Source code for ding.model.template.qac
from typing import Union, Dict, Optional
from easydict import EasyDict
import numpy as np
import torch
import torch.nn as nn
from ding.utils import SequenceType, squeeze, MODEL_REGISTRY
from ..common import RegressionHead, ReparameterizationHead, DiscreteHead, MultiHead, \
FCEncoder, ConvEncoder
[docs]@MODEL_REGISTRY.register('continuous_qac')
class ContinuousQAC(nn.Module):
"""
Overview:
The neural network and computation graph of algorithms related to Q-value Actor-Critic (QAC), such as \
DDPG/TD3/SAC. This model now supports continuous and hybrid action space. The ContinuousQAC is composed of \
four parts: ``actor_encoder``, ``critic_encoder``, ``actor_head`` and ``critic_head``. Encoders are used to \
extract the feature from various observation. Heads are used to predict corresponding Q-value or action logit. \
In high-dimensional observation space like 2D image, we often use a shared encoder for both ``actor_encoder`` \
and ``critic_encoder``. In low-dimensional observation space like 1D vector, we often use different encoders.
Interfaces:
``__init__``, ``forward``, ``compute_actor``, ``compute_critic``
"""
mode = ['compute_actor', 'compute_critic']
[docs] def __init__(
self,
obs_shape: Union[int, SequenceType],
action_shape: Union[int, SequenceType, EasyDict],
action_space: str,
twin_critic: bool = False,
actor_head_hidden_size: int = 64,
actor_head_layer_num: int = 1,
critic_head_hidden_size: int = 64,
critic_head_layer_num: int = 1,
activation: Optional[nn.Module] = nn.ReLU(),
norm_type: Optional[str] = None,
encoder_hidden_size_list: Optional[SequenceType] = None,
share_encoder: Optional[bool] = False,
) -> None:
"""
Overview:
Initailize the ContinuousQAC Model according to input arguments.
Arguments:
- obs_shape (:obj:`Union[int, SequenceType]`): Observation's shape, such as 128, (156, ).
- action_shape (:obj:`Union[int, SequenceType, EasyDict]`): Action's shape, such as 4, (3, ), \
EasyDict({'action_type_shape': 3, 'action_args_shape': 4}).
- action_space (:obj:`str`): The type of action space, including [``regression``, ``reparameterization``, \
``hybrid``], ``regression`` is used for DDPG/TD3, ``reparameterization`` is used for SAC and \
``hybrid`` for PADDPG.
- twin_critic (:obj:`bool`): Whether to use twin critic, one of tricks in TD3.
- actor_head_hidden_size (:obj:`Optional[int]`): The ``hidden_size`` to pass to actor head.
- actor_head_layer_num (:obj:`int`): The num of layers used in the actor network to compute action.
- critic_head_hidden_size (:obj:`Optional[int]`): The ``hidden_size`` to pass to critic head.
- critic_head_layer_num (:obj:`int`): The num of layers used in the critic network to compute Q-value.
- activation (:obj:`Optional[nn.Module]`): The type of activation function to use in ``MLP`` \
after each FC layer, if ``None`` then default set to ``nn.ReLU()``.
- norm_type (:obj:`Optional[str]`): The type of normalization to after network layer (FC, Conv), \
see ``ding.torch_utils.network`` for more details.
- encoder_hidden_size_list (:obj:`SequenceType`): Collection of ``hidden_size`` to pass to ``Encoder``, \
the last element must match ``head_hidden_size``, this argument is only used in image observation.
- share_encoder (:obj:`Optional[bool]`): Whether to share encoder between actor and critic.
"""
super(ContinuousQAC, self).__init__()
obs_shape: int = squeeze(obs_shape)
action_shape = squeeze(action_shape)
self.action_shape = action_shape
self.action_space = action_space
assert self.action_space in ['regression', 'reparameterization', 'hybrid'], self.action_space
# encoder
self.share_encoder = share_encoder
if np.isscalar(obs_shape) or len(obs_shape) == 1:
assert not self.share_encoder, "Vector observation doesn't need share encoder."
assert encoder_hidden_size_list is None, "Vector obs encoder only uses one layer nn.Linear"
# Because there is already a layer nn.Linear in the head, so we use nn.Identity here to keep
# compatible with the image observation and avoid adding an extra layer nn.Linear.
self.actor_encoder = nn.Identity()
self.critic_encoder = nn.Identity()
encoder_output_size = obs_shape
elif len(obs_shape) == 3:
def setup_conv_encoder():
kernel_size = [3 for _ in range(len(encoder_hidden_size_list))]
stride = [2] + [1 for _ in range(len(encoder_hidden_size_list) - 1)]
return ConvEncoder(
obs_shape,
encoder_hidden_size_list,
activation=activation,
norm_type=norm_type,
kernel_size=kernel_size,
stride=stride
)
if self.share_encoder:
encoder = setup_conv_encoder()
self.actor_encoder = self.critic_encoder = encoder
else:
self.actor_encoder = setup_conv_encoder()
self.critic_encoder = setup_conv_encoder()
encoder_output_size = self.actor_encoder.output_size
else:
raise RuntimeError("not support observation shape: {}".format(obs_shape))
# head
if self.action_space == 'regression': # DDPG, TD3
self.actor_head = nn.Sequential(
nn.Linear(encoder_output_size, actor_head_hidden_size), activation,
RegressionHead(
actor_head_hidden_size,
action_shape,
actor_head_layer_num,
final_tanh=True,
activation=activation,
norm_type=norm_type
)
)
elif self.action_space == 'reparameterization': # SAC
self.actor_head = nn.Sequential(
nn.Linear(encoder_output_size, actor_head_hidden_size), activation,
ReparameterizationHead(
actor_head_hidden_size,
action_shape,
actor_head_layer_num,
sigma_type='conditioned',
activation=activation,
norm_type=norm_type
)
)
elif self.action_space == 'hybrid': # PADDPG
# hybrid action space: action_type(discrete) + action_args(continuous),
# such as {'action_type_shape': torch.LongTensor([0]), 'action_args_shape': torch.FloatTensor([0.1, -0.27])}
action_shape.action_args_shape = squeeze(action_shape.action_args_shape)
action_shape.action_type_shape = squeeze(action_shape.action_type_shape)
actor_action_args = nn.Sequential(
nn.Linear(encoder_output_size, actor_head_hidden_size), activation,
RegressionHead(
actor_head_hidden_size,
action_shape.action_args_shape,
actor_head_layer_num,
final_tanh=True,
activation=activation,
norm_type=norm_type
)
)
actor_action_type = nn.Sequential(
nn.Linear(encoder_output_size, actor_head_hidden_size), activation,
DiscreteHead(
actor_head_hidden_size,
action_shape.action_type_shape,
actor_head_layer_num,
activation=activation,
norm_type=norm_type,
)
)
self.actor_head = nn.ModuleList([actor_action_type, actor_action_args])
self.twin_critic = twin_critic
if self.action_space == 'hybrid':
critic_input_size = encoder_output_size + action_shape.action_type_shape + action_shape.action_args_shape
else:
critic_input_size = encoder_output_size + action_shape
if self.twin_critic:
self.critic_head = nn.ModuleList()
for _ in range(2):
self.critic_head.append(
nn.Sequential(
nn.Linear(critic_input_size, critic_head_hidden_size), activation,
RegressionHead(
critic_head_hidden_size,
1,
critic_head_layer_num,
final_tanh=False,
activation=activation,
norm_type=norm_type
)
)
)
else:
self.critic_head = nn.Sequential(
nn.Linear(critic_input_size, critic_head_hidden_size), activation,
RegressionHead(
critic_head_hidden_size,
1,
critic_head_layer_num,
final_tanh=False,
activation=activation,
norm_type=norm_type
)
)
# Convenient for calling some apis (e.g. self.critic.parameters()),
# but may cause misunderstanding when `print(self)`
self.actor = nn.ModuleList([self.actor_encoder, self.actor_head])
self.critic = nn.ModuleList([self.critic_encoder, self.critic_head])
[docs] def forward(self, inputs: Union[torch.Tensor, Dict[str, torch.Tensor]], mode: str) -> Dict[str, torch.Tensor]:
"""
Overview:
QAC forward computation graph, input observation tensor to predict Q-value or action logit. Different \
``mode`` will forward with different network modules to get different outputs and save computation.
Arguments:
- inputs (:obj:`Union[torch.Tensor, Dict[str, torch.Tensor]]`): The input data for forward computation \
graph, for ``compute_actor``, it is the observation tensor, for ``compute_critic``, it is the \
dict data including obs and action tensor.
- mode (:obj:`str`): The forward mode, all the modes are defined in the beginning of this class.
Returns:
- output (:obj:`Dict[str, torch.Tensor]`): The output dict of QAC forward computation graph, whose \
key-values vary in different forward modes.
Examples (Actor):
>>> # Regression mode
>>> model = ContinuousQAC(64, 6, 'regression')
>>> obs = torch.randn(4, 64)
>>> actor_outputs = model(obs,'compute_actor')
>>> assert actor_outputs['action'].shape == torch.Size([4, 6])
>>> # Reparameterization Mode
>>> model = ContinuousQAC(64, 6, 'reparameterization')
>>> obs = torch.randn(4, 64)
>>> actor_outputs = model(obs,'compute_actor')
>>> assert actor_outputs['logit'][0].shape == torch.Size([4, 6]) # mu
>>> actor_outputs['logit'][1].shape == torch.Size([4, 6]) # sigma
Examples (Critic):
>>> inputs = {'obs': torch.randn(4, 8), 'action': torch.randn(4, 1)}
>>> model = ContinuousQAC(obs_shape=(8, ),action_shape=1, action_space='regression')
>>> assert model(inputs, mode='compute_critic')['q_value'].shape == (4, ) # q value
"""
assert mode in self.mode, "not support forward mode: {}/{}".format(mode, self.mode)
return getattr(self, mode)(inputs)
[docs] def compute_actor(self, obs: torch.Tensor) -> Dict[str, Union[torch.Tensor, Dict[str, torch.Tensor]]]:
"""
Overview:
QAC forward computation graph for actor part, input observation tensor to predict action or action logit.
Arguments:
- x (:obj:`torch.Tensor`): The input observation tensor data.
Returns:
- outputs (:obj:`Dict[str, Union[torch.Tensor, Dict[str, torch.Tensor]]]`): Actor output dict varying \
from action_space: ``regression``, ``reparameterization``, ``hybrid``.
ReturnsKeys (regression):
- action (:obj:`torch.Tensor`): Continuous action with same size as ``action_shape``, usually in DDPG/TD3.
ReturnsKeys (reparameterization):
- logit (:obj:`Dict[str, torch.Tensor]`): The predictd reparameterization action logit, usually in SAC. \
It is a list containing two tensors: ``mu`` and ``sigma``. The former is the mean of the gaussian \
distribution, the latter is the standard deviation of the gaussian distribution.
ReturnsKeys (hybrid):
- logit (:obj:`torch.Tensor`): The predicted discrete action type logit, it will be the same dimension \
as ``action_type_shape``, i.e., all the possible discrete action types.
- action_args (:obj:`torch.Tensor`): Continuous action arguments with same size as ``action_args_shape``.
Shapes:
- obs (:obj:`torch.Tensor`): :math:`(B, N0)`, B is batch size and N0 corresponds to ``obs_shape``.
- action (:obj:`torch.Tensor`): :math:`(B, N1)`, B is batch size and N1 corresponds to ``action_shape``.
- logit.mu (:obj:`torch.Tensor`): :math:`(B, N1)`, B is batch size and N1 corresponds to ``action_shape``.
- logit.sigma (:obj:`torch.Tensor`): :math:`(B, N1)`, B is batch size.
- logit (:obj:`torch.Tensor`): :math:`(B, N2)`, B is batch size and N2 corresponds to \
``action_shape.action_type_shape``.
- action_args (:obj:`torch.Tensor`): :math:`(B, N3)`, B is batch size and N3 corresponds to \
``action_shape.action_args_shape``.
Examples:
>>> # Regression mode
>>> model = ContinuousQAC(64, 6, 'regression')
>>> obs = torch.randn(4, 64)
>>> actor_outputs = model(obs,'compute_actor')
>>> assert actor_outputs['action'].shape == torch.Size([4, 6])
>>> # Reparameterization Mode
>>> model = ContinuousQAC(64, 6, 'reparameterization')
>>> obs = torch.randn(4, 64)
>>> actor_outputs = model(obs,'compute_actor')
>>> assert actor_outputs['logit'][0].shape == torch.Size([4, 6]) # mu
>>> actor_outputs['logit'][1].shape == torch.Size([4, 6]) # sigma
"""
obs = self.actor_encoder(obs)
if self.action_space == 'regression':
x = self.actor_head(obs)
return {'action': x['pred']}
elif self.action_space == 'reparameterization':
x = self.actor_head(obs)
return {'logit': [x['mu'], x['sigma']]}
elif self.action_space == 'hybrid':
logit = self.actor_head[0](obs)
action_args = self.actor_head[1](obs)
return {'logit': logit['logit'], 'action_args': action_args['pred']}
[docs] def compute_critic(self, inputs: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
"""
Overview:
QAC forward computation graph for critic part, input observation and action tensor to predict Q-value.
Arguments:
- inputs (:obj:`Dict[str, torch.Tensor]`): The dict of input data, including ``obs`` and ``action`` \
tensor, also contains ``logit`` and ``action_args`` tensor in hybrid action_space.
ArgumentsKeys:
- obs: (:obj:`torch.Tensor`): Observation tensor data, now supports a batch of 1-dim vector data.
- action (:obj:`Union[torch.Tensor, Dict]`): Continuous action with same size as ``action_shape``.
- logit (:obj:`torch.Tensor`): Discrete action logit, only in hybrid action_space.
- action_args (:obj:`torch.Tensor`): Continuous action arguments, only in hybrid action_space.
Returns:
- outputs (:obj:`Dict[str, torch.Tensor]`): The output dict of QAC's forward computation graph for critic, \
including ``q_value``.
ReturnKeys:
- q_value (:obj:`torch.Tensor`): Q value tensor with same size as batch size.
Shapes:
- obs (:obj:`torch.Tensor`): :math:`(B, N1)`, where B is batch size and N1 is ``obs_shape``.
- logit (:obj:`torch.Tensor`): :math:`(B, N2)`, B is batch size and N2 corresponds to \
``action_shape.action_type_shape``.
- action_args (:obj:`torch.Tensor`): :math:`(B, N3)`, B is batch size and N3 corresponds to \
``action_shape.action_args_shape``.
- action (:obj:`torch.Tensor`): :math:`(B, N4)`, where B is batch size and N4 is ``action_shape``.
- q_value (:obj:`torch.Tensor`): :math:`(B, )`, where B is batch size.
Examples:
>>> inputs = {'obs': torch.randn(4, 8), 'action': torch.randn(4, 1)}
>>> model = ContinuousQAC(obs_shape=(8, ),action_shape=1, action_space='regression')
>>> assert model(inputs, mode='compute_critic')['q_value'].shape == (4, ) # q value
"""
obs, action = inputs['obs'], inputs['action']
obs = self.critic_encoder(obs)
assert len(obs.shape) == 2
if self.action_space == 'hybrid':
action_type_logit = inputs['logit']
action_type_logit = torch.softmax(action_type_logit, dim=-1)
action_args = action['action_args']
if len(action_args.shape) == 1:
action_args = action_args.unsqueeze(1)
x = torch.cat([obs, action_type_logit, action_args], dim=1)
else:
if len(action.shape) == 1: # (B, ) -> (B, 1)
action = action.unsqueeze(1)
x = torch.cat([obs, action], dim=1)
if self.twin_critic:
x = [m(x)['pred'] for m in self.critic_head]
else:
x = self.critic_head(x)['pred']
return {'q_value': x}
[docs]@MODEL_REGISTRY.register('discrete_qac')
class DiscreteQAC(nn.Module):
"""
Overview:
The neural network and computation graph of algorithms related to discrete action Q-value Actor-Critic (QAC), \
such as DiscreteSAC. This model now supports only discrete action space. The DiscreteQAC is composed of \
four parts: ``actor_encoder``, ``critic_encoder``, ``actor_head`` and ``critic_head``. Encoders are used to \
extract the feature from various observation. Heads are used to predict corresponding Q-value or action logit. \
In high-dimensional observation space like 2D image, we often use a shared encoder for both ``actor_encoder`` \
and ``critic_encoder``. In low-dimensional observation space like 1D vector, we often use different encoders.
Interfaces:
``__init__``, ``forward``, ``compute_actor``, ``compute_critic``
"""
mode = ['compute_actor', 'compute_critic']
[docs] def __init__(
self,
obs_shape: Union[int, SequenceType],
action_shape: Union[int, SequenceType],
twin_critic: bool = False,
actor_head_hidden_size: int = 64,
actor_head_layer_num: int = 1,
critic_head_hidden_size: int = 64,
critic_head_layer_num: int = 1,
activation: Optional[nn.Module] = nn.ReLU(),
norm_type: Optional[str] = None,
encoder_hidden_size_list: SequenceType = None,
share_encoder: Optional[bool] = False,
) -> None:
"""
Overview:
Initailize the DiscreteQAC Model according to input arguments.
Arguments:
- obs_shape (:obj:`Union[int, SequenceType]`): Observation's shape, such as 128, (156, ).
- action_shape (:obj:`Union[int, SequenceType, EasyDict]`): Action's shape, such as 4, (3, ).
- twin_critic (:obj:`bool`): Whether to use twin critic.
- actor_head_hidden_size (:obj:`Optional[int]`): The ``hidden_size`` to pass to actor head.
- actor_head_layer_num (:obj:`int`): The num of layers used in the actor network to compute action.
- critic_head_hidden_size (:obj:`Optional[int]`): The ``hidden_size`` to pass to critic head.
- critic_head_layer_num (:obj:`int`): The num of layers used in the critic network to compute Q-value.
- activation (:obj:`Optional[nn.Module]`): The type of activation function to use in ``MLP`` \
after each FC layer, if ``None`` then default set to ``nn.ReLU()``.
- norm_type (:obj:`Optional[str]`): The type of normalization to after network layer (FC, Conv), \
see ``ding.torch_utils.network`` for more details.
- encoder_hidden_size_list (:obj:`SequenceType`): Collection of ``hidden_size`` to pass to ``Encoder``, \
the last element must match ``head_hidden_size``, this argument is only used in image observation.
- share_encoder (:obj:`Optional[bool]`): Whether to share encoder between actor and critic.
"""
super(DiscreteQAC, self).__init__()
obs_shape: int = squeeze(obs_shape)
action_shape: int = squeeze(action_shape)
# encoder
self.share_encoder = share_encoder
if np.isscalar(obs_shape) or len(obs_shape) == 1:
assert not self.share_encoder, "Vector observation doesn't need share encoder."
assert encoder_hidden_size_list is None, "Vector obs encoder only uses one layer nn.Linear"
# Because there is already a layer nn.Linear in the head, so we use nn.Identity here to keep
# compatible with the image observation and avoid adding an extra layer nn.Linear.
self.actor_encoder = nn.Identity()
self.critic_encoder = nn.Identity()
encoder_output_size = obs_shape
elif len(obs_shape) == 3:
def setup_conv_encoder():
kernel_size = [3 for _ in range(len(encoder_hidden_size_list))]
stride = [2] + [1 for _ in range(len(encoder_hidden_size_list) - 1)]
return ConvEncoder(
obs_shape,
encoder_hidden_size_list,
activation=activation,
norm_type=norm_type,
kernel_size=kernel_size,
stride=stride
)
if self.share_encoder:
encoder = setup_conv_encoder()
self.actor_encoder = self.critic_encoder = encoder
else:
self.actor_encoder = setup_conv_encoder()
self.critic_encoder = setup_conv_encoder()
encoder_output_size = self.actor_encoder.output_size
else:
raise RuntimeError("not support observation shape: {}".format(obs_shape))
# head
self.actor_head = nn.Sequential(
nn.Linear(encoder_output_size, actor_head_hidden_size), activation,
DiscreteHead(
actor_head_hidden_size, action_shape, actor_head_layer_num, activation=activation, norm_type=norm_type
)
)
self.twin_critic = twin_critic
if self.twin_critic:
self.critic_head = nn.ModuleList()
for _ in range(2):
self.critic_head.append(
nn.Sequential(
nn.Linear(encoder_output_size, critic_head_hidden_size), activation,
DiscreteHead(
critic_head_hidden_size,
action_shape,
critic_head_layer_num,
activation=activation,
norm_type=norm_type
)
)
)
else:
self.critic_head = nn.Sequential(
nn.Linear(encoder_output_size, critic_head_hidden_size), activation,
DiscreteHead(
critic_head_hidden_size,
action_shape,
critic_head_layer_num,
activation=activation,
norm_type=norm_type
)
)
# Convenient for calling some apis (e.g. self.critic.parameters()),
# but may cause misunderstanding when `print(self)`
self.actor = nn.ModuleList([self.actor_encoder, self.actor_head])
self.critic = nn.ModuleList([self.critic_encoder, self.critic_head])
[docs] def forward(self, inputs: torch.Tensor, mode: str) -> Dict[str, torch.Tensor]:
"""
Overview:
QAC forward computation graph, input observation tensor to predict Q-value or action logit. Different \
``mode`` will forward with different network modules to get different outputs and save computation.
Arguments:
- inputs (:obj:`torch.Tensor`): The input observation tensor data.
- mode (:obj:`str`): The forward mode, all the modes are defined in the beginning of this class.
Returns:
- output (:obj:`Dict[str, torch.Tensor]`): The output dict of QAC forward computation graph, whose \
key-values vary in different forward modes.
Examples (Actor):
>>> model = DiscreteQAC(64, 6)
>>> obs = torch.randn(4, 64)
>>> actor_outputs = model(obs,'compute_actor')
>>> assert actor_outputs['logit'].shape == torch.Size([4, 6])
Examples(Critic):
>>> model = DiscreteQAC(64, 6, twin_critic=False)
>>> obs = torch.randn(4, 64)
>>> actor_outputs = model(obs,'compute_critic')
>>> assert actor_outputs['q_value'].shape == torch.Size([4, 6])
"""
assert mode in self.mode, "not support forward mode: {}/{}".format(mode, self.mode)
return getattr(self, mode)(inputs)
[docs] def compute_actor(self, inputs: torch.Tensor) -> Dict[str, torch.Tensor]:
"""
Overview:
QAC forward computation graph for actor part, input observation tensor to predict action or action logit.
Arguments:
- inputs (:obj:`torch.Tensor`): The input observation tensor data.
Returns:
- outputs (:obj:`Dict[str, torch.Tensor]`): The output dict of QAC forward computation graph for actor, \
including discrete action ``logit``.
ReturnsKeys:
- logit (:obj:`torch.Tensor`): The predicted discrete action type logit, it will be the same dimension \
as ``action_shape``, i.e., all the possible discrete action choices.
Shapes:
- inputs (:obj:`torch.Tensor`): :math:`(B, N0)`, B is batch size and N0 corresponds to ``obs_shape``.
- logit (:obj:`torch.Tensor`): :math:`(B, N2)`, B is batch size and N2 corresponds to \
``action_shape``.
Examples:
>>> model = DiscreteQAC(64, 6)
>>> obs = torch.randn(4, 64)
>>> actor_outputs = model(obs,'compute_actor')
>>> assert actor_outputs['logit'].shape == torch.Size([4, 6])
"""
x = self.actor_encoder(inputs)
x = self.actor_head(x)
return {'logit': x['logit']}
[docs] def compute_critic(self, inputs: torch.Tensor) -> Dict[str, torch.Tensor]:
"""
Overview:
QAC forward computation graph for critic part, input observation to predict Q-value for each possible \
discrete action choices.
Arguments:
- inputs (:obj:`torch.Tensor`): The input observation tensor data.
Returns:
- outputs (:obj:`Dict[str, torch.Tensor]`): The output dict of QAC forward computation graph for critic, \
including ``q_value`` for each possible discrete action choices.
ReturnKeys:
- q_value (:obj:`torch.Tensor`): The predicted Q-value for each possible discrete action choices, it will \
be the same dimension as ``action_shape`` and used to calculate the loss.
Shapes:
- obs (:obj:`torch.Tensor`): :math:`(B, N1)`, where B is batch size and N1 is ``obs_shape``.
- q_value (:obj:`torch.Tensor`): :math:`(B, N2)`, where B is batch size and N2 is ``action_shape``.
Examples:
>>> model = DiscreteQAC(64, 6, twin_critic=False)
>>> obs = torch.randn(4, 64)
>>> actor_outputs = model(obs,'compute_critic')
>>> assert actor_outputs['q_value'].shape == torch.Size([4, 6])
"""
inputs = self.critic_encoder(inputs)
if self.twin_critic:
x = [m(inputs)['logit'] for m in self.critic_head]
else:
x = self.critic_head(inputs)['logit']
return {'q_value': x}