None else 20
+        self._seed = seed if seed is not None else 20
         self._learner_selector = learner_selector
         old_level = logger.getEffectiveLevel()
         self.verbose = verbose
-        # if verbose == 0:
         logger.setLevel(50 - verbose * 10)
         if (not mlflow or not mlflow.active_run()) and not logger.handlers:
             # Add the console handler.
diff --git a/flaml/nlp/utils.py b/flaml/nlp/utils.py
index 63ac1816a..57ae8ba98 100644
--- a/flaml/nlp/utils.py
+++ b/flaml/nlp/utils.py
@@ -1,7 +1,6 @@
 import argparse
 from dataclasses import dataclass, field
 from typing import Dict, Any
-
 from ..data import SUMMARIZATION, SEQREGRESSION, SEQCLASSIFICATION, NLG_TASKS
 
 
diff --git a/flaml/searcher/blendsearch.py b/flaml/searcher/blendsearch.py
index 5317ea35c..171c3bfd0 100644
--- a/flaml/searcher/blendsearch.py
+++ b/flaml/searcher/blendsearch.py
@@ -113,7 +113,7 @@ class BlendSearch(Searcher):
                 "For cost-frugal search, "
                 "consider providing low-cost values for cost-related hps via "
                 "'low_cost_partial_config'. More info can be found at "
-                "https://github.com/microsoft/FLAML/wiki/About-%60low_cost_partial_config%60"
+                "https://microsoft.github.io/FLAML/docs/FAQ#about-low_cost_partial_config-in-tune"
             )
         if evaluated_rewards and mode:
             self._points_to_evaluate = []
diff --git a/flaml/searcher/flow2.py b/flaml/searcher/flow2.py
index 88e4c0507..ab349cc3b 100644
--- a/flaml/searcher/flow2.py
+++ b/flaml/searcher/flow2.py
@@ -2,27 +2,28 @@
 #  * Copyright (c) Microsoft Corporation. All rights reserved.
 #  * Licensed under the MIT License. See LICENSE file in the
 #  * project root for license information.
-from flaml.tune.sample import Domain
 from typing import Dict, Optional, Tuple
 import numpy as np
+import logging
 
 try:
     from ray import __version__ as ray_version
 
     assert ray_version >= "1.0.0"
     from ray.tune.suggest import Searcher
-    from ray.tune.suggest.variant_generator import generate_variants
     from ray.tune import sample
     from ray.tune.utils.util import flatten_dict, unflatten_dict
 except (ImportError, AssertionError):
     from .suggestion import Searcher
-    from .variant_generator import generate_variants
     from ..tune import sample
     from ..tune.trial import flatten_dict, unflatten_dict
-from ..tune.space import complete_config, denormalize, normalize
-
-
-import logging
+from flaml.tune.sample import _BackwardsCompatibleNumpyRng
+from ..tune.space import (
+    complete_config,
+    denormalize,
+    normalize,
+    generate_variants_compatible,
+)
 
 logger = logging.getLogger(__name__)
 
@@ -84,6 +85,7 @@ class FLOW2(Searcher):
         self.space = space or {}
         self._space = flatten_dict(self.space, prevent_delimiter=True)
         self._random = np.random.RandomState(seed)
+        self.rs_random = _BackwardsCompatibleNumpyRng(seed + 19823)
         self.seed = seed
         self.init_config = init_config
         self.best_config = flatten_dict(init_config)
@@ -464,8 +466,8 @@ class FLOW2(Searcher):
             # random
             for i, key in enumerate(self._tunable_keys):
                 if self._direction_tried[i] != 0:
-                    for _, generated in generate_variants(
-                        {"config": {key: self._space[key]}}
+                    for _, generated in generate_variants_compatible(
+                        {"config": {key: self._space[key]}}, random_state=self.rs_random
                     ):
                         if generated["config"][key] != best_config[key]:
                             config[key] = generated["config"][key]
diff --git a/flaml/searcher/suggestion.py b/flaml/searcher/suggestion.py
index 95c1d35c1..69c27cc73 100644
--- a/flaml/searcher/suggestion.py
+++ b/flaml/searcher/suggestion.py
@@ -178,7 +178,7 @@ class ConcurrencyLimiter(Searcher):
         batch (bool): Whether to wait for all concurrent samples
             to finish before updating the underlying searcher.
     Example:
-    ```python 
+    ```python
     from ray.tune.suggest import ConcurrencyLimiter
     search_alg = HyperOptSearch(metric="accuracy")
     search_alg = ConcurrencyLimiter(search_alg, max_concurrent=2)
@@ -366,81 +366,81 @@ class _OptunaTrialSuggestCaptor:
 
 class OptunaSearch(Searcher):
     """A wrapper around Optuna to provide trial suggestions.
-    [Optuna](https://optuna.org/)
-    is a hyperparameter optimization library.
-    In contrast to other libraries, it employs define-by-run style
-    hyperparameter definitions.
-    This Searcher is a thin wrapper around Optuna's search algorithms.
-    You can pass any Optuna sampler, which will be used to generate
-    hyperparameter suggestions.
-    Args:
-        space (dict|Callable): Hyperparameter search space definition for
-            Optuna's sampler. This can be either a class `dict` with
-            parameter names as keys and ``optuna.distributions`` as values,
-            or a Callable - in which case, it should be a define-by-run
-            function using ``optuna.trial`` to obtain the hyperparameter
-            values. The function should return either a class `dict` of
-            constant values with names as keys, or None.
-            For more information, see 
-            [tutorial](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/002_configurations.html).
-            Warning - No actual computation should take place in the define-by-run
-            function. Instead, put the training logic inside the function
-            or class trainable passed to tune.run.
-        metric (str): The training result objective value attribute. If None
-            but a mode was passed, the anonymous metric `_metric` will be used
-            per default.
-        mode (str): One of {min, max}. Determines whether objective is
-            minimizing or maximizing the metric attribute.
-        points_to_evaluate (list): Initial parameter suggestions to be run
-            first. This is for when you already have some good parameters
-            you want to run first to help the algorithm make better suggestions
-            for future parameters. Needs to be a list of dicts containing the
-            configurations.
-        sampler (optuna.samplers.BaseSampler): Optuna sampler used to
-            draw hyperparameter configurations. Defaults to ``TPESampler``.
-        seed (int): Seed to initialize sampler with. This parameter is only
-            used when ``sampler=None``. In all other cases, the sampler
-            you pass should be initialized with the seed already.
-        evaluated_rewards (list): If you have previously evaluated the
-            parameters passed in as points_to_evaluate you can avoid
-            re-running those trials by passing in the reward attributes
-            as a list so the optimiser can be told the results without
-            needing to re-compute the trial. Must be the same length as
-            points_to_evaluate.
+        [Optuna](https://optuna.org/)
+        is a hyperparameter optimization library.
+        In contrast to other libraries, it employs define-by-run style
+        hyperparameter definitions.
+        This Searcher is a thin wrapper around Optuna's search algorithms.
+        You can pass any Optuna sampler, which will be used to generate
+        hyperparameter suggestions.
+        Args:
+            space (dict|Callable): Hyperparameter search space definition for
+                Optuna's sampler. This can be either a class `dict` with
+                parameter names as keys and ``optuna.distributions`` as values,
+                or a Callable - in which case, it should be a define-by-run
+                function using ``optuna.trial`` to obtain the hyperparameter
+                values. The function should return either a class `dict` of
+                constant values with names as keys, or None.
+                For more information, see
+                [tutorial](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/002_configurations.html).
+                Warning - No actual computation should take place in the define-by-run
+                function. Instead, put the training logic inside the function
+                or class trainable passed to tune.run.
+            metric (str): The training result objective value attribute. If None
+                but a mode was passed, the anonymous metric `_metric` will be used
+                per default.
+            mode (str): One of {min, max}. Determines whether objective is
+                minimizing or maximizing the metric attribute.
+            points_to_evaluate (list): Initial parameter suggestions to be run
+                first. This is for when you already have some good parameters
+                you want to run first to help the algorithm make better suggestions
+                for future parameters. Needs to be a list of dicts containing the
+                configurations.
+            sampler (optuna.samplers.BaseSampler): Optuna sampler used to
+                draw hyperparameter configurations. Defaults to ``TPESampler``.
+            seed (int): Seed to initialize sampler with. This parameter is only
+                used when ``sampler=None``. In all other cases, the sampler
+                you pass should be initialized with the seed already.
+            evaluated_rewards (list): If you have previously evaluated the
+                parameters passed in as points_to_evaluate you can avoid
+                re-running those trials by passing in the reward attributes
+                as a list so the optimiser can be told the results without
+                needing to re-compute the trial. Must be the same length as
+                points_to_evaluate.
 
-    Tune automatically converts search spaces to Optuna's format:
+        Tune automatically converts search spaces to Optuna's format:
 
-````python
-from ray.tune.suggest.optuna import OptunaSearch
-config = { "a": tune.uniform(6, 8),
-           "b": tune.loguniform(1e-4, 1e-2)}
-optuna_search = OptunaSearch(metric="loss", mode="min")
-tune.run(trainable, config=config, search_alg=optuna_search)
-````
+    ````python
+    from ray.tune.suggest.optuna import OptunaSearch
+    config = { "a": tune.uniform(6, 8),
+               "b": tune.loguniform(1e-4, 1e-2)}
+    optuna_search = OptunaSearch(metric="loss", mode="min")
+    tune.run(trainable, config=config, search_alg=optuna_search)
+    ````
 
-    If you would like to pass the search space manually, the code would
-    look like this:
+        If you would like to pass the search space manually, the code would
+        look like this:
 
-```python
-from ray.tune.suggest.optuna import OptunaSearch
-import optuna
-config = { "a": optuna.distributions.UniformDistribution(6, 8),
-           "b": optuna.distributions.LogUniformDistribution(1e-4, 1e-2)}
-optuna_search = OptunaSearch(space,metric="loss",mode="min")
-tune.run(trainable, search_alg=optuna_search)
-# Equivalent Optuna define-by-run function approach:
-def define_search_space(trial: optuna.Trial):
-    trial.suggest_float("a", 6, 8)
-    trial.suggest_float("b", 1e-4, 1e-2, log=True)
-    # training logic goes into trainable, this is just
-    # for search space definition
-optuna_search = OptunaSearch(
-    define_search_space,
-    metric="loss",
-    mode="min")
-tune.run(trainable, search_alg=optuna_search)
-.. versionadded:: 0.8.8
-```
+    ```python
+    from ray.tune.suggest.optuna import OptunaSearch
+    import optuna
+    config = { "a": optuna.distributions.UniformDistribution(6, 8),
+               "b": optuna.distributions.LogUniformDistribution(1e-4, 1e-2)}
+    optuna_search = OptunaSearch(space,metric="loss",mode="min")
+    tune.run(trainable, search_alg=optuna_search)
+    # Equivalent Optuna define-by-run function approach:
+    def define_search_space(trial: optuna.Trial):
+        trial.suggest_float("a", 6, 8)
+        trial.suggest_float("b", 1e-4, 1e-2, log=True)
+        # training logic goes into trainable, this is just
+        # for search space definition
+    optuna_search = OptunaSearch(
+        define_search_space,
+        metric="loss",
+        mode="min")
+    tune.run(trainable, search_alg=optuna_search)
+    .. versionadded:: 0.8.8
+    ```
 
     """
 
diff --git a/flaml/searcher/variant_generator.py b/flaml/searcher/variant_generator.py
index d87a0bc9a..76b18d88e 100644
--- a/flaml/searcher/variant_generator.py
+++ b/flaml/searcher/variant_generator.py
@@ -18,11 +18,9 @@
 import copy
 import logging
 from typing import Any, Dict, Generator, List, Tuple
-
 import numpy
 import random
-
-from ..tune.sample import Categorical, Domain
+from ..tune.sample import Categorical, Domain, RandomState
 
 logger = logging.getLogger(__name__)
 
@@ -35,6 +33,8 @@ class TuneError(Exception):
 
 def generate_variants(
     unresolved_spec: Dict,
+    constant_grid_search: bool = False,
+    random_state: "RandomState" = None,
 ) -> Generator[Tuple[Dict, Dict], None, None]:
     """Generates variants from a spec (dict) with unresolved values.
     There are two types of unresolved values:
@@ -43,14 +43,25 @@ def generate_variants(
         variants in combination:
             "activation": grid_search(["relu", "tanh"])
             "learning_rate": grid_search([1e-3, 1e-4, 1e-5])
+        Lambda functions: These are evaluated to produce a concrete value, and
+        can express dependencies or conditional distributions between values.
+        They can also be used to express random search (e.g., by calling
+        into the `random` or `np` module).
+            "cpu": lambda spec: spec.config.num_workers
+            "batch_size": lambda spec: random.uniform(1, 1000)
     Finally, to support defining specs in plain JSON / YAML, grid search
-    can also be defined alternatively as follows:
+    and lambda functions can also be defined alternatively as follows:
         "activation": {"grid_search": ["relu", "tanh"]}
+        "cpu": {"eval": "spec.config.num_workers"}
     Use `format_vars` to format the returned dict of hyperparameters.
     Yields:
         (Dict of resolved variables, Spec object)
     """
-    for resolved_vars, spec in _generate_variants(unresolved_spec):
+    for resolved_vars, spec in _generate_variants(
+        unresolved_spec,
+        constant_grid_search=constant_grid_search,
+        random_state=random_state,
+    ):
         assert not _unresolved_values(spec)
         yield resolved_vars, spec
 
@@ -93,7 +104,9 @@ def parse_spec_vars(
     return resolved_vars, domain_vars, grid_vars
 
 
-def _generate_variants(spec: Dict) -> Tuple[Dict, Dict]:
+def _generate_variants(
+    spec: Dict, constant_grid_search: bool = False, random_state: "RandomState" = None
+) -> Tuple[Dict, Dict]:
     spec = copy.deepcopy(spec)
     _, domain_vars, grid_vars = parse_spec_vars(spec)
 
@@ -101,10 +114,34 @@ def _generate_variants(spec: Dict) -> Tuple[Dict, Dict]:
         yield {}, spec
         return
 
+    # Variables to resolve
+    to_resolve = domain_vars
+
+    all_resolved = True
+    if constant_grid_search:
+        # In this path, we first sample random variables and keep them constant
+        # for grid search.
+        # `_resolve_domain_vars` will alter `spec` directly
+        all_resolved, resolved_vars = _resolve_domain_vars(
+            spec, domain_vars, allow_fail=True, random_state=random_state
+        )
+        if not all_resolved:
+            # Not all variables have been resolved, but remove those that have
+            # from the `to_resolve` list.
+            to_resolve = [(r, d) for r, d in to_resolve if r not in resolved_vars]
     grid_search = _grid_search_generator(spec, grid_vars)
     for resolved_spec in grid_search:
-        resolved_vars = _resolve_domain_vars(resolved_spec, domain_vars)
-        for resolved, spec in _generate_variants(resolved_spec):
+        if not constant_grid_search or not all_resolved:
+            # In this path, we sample the remaining random variables
+            _, resolved_vars = _resolve_domain_vars(
+                resolved_spec, to_resolve, random_state=random_state
+            )
+
+        for resolved, spec in _generate_variants(
+            resolved_spec,
+            constant_grid_search=constant_grid_search,
+            random_state=random_state,
+        ):
             for path, value in grid_vars:
                 resolved_vars[path] = _get_value(spec, path)
             for k, v in resolved.items():
@@ -134,7 +171,12 @@ def _get_value(spec: Dict, path: Tuple) -> Any:
     return spec
 
 
-def _resolve_domain_vars(spec: Dict, domain_vars: List[Tuple[Tuple, Domain]]) -> Dict:
+def _resolve_domain_vars(
+    spec: Dict,
+    domain_vars: List[Tuple[Tuple, Domain]],
+    allow_fail: bool = False,
+    random_state: "RandomState" = None,
+) -> Tuple[bool, Dict]:
     resolved = {}
     error = True
     num_passes = 0
@@ -145,7 +187,9 @@ def _resolve_domain_vars(spec: Dict, domain_vars: List[Tuple[Tuple, Domain]]) ->
             if path in resolved:
                 continue
             try:
-                value = domain.sample(_UnresolvedAccessGuard(spec))
+                value = domain.sample(
+                    _UnresolvedAccessGuard(spec), random_state=random_state
+                )
             except RecursiveDependencyError as e:
                 error = e
             except Exception:
@@ -156,8 +200,11 @@ def _resolve_domain_vars(spec: Dict, domain_vars: List[Tuple[Tuple, Domain]]) ->
                 assign_value(spec, path, value)
                 resolved[path] = value
     if error:
-        raise error
-    return resolved
+        if not allow_fail:
+            raise error
+        else:
+            return False, resolved
+    return True, resolved
 
 
 def _grid_search_generator(
diff --git a/flaml/tune/sample.py b/flaml/tune/sample.py
index dcc6fca56..e03edf2ef 100644
--- a/flaml/tune/sample.py
+++ b/flaml/tune/sample.py
@@ -12,21 +12,76 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-# This source file is included here because ray does not fully support Windows.
+# This source file is adapted here because ray does not fully support Windows.
 
 # Copyright (c) Microsoft Corporation.
 import logging
-import random
 from copy import copy
-from inspect import signature
 from math import isclose
-from typing import Any, Callable, Dict, List, Optional, Sequence, Union
-
+from typing import Any, Dict, List, Optional, Sequence, Union
 import numpy as np
 
+# Backwards compatibility
+try:
+    # Added in numpy>=1.17 but we require numpy>=1.16
+    np_random_generator = np.random.Generator
+    LEGACY_RNG = False
+except AttributeError:
+
+    class np_random_generator:
+        pass
+
+    LEGACY_RNG = True
+
 logger = logging.getLogger(__name__)
 
 
+class _BackwardsCompatibleNumpyRng:
+    """Thin wrapper to ensure backwards compatibility between
+    new and old numpy randomness generators.
+    """
+
+    _rng = None
+
+    def __init__(
+        self,
+        generator_or_seed: Optional[
+            Union["np_random_generator", np.random.RandomState, int]
+        ] = None,
+    ):
+        if generator_or_seed is None or isinstance(
+            generator_or_seed, (np.random.RandomState, np_random_generator)
+        ):
+            self._rng = generator_or_seed
+        elif LEGACY_RNG:
+            self._rng = np.random.RandomState(generator_or_seed)
+        else:
+            self._rng = np.random.default_rng(generator_or_seed)
+
+    @property
+    def legacy_rng(self) -> bool:
+        return not isinstance(self._rng, np_random_generator)
+
+    @property
+    def rng(self):
+        # don't set self._rng to np.random to avoid picking issues
+        return self._rng if self._rng is not None else np.random
+
+    def __getattr__(self, name: str) -> Any:
+        # https://numpy.org/doc/stable/reference/random/new-or-different.html
+        if self.legacy_rng:
+            if name == "integers":
+                name = "randint"
+            elif name == "random":
+                name = "rand"
+        return getattr(self.rng, name)
+
+
+RandomState = Union[
+    None, _BackwardsCompatibleNumpyRng, np_random_generator, np.random.RandomState, int
+]
+
+
 class Domain:
     """Base class to specify a type and valid range to sample parameters from.
     This base class is implemented by parameter spaces, like float ranges
@@ -61,9 +116,16 @@ class Domain:
             sampler = self.default_sampler_cls()
         return sampler
 
-    def sample(self, spec=None, size=1):
+    def sample(
+        self,
+        spec: Optional[Union[List[Dict], Dict]] = None,
+        size: int = 1,
+        random_state: "RandomState" = None,
+    ):
+        if not isinstance(random_state, _BackwardsCompatibleNumpyRng):
+            random_state = _BackwardsCompatibleNumpyRng(random_state)
         sampler = self.get_sampler()
-        return sampler.sample(self, spec=spec, size=size)
+        return sampler.sample(self, spec=spec, size=size, random_state=random_state)
 
     def is_grid(self):
         return isinstance(self.sampler, Grid)
@@ -86,6 +148,7 @@ class Sampler:
         domain: Domain,
         spec: Optional[Union[List[Dict], Dict]] = None,
         size: int = 1,
+        random_state: "RandomState" = None,
     ):
         raise NotImplementedError
 
@@ -128,6 +191,7 @@ class Grid(Sampler):
         domain: Domain,
         spec: Optional[Union[List[Dict], Dict]] = None,
         size: int = 1,
+        random_state: "RandomState" = None,
     ):
         return RuntimeError("Do not call `sample()` on grid.")
 
@@ -139,10 +203,13 @@ class Float(Domain):
             domain: "Float",
             spec: Optional[Union[List[Dict], Dict]] = None,
             size: int = 1,
+            random_state: "RandomState" = None,
         ):
+            if not isinstance(random_state, _BackwardsCompatibleNumpyRng):
+                random_state = _BackwardsCompatibleNumpyRng(random_state)
             assert domain.lower > float("-inf"), "Uniform needs a lower bound"
             assert domain.upper < float("inf"), "Uniform needs a upper bound"
-            items = np.random.uniform(domain.lower, domain.upper, size=size)
+            items = random_state.uniform(domain.lower, domain.upper, size=size)
             return items if len(items) > 1 else domain.cast(items[0])
 
     class _LogUniform(LogUniform):
@@ -151,7 +218,10 @@ class Float(Domain):
             domain: "Float",
             spec: Optional[Union[List[Dict], Dict]] = None,
             size: int = 1,
+            random_state: "RandomState" = None,
         ):
+            if not isinstance(random_state, _BackwardsCompatibleNumpyRng):
+                random_state = _BackwardsCompatibleNumpyRng(random_state)
             assert domain.lower > 0, "LogUniform needs a lower bound greater than 0"
             assert (
                 0 < domain.upper < float("inf")
@@ -159,7 +229,7 @@ class Float(Domain):
             logmin = np.log(domain.lower) / np.log(self.base)
             logmax = np.log(domain.upper) / np.log(self.base)
 
-            items = self.base ** (np.random.uniform(logmin, logmax, size=size))
+            items = self.base ** (random_state.uniform(logmin, logmax, size=size))
             return items if len(items) > 1 else domain.cast(items[0])
 
     class _Normal(Normal):
@@ -168,14 +238,17 @@ class Float(Domain):
             domain: "Float",
             spec: Optional[Union[List[Dict], Dict]] = None,
             size: int = 1,
+            random_state: "RandomState" = None,
         ):
+            if not isinstance(random_state, _BackwardsCompatibleNumpyRng):
+                random_state = _BackwardsCompatibleNumpyRng(random_state)
             assert not domain.lower or domain.lower == float(
                 "-inf"
             ), "Normal sampling does not allow a lower value bound."
             assert not domain.upper or domain.upper == float(
                 "inf"
             ), "Normal sampling does not allow a upper value bound."
-            items = np.random.normal(self.mean, self.sd, size=size)
+            items = random_state.normal(self.mean, self.sd, size=size)
             return items if len(items) > 1 else domain.cast(items[0])
 
     default_sampler_cls = _Uniform
@@ -262,8 +335,11 @@ class Integer(Domain):
             domain: "Integer",
             spec: Optional[Union[List[Dict], Dict]] = None,
             size: int = 1,
+            random_state: "RandomState" = None,
         ):
-            items = np.random.randint(domain.lower, domain.upper, size=size)
+            if not isinstance(random_state, _BackwardsCompatibleNumpyRng):
+                random_state = _BackwardsCompatibleNumpyRng(random_state)
+            items = random_state.integers(domain.lower, domain.upper, size=size)
             return items if len(items) > 1 else domain.cast(items[0])
 
     class _LogUniform(LogUniform):
@@ -272,7 +348,10 @@ class Integer(Domain):
             domain: "Integer",
             spec: Optional[Union[List[Dict], Dict]] = None,
             size: int = 1,
+            random_state: "RandomState" = None,
         ):
+            if not isinstance(random_state, _BackwardsCompatibleNumpyRng):
+                random_state = _BackwardsCompatibleNumpyRng(random_state)
             assert domain.lower > 0, "LogUniform needs a lower bound greater than 0"
             assert (
                 0 < domain.upper < float("inf")
@@ -280,8 +359,8 @@ class Integer(Domain):
             logmin = np.log(domain.lower) / np.log(self.base)
             logmax = np.log(domain.upper) / np.log(self.base)
 
-            items = self.base ** (np.random.uniform(logmin, logmax, size=size))
-            items = np.round(items).astype(int)
+            items = self.base ** (random_state.uniform(logmin, logmax, size=size))
+            items = np.floor(items).astype(int)
             return items if len(items) > 1 else domain.cast(items[0])
 
     default_sampler_cls = _Uniform
@@ -337,9 +416,11 @@ class Categorical(Domain):
             domain: "Categorical",
             spec: Optional[Union[List[Dict], Dict]] = None,
             size: int = 1,
+            random_state: "RandomState" = None,
         ):
-
-            items = random.choices(domain.categories, k=size)
+            if not isinstance(random_state, _BackwardsCompatibleNumpyRng):
+                random_state = _BackwardsCompatibleNumpyRng(random_state)
+            items = random_state.choice(domain.categories, size=size).tolist()
             return items if len(items) > 1 else domain.cast(items[0])
 
     default_sampler_cls = _Uniform
@@ -352,6 +433,11 @@ class Categorical(Domain):
         new.set_sampler(self._Uniform())
         return new
 
+    def grid(self):
+        new = copy(self)
+        new.set_sampler(Grid())
+        return new
+
     def __len__(self):
         return len(self.categories)
 
@@ -381,8 +467,11 @@ class Quantized(Sampler):
         domain: Domain,
         spec: Optional[Union[List[Dict], Dict]] = None,
         size: int = 1,
+        random_state: "RandomState" = None,
     ):
-        values = self.sampler.sample(domain, spec, size)
+        if not isinstance(random_state, _BackwardsCompatibleNumpyRng):
+            random_state = _BackwardsCompatibleNumpyRng(random_state)
+        values = self.sampler.sample(domain, spec, size, random_state=random_state)
         quantized = np.round(np.divide(values, self.q)) * self.q
         if not isinstance(quantized, np.ndarray):
             return domain.cast(quantized)
@@ -462,10 +551,10 @@ def qloguniform(lower: float, upper: float, q: float, base: float = 10):
     return Float(lower, upper).loguniform(base).quantized(q)
 
 
-def choice(categories: List):
+def choice(categories: Sequence):
     """Sample a categorical value.
     Sampling from ``tune.choice([1, 2])`` is equivalent to sampling from
-    ``random.choice([1, 2])``
+    ``np.random.choice([1, 2])``
     """
     return Categorical(categories).uniform()
 
diff --git a/flaml/tune/space.py b/flaml/tune/space.py
index d050eed1a..b8122e43c 100644
--- a/flaml/tune/space.py
+++ b/flaml/tune/space.py
@@ -7,13 +7,22 @@ try:
 except (ImportError, AssertionError):
     from . import sample
     from ..searcher.variant_generator import generate_variants
-from typing import Dict, Optional, Any, Tuple
+from typing import Dict, Optional, Any, Tuple, Generator
 import numpy as np
 import logging
 
 logger = logging.getLogger(__name__)
 
 
+def generate_variants_compatible(
+    unresolved_spec: Dict, constant_grid_search: bool = False, random_state=None
+) -> Generator[Tuple[Dict, Dict], None, None]:
+    try:
+        return generate_variants(unresolved_spec, constant_grid_search, random_state)
+    except TypeError:
+        return generate_variants(unresolved_spec, constant_grid_search)
+
+
 def define_by_run_func(trial, space: Dict, path: str = "") -> Optional[Dict[str, Any]]:
     """Define-by-run function to create the search space.
 
@@ -417,7 +426,6 @@ def indexof(domain: Dict, config: Dict) -> int:
         return index
     if config in domain.categories:
         return domain.categories.index(config)
-    # print(config)
     for i, cat in enumerate(domain.categories):
         if not isinstance(cat, dict):
             continue
@@ -491,7 +499,9 @@ def complete_config(
     for key, value in space.items():
         if key not in config:
             config[key] = value
-    for _, generated in generate_variants({"config": config}):
+    for _, generated in generate_variants_compatible(
+        {"config": config}, random_state=flow2.rs_random
+    ):
         config = generated["config"]
         break
     subspace = {}
diff --git a/flaml/version.py b/flaml/version.py
index d69d16e98..a2fecb457 100644
--- a/flaml/version.py
+++ b/flaml/version.py
@@ -1 +1 @@
-__version__ = "0.9.1"
+__version__ = "0.9.2"
diff --git a/test/automl/test_regression.py b/test/automl/test_regression.py
index 0d1ae4818..5e302e9fd 100644
--- a/test/automl/test_regression.py
+++ b/test/automl/test_regression.py
@@ -214,15 +214,14 @@ def test_multioutput():
 
     # predict
     print(model.predict(X_test))
-    
-    #train the model
+
+    # train the model
     model = RegressorChain(AutoML(task="regression", time_budget=1))
     model.fit(X_train, y_train)
-    
+
     # predict
     print(model.predict(X_test))
 
- 
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/test/automl/test_warmstart.py b/test/automl/test_warmstart.py
index d54411229..0b7cfbb97 100644
--- a/test/automl/test_warmstart.py
+++ b/test/automl/test_warmstart.py
@@ -38,7 +38,7 @@ class TestWarmStart(unittest.TestCase):
         starting_points = automl_experiment.best_config_per_estimator
         print("starting_points", starting_points)
         print("loss of the starting_points", automl_experiment.best_loss_per_estimator)
-        starting_point = starting_points['lgbm']
+        starting_point = starting_points["lgbm"]
         hps_to_freeze = ["colsample_bytree", "reg_alpha", "reg_lambda", "log_max_bin"]
 
         # 2. Constrct a new class:
@@ -55,17 +55,13 @@ class TestWarmStart(unittest.TestCase):
                     # if an hp is specifed to be freezed, use tine value provided in the starting_point
                     # otherwise use the setting from the original search space
                     if hp_name in starting_point:
-                        space[hp_name] = {
-                            "domain": starting_point[hp_name]
-                        }
+                        space[hp_name] = {"domain": starting_point[hp_name]}
                 # (3.1) Configure the search space for hps that are in the original search space
                 #  but you want to change something, for example the range.
                 revised_hps_to_search = {
                     "n_estimators": {
                         "domain": tune.lograndint(lower=10, upper=32768),
-                        "init_value": starting_point.get(
-                            "n_estimators"
-                        )
+                        "init_value": starting_point.get("n_estimators")
                         or space["n_estimators"].get("init_value", 10),
                         "low_cost_init_value": space["n_estimators"].get(
                             "low_cost_init_value", 10
@@ -73,9 +69,7 @@ class TestWarmStart(unittest.TestCase):
                     },
                     "num_leaves": {
                         "domain": tune.lograndint(lower=10, upper=3276),
-                        "init_value": starting_point.get(
-                            "num_leaves"
-                        )
+                        "init_value": starting_point.get("num_leaves")
                         or space["num_leaves"].get("init_value", 10),
                         "low_cost_init_value": space["num_leaves"].get(
                             "low_cost_init_value", 10
@@ -95,7 +89,7 @@ class TestWarmStart(unittest.TestCase):
         new_automl_experiment.add_learner(
             learner_name=new_estimator_name, learner_class=MyPartiallyFreezedLargeLGBM
         )
-        
+
         automl_settings_resume = {
             "time_budget": 3,
             "metric": "accuracy",
diff --git a/test/rep.py b/test/rep.py
new file mode 100644
index 000000000..e78980e78
--- /dev/null
+++ b/test/rep.py
@@ -0,0 +1,36 @@
+from flaml.data import load_openml_dataset
+from flaml.ml import ExtraTreesEstimator
+from flaml import AutoML
+
+X_train, X_test, y_train, y_test = load_openml_dataset(dataset_id=1169, data_dir="./")
+X_train = X_train.iloc[:1000]
+y_train = y_train.iloc[:1000]
+
+
+class ExtraTreesEstimatorSeeded(ExtraTreesEstimator):
+    """ExtraTreesEstimator for reproducible FLAML run."""
+
+    def config2params(self, config: dict) -> dict:
+        params = super().config2params(config)
+        params["random_state"] = 0
+        return params
+
+
+settings = {
+    "time_budget": 1e10,  # total running time in seconds
+    "max_iter": 3,
+    "metric": "ap",  # average_precision
+    "task": "classification",  # task type
+    "seed": 7654321,  # random seed
+    "estimator_list": ["extra_trees_seeded"],
+    "verbose": False,
+}
+
+for trial_num in range(8):
+    automl = AutoML()
+    automl.add_learner(
+        learner_name="extra_trees_seeded", learner_class=ExtraTreesEstimatorSeeded
+    )
+    automl.fit(X_train=X_train, y_train=y_train, **settings)
+    print(automl.best_loss)
+    print(automl.best_config)
diff --git a/test/test_conda_distribution.py b/test/test_conda_distribution.py
index a028cec95..7347a535a 100644
--- a/test/test_conda_distribution.py
+++ b/test/test_conda_distribution.py
@@ -11,8 +11,8 @@ def test_package_minimum():
     # Specify automl goal and constraint
     automl_settings = {
         "time_budget": 10,  # in seconds
-        "metric": 'accuracy',
-        "task": 'classification',
+        "metric": "accuracy",
+        "task": "classification",
         "log_file_name": "iris.log",
     }
     X_train, y_train = load_iris(return_X_y=True)
@@ -27,4 +27,3 @@ def test_package_minimum():
     preds = automl.predict_proba(X_train)
     assert preds.shape == (150, 3)
     print(preds)
-
diff --git a/website/docs/Use-Cases/Tune-User-Defined-Function.md b/website/docs/Use-Cases/Tune-User-Defined-Function.md
index 72568e20f..5cabe6458 100644
--- a/website/docs/Use-Cases/Tune-User-Defined-Function.md
+++ b/website/docs/Use-Cases/Tune-User-Defined-Function.md
@@ -436,13 +436,12 @@ analysis = tune.run(
 
 ### Reproducibility
 
-By default, there is randomness in our tuning process. If reproducibility is desired, you could
-manually set a random seed before calling `tune.run()`. For example, in the following code, we call `np.random.seed(100)` to set the random seed.
-With this random seed, running the following code multiple times will generate exactly the same search trajectory.
+By default, there is randomness in our tuning process (for versions <= 0.9.0). If reproducibility is desired, you could manually set a random seed before calling `tune.run()`. For example, in the following code, we call `np.random.seed(100)` to set the random seed.
+With this random seed, running the following code multiple times will generate exactly the same search trajectory. The reproducibility can only be guaranteed in sequential tuning.
 
 ```python
 import numpy as np
-np.random.seed(100)
+np.random.seed(100)  # This line is not needed starting from version v0.9.1.
 analysis = tune.run(
     simple_obj,
     config=config_search_space,