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lerobot/tests/policies/test_gaussian_actor_policy.py
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Khalil Meftah e963e5a0c4 RL stack refactoring (#3075)
* refactor: RL stack refactoring — RLAlgorithm, RLTrainer, DataMixer, and SAC restructuring

* chore: clarify torch.compile disabled note in SACAlgorithm

* fix(teleop): keyboard EE teleop not registering special keys and losing intervention state

Fixes #2345

Co-authored-by: jpizarrom <jpizarrom@gmail.com>

* fix: remove leftover normalization calls from reward classifier predict_reward

Fixes #2355

* fix: add thread synchronization to ReplayBuffer to prevent race condition between add() and sample()

* refactor: update SACAlgorithm to pass action_dim to _init_critics and fix encoder reference

* perf: remove redundant CPU→GPU→CPU transition move in learner

* Fix: add kwargs in reward classifier __init__()

* fix: include IS_INTERVENTION in complementary_info sent to learner for offline replay buffer

* fix: add try/finally to control_loop to ensure image writer cleanup on exit

* fix: use string key for IS_INTERVENTION in complementary_info to avoid torch.load serialization error

* fix: skip tests that require grpc if not available

* fix(tests): ensure tensor stats comparison accounts for reshaping in normalization tests

* fix(tests): skip tests that require grpc if not available

* refactor(rl): expose public API in rl/__init__ and use relative imports in sub-packages

* fix(config): update vision encoder model name to lerobot/resnet10

* fix(sac): clarify torch.compile status

* refactor(rl): update shutdown_event type hints from 'any' to 'Any' for consistency and clarity

* refactor(sac): simplify optimizer return structure

* perf(rl): use async iterators in OnlineOfflineMixer.get_iterator

* refactor(sac): decouple algorithm hyperparameters from policy config

* update losses names in tests

* fix docstring

* remove unused type alias

* fix test for flat dict structure

* refactor(policies): rename policies/sac → policies/gaussian_actor

* refactor(rl/sac): consolidate hyperparameter ownership and clean up discrete critic

* perf(observation_processor): add CUDA support for image processing

* fix(rl): correctly wire HIL-SERL gripper penalty through processor pipeline

(cherry picked from commit 9c2af818ff)

* fix(rl): add time limit processor to environment pipeline

(cherry picked from commit cd105f65cb)

* fix(rl): clarify discrete gripper action mapping in GripperVelocityToJoint for SO100

(cherry picked from commit 494f469a2b)

* fix(rl): update neutral gripper action

(cherry picked from commit 9c9064e5be)

* fix(rl): merge environment and action-processor info in transition processing

(cherry picked from commit 30e1886b64)

* fix(rl): mirror gym_manipulator in actor

(cherry picked from commit d2a046dfc5)

* fix(rl): postprocess action in actor

(cherry picked from commit c2556439e5)

* fix(rl): improve action processing for discrete and continuous actions

(cherry picked from commit f887ab3f6a)

* fix(rl): enhance intervention handling in actor and learner

(cherry picked from commit ef8bfffbd7)

* Revert "perf(observation_processor): add CUDA support for image processing"

This reverts commit 38b88c414c.

* refactor(rl): make algorithm a nested config so all SAC hyperparameters are JSON-addressable

* refactor(rl): add make_algorithm_config function for RLAlgorithmConfig instantiation

* refactor(rl): add type property to RLAlgorithmConfig for better clarity

* refactor(rl): make RLAlgorithmConfig an abstract base class for better extensibility

* refactor(tests): remove grpc import checks from test files for cleaner code

* fix(tests): gate RL tests on the `datasets` extra

* refactor: simplify docstrings for clarity and conciseness across multiple files

* fix(rl): update gripper position key and handle action absence during reset

* fix(rl): record pre-step observation so (obs, action, next.reward) align in gym_manipulator dataset

* refactor: clean up import statements

* chore: address reviewer comments

* chore: improve visual stats reshaping logic and update docstring for clarity

* refactor: enforce mandatory config_class and name attributes in RLAlgorithm

* refactor: implement NotImplementedError for abstract methods in RLAlgorithm and DataMixer

* refactor: replace build_algorithm with make_algorithm for SACAlgorithmConfig and update related tests

* refactor: add require_package calls for grpcio and gym-hil in relevant modules

* refactor(rl): move grpcio guards to runtime entry points

* feat(rl): consolidate HIL-SERL checkpoint into HF-style components

Make `RLAlgorithmConfig` and `RLAlgorithm` `HubMixin`s, add abstract
`state_dict()` / `load_state_dict()` for critic ensemble, target nets
and `log_alpha`, and persist them as a sibling `algorithm/` component
next to `pretrained_model/`. Replace the pickled `training_state.pt`
with an enriched `training_step.json` carrying `step` and
`interaction_step`, so resume restores actor + critics + target nets +
temperature + optimizers + RNG + counters from HF-standard files.

* refactor(rl): move actor weight-sync wire format from policy to algorithm

* refactor(rl): update type hints for learner and actor functions

* refactor(rl): hoist grpcio guard to module top in actor/learner

* chore(rl): manage import pattern in actor (#3564)

* chore(rl): manage import pattern in actor

* chore(rl): optional grpc imports in learner; quote grpc ServicerContext types

---------

Co-authored-by: Khalil Meftah <khalil.meftah@huggingface.co>

* update uv.lock

* chore(doc): update doc

---------

Co-authored-by: jpizarrom <jpizarrom@gmail.com>
Co-authored-by: Steven Palma <imstevenpmwork@ieee.org>
2026-05-12 15:49:54 +02:00

529 lines
19 KiB
Python

# !/usr/bin/env python
# Copyright 2025 The HuggingFace Inc. team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import pytest
pytest.importorskip("datasets", reason="datasets is required (install lerobot[dataset])")
import torch # noqa: E402
from torch import Tensor, nn # noqa: E402
from lerobot.configs.types import FeatureType, PolicyFeature # noqa: E402
from lerobot.policies.gaussian_actor.configuration_gaussian_actor import GaussianActorConfig # noqa: E402
from lerobot.policies.gaussian_actor.modeling_gaussian_actor import MLP, GaussianActorPolicy # noqa: E402
from lerobot.rl.algorithms.sac import SACAlgorithm, SACAlgorithmConfig # noqa: E402
from lerobot.utils.constants import ACTION, OBS_IMAGE, OBS_STATE # noqa: E402
from lerobot.utils.random_utils import seeded_context, set_seed # noqa: E402
try:
import transformers # noqa: F401
TRANSFORMERS_AVAILABLE = True
except ImportError:
TRANSFORMERS_AVAILABLE = False
@pytest.fixture(autouse=True)
def set_random_seed():
seed = 42
set_seed(seed)
def test_mlp_with_default_args():
mlp = MLP(input_dim=10, hidden_dims=[256, 256])
x = torch.randn(10)
y = mlp(x)
assert y.shape == (256,)
def test_mlp_with_batch_dim():
mlp = MLP(input_dim=10, hidden_dims=[256, 256])
x = torch.randn(2, 10)
y = mlp(x)
assert y.shape == (2, 256)
def test_forward_with_empty_hidden_dims():
mlp = MLP(input_dim=10, hidden_dims=[])
x = torch.randn(1, 10)
assert mlp(x).shape == (1, 10)
def test_mlp_with_dropout():
mlp = MLP(input_dim=10, hidden_dims=[256, 256, 11], dropout_rate=0.1)
x = torch.randn(1, 10)
y = mlp(x)
assert y.shape == (1, 11)
drop_out_layers_count = sum(isinstance(layer, nn.Dropout) for layer in mlp.net)
assert drop_out_layers_count == 2
def test_mlp_with_custom_final_activation():
mlp = MLP(input_dim=10, hidden_dims=[256, 256], final_activation=torch.nn.Tanh())
x = torch.randn(1, 10)
y = mlp(x)
assert y.shape == (1, 256)
assert (y >= -1).all() and (y <= 1).all()
def test_gaussian_actor_policy_with_default_args():
with pytest.raises(ValueError, match="should be an instance of class `PreTrainedConfig`"):
GaussianActorPolicy()
def create_dummy_state(batch_size: int, state_dim: int = 10) -> Tensor:
return {
OBS_STATE: torch.randn(batch_size, state_dim),
}
def create_dummy_with_visual_input(batch_size: int, state_dim: int = 10) -> Tensor:
return {
OBS_IMAGE: torch.randn(batch_size, 3, 84, 84),
OBS_STATE: torch.randn(batch_size, state_dim),
}
def create_dummy_action(batch_size: int, action_dim: int = 10) -> Tensor:
return torch.randn(batch_size, action_dim)
def create_default_train_batch(
batch_size: int = 8, state_dim: int = 10, action_dim: int = 10
) -> dict[str, Tensor]:
return {
ACTION: create_dummy_action(batch_size, action_dim),
"reward": torch.randn(batch_size),
"state": create_dummy_state(batch_size, state_dim),
"next_state": create_dummy_state(batch_size, state_dim),
"done": torch.randn(batch_size),
}
def create_train_batch_with_visual_input(
batch_size: int = 8, state_dim: int = 10, action_dim: int = 10
) -> dict[str, Tensor]:
return {
ACTION: create_dummy_action(batch_size, action_dim),
"reward": torch.randn(batch_size),
"state": create_dummy_with_visual_input(batch_size, state_dim),
"next_state": create_dummy_with_visual_input(batch_size, state_dim),
"done": torch.randn(batch_size),
}
def create_observation_batch(batch_size: int = 8, state_dim: int = 10) -> dict[str, Tensor]:
return {
OBS_STATE: torch.randn(batch_size, state_dim),
}
def create_observation_batch_with_visual_input(batch_size: int = 8, state_dim: int = 10) -> dict[str, Tensor]:
return {
OBS_STATE: torch.randn(batch_size, state_dim),
OBS_IMAGE: torch.randn(batch_size, 3, 84, 84),
}
def create_default_config(
state_dim: int, continuous_action_dim: int, has_discrete_action: bool = False
) -> GaussianActorConfig:
action_dim = continuous_action_dim
if has_discrete_action:
action_dim += 1
config = GaussianActorConfig(
input_features={OBS_STATE: PolicyFeature(type=FeatureType.STATE, shape=(state_dim,))},
output_features={ACTION: PolicyFeature(type=FeatureType.ACTION, shape=(continuous_action_dim,))},
dataset_stats={
OBS_STATE: {
"min": [0.0] * state_dim,
"max": [1.0] * state_dim,
},
ACTION: {
"min": [0.0] * continuous_action_dim,
"max": [1.0] * continuous_action_dim,
},
},
)
config.validate_features()
return config
def create_config_with_visual_input(
state_dim: int, continuous_action_dim: int, has_discrete_action: bool = False
) -> GaussianActorConfig:
config = create_default_config(
state_dim=state_dim,
continuous_action_dim=continuous_action_dim,
has_discrete_action=has_discrete_action,
)
config.input_features[OBS_IMAGE] = PolicyFeature(type=FeatureType.VISUAL, shape=(3, 84, 84))
config.dataset_stats[OBS_IMAGE] = {
"mean": torch.randn(3, 1, 1),
"std": torch.randn(3, 1, 1),
}
config.state_encoder_hidden_dim = 32
config.latent_dim = 32
config.validate_features()
return config
def _make_algorithm(config: GaussianActorConfig) -> tuple[SACAlgorithm, GaussianActorPolicy]:
"""Helper to create policy + algorithm pair for tests that need critics."""
policy = GaussianActorPolicy(config=config)
policy.train()
algo_config = SACAlgorithmConfig.from_policy_config(config)
algorithm = SACAlgorithm(policy=policy, config=algo_config)
algorithm.make_optimizers_and_scheduler()
return algorithm, policy
@pytest.mark.parametrize("batch_size,state_dim,action_dim", [(2, 6, 6), (1, 10, 10)])
def test_gaussian_actor_policy_select_action(batch_size: int, state_dim: int, action_dim: int):
config = create_default_config(state_dim=state_dim, continuous_action_dim=action_dim)
policy = GaussianActorPolicy(config=config)
policy.eval()
with torch.no_grad():
observation_batch = create_observation_batch(batch_size=batch_size, state_dim=state_dim)
selected_action = policy.select_action(observation_batch)
# squeeze(0) removes batch dim when batch_size==1
assert selected_action.shape[-1] == action_dim
def test_gaussian_actor_policy_select_action_with_discrete():
"""select_action should return continuous + discrete actions."""
config = create_default_config(state_dim=10, continuous_action_dim=6)
config.num_discrete_actions = 3
policy = GaussianActorPolicy(config=config)
policy.eval()
with torch.no_grad():
observation_batch = create_observation_batch(batch_size=1, state_dim=10)
# Squeeze to unbatched (single observation)
observation_batch = {k: v.squeeze(0) for k, v in observation_batch.items()}
selected_action = policy.select_action(observation_batch)
assert selected_action.shape[-1] == 7 # 6 continuous + 1 discrete
@pytest.mark.parametrize("batch_size,state_dim,action_dim", [(2, 6, 6), (1, 10, 10)])
def test_gaussian_actor_policy_forward(batch_size: int, state_dim: int, action_dim: int):
config = create_default_config(state_dim=state_dim, continuous_action_dim=action_dim)
policy = GaussianActorPolicy(config=config)
policy.eval()
batch = create_default_train_batch(batch_size=batch_size, action_dim=action_dim, state_dim=state_dim)
with torch.no_grad():
output = policy.forward(batch)
assert "action" in output
assert "log_prob" in output
assert "action_mean" in output
assert output["action"].shape == (batch_size, action_dim)
@pytest.mark.parametrize("batch_size,state_dim,action_dim", [(2, 6, 6), (1, 10, 10)])
def test_gaussian_actor_training_through_sac(batch_size: int, state_dim: int, action_dim: int):
config = create_default_config(state_dim=state_dim, continuous_action_dim=action_dim)
algorithm, policy = _make_algorithm(config)
batch = create_default_train_batch(batch_size=batch_size, action_dim=action_dim, state_dim=state_dim)
forward_batch = algorithm._prepare_forward_batch(batch)
critic_loss = algorithm._compute_loss_critic(forward_batch)
assert critic_loss.item() is not None
assert critic_loss.shape == ()
algorithm.optimizers["critic"].zero_grad()
critic_loss.backward()
algorithm.optimizers["critic"].step()
actor_loss = algorithm._compute_loss_actor(forward_batch)
assert actor_loss.item() is not None
assert actor_loss.shape == ()
algorithm.optimizers["actor"].zero_grad()
actor_loss.backward()
algorithm.optimizers["actor"].step()
temp_loss = algorithm._compute_loss_temperature(forward_batch)
assert temp_loss.item() is not None
assert temp_loss.shape == ()
algorithm.optimizers["temperature"].zero_grad()
temp_loss.backward()
algorithm.optimizers["temperature"].step()
@pytest.mark.parametrize("batch_size,state_dim,action_dim", [(2, 6, 6), (1, 10, 10)])
def test_gaussian_actor_training_with_visual_input(batch_size: int, state_dim: int, action_dim: int):
config = create_config_with_visual_input(state_dim=state_dim, continuous_action_dim=action_dim)
algorithm, policy = _make_algorithm(config)
batch = create_train_batch_with_visual_input(
batch_size=batch_size, state_dim=state_dim, action_dim=action_dim
)
forward_batch = algorithm._prepare_forward_batch(batch)
critic_loss = algorithm._compute_loss_critic(forward_batch)
assert critic_loss.item() is not None
assert critic_loss.shape == ()
algorithm.optimizers["critic"].zero_grad()
critic_loss.backward()
algorithm.optimizers["critic"].step()
actor_loss = algorithm._compute_loss_actor(forward_batch)
assert actor_loss.item() is not None
assert actor_loss.shape == ()
algorithm.optimizers["actor"].zero_grad()
actor_loss.backward()
algorithm.optimizers["actor"].step()
policy.eval()
with torch.no_grad():
observation_batch = create_observation_batch_with_visual_input(
batch_size=batch_size, state_dim=state_dim
)
selected_action = policy.select_action(observation_batch)
assert selected_action.shape[-1] == action_dim
@pytest.mark.parametrize(
"batch_size,state_dim,action_dim,vision_encoder_name",
[(1, 6, 6, "lerobot/resnet10"), (1, 6, 6, "facebook/convnext-base-224")],
)
@pytest.mark.skipif(not TRANSFORMERS_AVAILABLE, reason="Transformers are not installed")
def test_gaussian_actor_policy_with_pretrained_encoder(
batch_size: int, state_dim: int, action_dim: int, vision_encoder_name: str
):
config = create_config_with_visual_input(state_dim=state_dim, continuous_action_dim=action_dim)
config.vision_encoder_name = vision_encoder_name
algorithm, policy = _make_algorithm(config)
batch = create_train_batch_with_visual_input(
batch_size=batch_size, state_dim=state_dim, action_dim=action_dim
)
forward_batch = algorithm._prepare_forward_batch(batch)
critic_loss = algorithm._compute_loss_critic(forward_batch)
assert critic_loss.item() is not None
assert critic_loss.shape == ()
algorithm.optimizers["critic"].zero_grad()
critic_loss.backward()
algorithm.optimizers["critic"].step()
actor_loss = algorithm._compute_loss_actor(forward_batch)
assert actor_loss.item() is not None
assert actor_loss.shape == ()
def test_gaussian_actor_training_with_shared_encoder():
batch_size = 2
action_dim = 10
state_dim = 10
config = create_config_with_visual_input(state_dim=state_dim, continuous_action_dim=action_dim)
config.shared_encoder = True
algorithm, policy = _make_algorithm(config)
batch = create_train_batch_with_visual_input(
batch_size=batch_size, state_dim=state_dim, action_dim=action_dim
)
forward_batch = algorithm._prepare_forward_batch(batch)
critic_loss = algorithm._compute_loss_critic(forward_batch)
assert critic_loss.shape == ()
algorithm.optimizers["critic"].zero_grad()
critic_loss.backward()
algorithm.optimizers["critic"].step()
actor_loss = algorithm._compute_loss_actor(forward_batch)
assert actor_loss.shape == ()
algorithm.optimizers["actor"].zero_grad()
actor_loss.backward()
algorithm.optimizers["actor"].step()
def test_gaussian_actor_training_with_discrete_critic():
batch_size = 2
continuous_action_dim = 9
full_action_dim = continuous_action_dim + 1
state_dim = 10
config = create_config_with_visual_input(
state_dim=state_dim, continuous_action_dim=continuous_action_dim, has_discrete_action=True
)
config.num_discrete_actions = 5
algorithm, policy = _make_algorithm(config)
batch = create_train_batch_with_visual_input(
batch_size=batch_size, state_dim=state_dim, action_dim=full_action_dim
)
forward_batch = algorithm._prepare_forward_batch(batch)
critic_loss = algorithm._compute_loss_critic(forward_batch)
assert critic_loss.shape == ()
algorithm.optimizers["critic"].zero_grad()
critic_loss.backward()
algorithm.optimizers["critic"].step()
discrete_critic_loss = algorithm._compute_loss_discrete_critic(forward_batch)
assert discrete_critic_loss.shape == ()
algorithm.optimizers["discrete_critic"].zero_grad()
discrete_critic_loss.backward()
algorithm.optimizers["discrete_critic"].step()
actor_loss = algorithm._compute_loss_actor(forward_batch)
assert actor_loss.shape == ()
algorithm.optimizers["actor"].zero_grad()
actor_loss.backward()
algorithm.optimizers["actor"].step()
policy.eval()
with torch.no_grad():
observation_batch = create_observation_batch_with_visual_input(
batch_size=batch_size, state_dim=state_dim
)
# Policy.select_action now handles both continuous + discrete
selected_action = policy.select_action({k: v.squeeze(0) for k, v in observation_batch.items()})
assert selected_action.shape[-1] == continuous_action_dim + 1
def test_sac_algorithm_target_entropy():
"""Target entropy is an SAC hyperparameter and lives on the algorithm."""
config = create_default_config(continuous_action_dim=10, state_dim=10)
algorithm, _ = _make_algorithm(config)
assert algorithm.target_entropy == -5.0
def test_sac_algorithm_target_entropy_with_discrete_action():
config = create_config_with_visual_input(state_dim=10, continuous_action_dim=6, has_discrete_action=True)
config.num_discrete_actions = 5
algorithm, _ = _make_algorithm(config)
assert algorithm.target_entropy == -3.5
def test_sac_algorithm_temperature():
import math
config = create_default_config(continuous_action_dim=10, state_dim=10)
algo_config = SACAlgorithmConfig.from_policy_config(config)
policy = GaussianActorPolicy(config=config)
algorithm = SACAlgorithm(policy=policy, config=algo_config)
assert algorithm.temperature == pytest.approx(1.0)
algorithm.log_alpha.data = torch.tensor([math.log(0.1)])
assert algorithm.temperature == pytest.approx(0.1)
def test_sac_algorithm_update_target_network():
config = create_default_config(state_dim=10, continuous_action_dim=6)
algo_config = SACAlgorithmConfig.from_policy_config(config)
algo_config.critic_target_update_weight = 1.0
policy = GaussianActorPolicy(config=config)
algorithm = SACAlgorithm(policy=policy, config=algo_config)
for p in algorithm.critic_ensemble.parameters():
p.data = torch.ones_like(p.data)
algorithm._update_target_networks()
for p in algorithm.critic_target.parameters():
assert torch.allclose(p.data, torch.ones_like(p.data))
@pytest.mark.parametrize("num_critics", [1, 3])
def test_sac_algorithm_with_critics_number_of_heads(num_critics: int):
batch_size = 2
action_dim = 10
state_dim = 10
config = create_config_with_visual_input(state_dim=state_dim, continuous_action_dim=action_dim)
policy = GaussianActorPolicy(config=config)
policy.train()
algo_config = SACAlgorithmConfig.from_policy_config(config)
algo_config.num_critics = num_critics
algorithm = SACAlgorithm(policy=policy, config=algo_config)
algorithm.make_optimizers_and_scheduler()
assert len(algorithm.critic_ensemble.critics) == num_critics
batch = create_train_batch_with_visual_input(
batch_size=batch_size, state_dim=state_dim, action_dim=action_dim
)
forward_batch = algorithm._prepare_forward_batch(batch)
critic_loss = algorithm._compute_loss_critic(forward_batch)
assert critic_loss.shape == ()
algorithm.optimizers["critic"].zero_grad()
critic_loss.backward()
algorithm.optimizers["critic"].step()
def test_gaussian_actor_policy_save_and_load(tmp_path):
"""Test that the policy can be saved and loaded from pretrained."""
root = tmp_path / "test_gaussian_actor_save_and_load"
state_dim = 10
action_dim = 10
batch_size = 2
config = create_default_config(state_dim=state_dim, continuous_action_dim=action_dim)
policy = GaussianActorPolicy(config=config)
policy.eval()
policy.save_pretrained(root)
loaded_policy = GaussianActorPolicy.from_pretrained(root, config=config)
loaded_policy.eval()
assert policy.state_dict().keys() == loaded_policy.state_dict().keys()
for k in policy.state_dict():
assert torch.allclose(policy.state_dict()[k], loaded_policy.state_dict()[k], atol=1e-6)
with torch.no_grad():
with seeded_context(12):
observation_batch = create_observation_batch(batch_size=batch_size, state_dim=state_dim)
actions = policy.select_action(observation_batch)
with seeded_context(12):
loaded_observation_batch = create_observation_batch(batch_size=batch_size, state_dim=state_dim)
loaded_actions = loaded_policy.select_action(loaded_observation_batch)
assert torch.allclose(actions, loaded_actions)
def test_gaussian_actor_policy_save_and_load_with_discrete_critic(tmp_path):
"""Discrete critic should be saved/loaded as part of the policy."""
root = tmp_path / "test_gaussian_actor_save_and_load_discrete"
state_dim = 10
action_dim = 6
config = create_default_config(state_dim=state_dim, continuous_action_dim=action_dim)
config.num_discrete_actions = 3
policy = GaussianActorPolicy(config=config)
policy.eval()
policy.save_pretrained(root)
loaded_policy = GaussianActorPolicy.from_pretrained(root, config=config)
loaded_policy.eval()
assert loaded_policy.discrete_critic is not None
dc_keys = [k for k in loaded_policy.state_dict() if k.startswith("discrete_critic.")]
assert len(dc_keys) > 0
for k in policy.state_dict():
assert torch.allclose(policy.state_dict()[k], loaded_policy.state_dict()[k], atol=1e-6)