Module keras.optimizer_v2.gradient_descent
SGD optimizer implementation.
Expand source code
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# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
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# ==============================================================================
"""SGD optimizer implementation."""
import tensorflow.compat.v2 as tf
from keras.optimizer_v2 import optimizer_v2
from tensorflow.python.util.tf_export import keras_export
@keras_export("keras.optimizers.SGD")
class SGD(optimizer_v2.OptimizerV2):
r"""Gradient descent (with momentum) optimizer.
Update rule for parameter `w` with gradient `g` when `momentum` is 0:
```python
w = w - learning_rate * g
```
Update rule when `momentum` is larger than 0:
```python
velocity = momentum * velocity - learning_rate * g
w = w + velocity
```
When `nesterov=True`, this rule becomes:
```python
velocity = momentum * velocity - learning_rate * g
w = w + momentum * velocity - learning_rate * g
```
Args:
learning_rate: A `Tensor`, floating point value, or a schedule that is a
`tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable
that takes no arguments and returns the actual value to use. The
learning rate. Defaults to 0.01.
momentum: float hyperparameter >= 0 that accelerates gradient descent
in the relevant
direction and dampens oscillations. Defaults to 0, i.e., vanilla gradient
descent.
nesterov: boolean. Whether to apply Nesterov momentum.
Defaults to `False`.
name: Optional name prefix for the operations created when applying
gradients. Defaults to `"SGD"`.
**kwargs: Keyword arguments. Allowed to be one of
`"clipnorm"` or `"clipvalue"`.
`"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
gradients by value.
Usage:
>>> opt = tf.keras.optimizers.SGD(learning_rate=0.1)
>>> var = tf.Variable(1.0)
>>> loss = lambda: (var ** 2)/2.0 # d(loss)/d(var1) = var1
>>> step_count = opt.minimize(loss, [var]).numpy()
>>> # Step is `- learning_rate * grad`
>>> var.numpy()
0.9
>>> opt = tf.keras.optimizers.SGD(learning_rate=0.1, momentum=0.9)
>>> var = tf.Variable(1.0)
>>> val0 = var.value()
>>> loss = lambda: (var ** 2)/2.0 # d(loss)/d(var1) = var1
>>> # First step is `- learning_rate * grad`
>>> step_count = opt.minimize(loss, [var]).numpy()
>>> val1 = var.value()
>>> (val0 - val1).numpy()
0.1
>>> # On later steps, step-size increases because of momentum
>>> step_count = opt.minimize(loss, [var]).numpy()
>>> val2 = var.value()
>>> (val1 - val2).numpy()
0.18
Reference:
- For `nesterov=True`, See [Sutskever et al., 2013](
http://jmlr.org/proceedings/papers/v28/sutskever13.pdf).
"""
_HAS_AGGREGATE_GRAD = True
def __init__(self,
learning_rate=0.01,
momentum=0.0,
nesterov=False,
name="SGD",
**kwargs):
super(SGD, self).__init__(name, **kwargs)
self._set_hyper("learning_rate", kwargs.get("lr", learning_rate))
self._set_hyper("decay", self._initial_decay)
self._momentum = False
if isinstance(momentum, tf.Tensor) or callable(momentum) or momentum > 0:
self._momentum = True
if isinstance(momentum, (int, float)) and (momentum < 0 or momentum > 1):
raise ValueError("`momentum` must be between [0, 1].")
self._set_hyper("momentum", momentum)
self.nesterov = nesterov
def _create_slots(self, var_list):
if self._momentum:
for var in var_list:
self.add_slot(var, "momentum")
def _prepare_local(self, var_device, var_dtype, apply_state):
super(SGD, self)._prepare_local(var_device, var_dtype, apply_state)
apply_state[(var_device, var_dtype)]["momentum"] = tf.identity(
self._get_hyper("momentum", var_dtype))
def _resource_apply_dense(self, grad, var, apply_state=None):
var_device, var_dtype = var.device, var.dtype.base_dtype
coefficients = ((apply_state or {}).get((var_device, var_dtype))
or self._fallback_apply_state(var_device, var_dtype))
if self._momentum:
momentum_var = self.get_slot(var, "momentum")
return tf.raw_ops.ResourceApplyKerasMomentum(
var=var.handle,
accum=momentum_var.handle,
lr=coefficients["lr_t"],
grad=grad,
momentum=coefficients["momentum"],
use_locking=self._use_locking,
use_nesterov=self.nesterov)
else:
return tf.raw_ops.ResourceApplyGradientDescent(
var=var.handle,
alpha=coefficients["lr_t"],
delta=grad,
use_locking=self._use_locking)
def _resource_apply_sparse_duplicate_indices(self, grad, var, indices,
**kwargs):
if self._momentum:
return super(SGD, self)._resource_apply_sparse_duplicate_indices(
grad, var, indices, **kwargs)
else:
var_device, var_dtype = var.device, var.dtype.base_dtype
coefficients = (kwargs.get("apply_state", {}).get((var_device, var_dtype))
or self._fallback_apply_state(var_device, var_dtype))
return tf.raw_ops.ResourceScatterAdd(
resource=var.handle,
indices=indices,
updates=-grad * coefficients["lr_t"])
def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
# This method is only needed for momentum optimization.
var_device, var_dtype = var.device, var.dtype.base_dtype
coefficients = ((apply_state or {}).get((var_device, var_dtype))
or self._fallback_apply_state(var_device, var_dtype))
momentum_var = self.get_slot(var, "momentum")
return tf.raw_ops.ResourceSparseApplyKerasMomentum(
var=var.handle,
accum=momentum_var.handle,
lr=coefficients["lr_t"],
grad=grad,
indices=indices,
momentum=coefficients["momentum"],
use_locking=self._use_locking,
use_nesterov=self.nesterov)
def get_config(self):
config = super(SGD, self).get_config()
config.update({
"learning_rate": self._serialize_hyperparameter("learning_rate"),
"decay": self._initial_decay,
"momentum": self._serialize_hyperparameter("momentum"),
"nesterov": self.nesterov,
})
return config
Classes
class SGD (learning_rate=0.01, momentum=0.0, nesterov=False, name='SGD', **kwargs)
-
Gradient descent (with momentum) optimizer.
Update rule for parameter
w
with gradientg
whenmomentum
is 0:w = w - learning_rate * g
Update rule when
momentum
is larger than 0:velocity = momentum * velocity - learning_rate * g w = w + velocity
When
nesterov=True
, this rule becomes:velocity = momentum * velocity - learning_rate * g w = w + momentum * velocity - learning_rate * g
Args
learning_rate
- A
Tensor
, floating point value, or a schedule that is atf.keras.optimizers.schedules.LearningRateSchedule
, or a callable that takes no arguments and returns the actual value to use. The learning rate. Defaults to 0.01. momentum
- float hyperparameter >= 0 that accelerates gradient descent in the relevant direction and dampens oscillations. Defaults to 0, i.e., vanilla gradient descent.
nesterov
- boolean. Whether to apply Nesterov momentum.
Defaults to
False
. name
- Optional name prefix for the operations created when applying
gradients.
Defaults to
"SGD"
. **kwargs
- Keyword arguments. Allowed to be one of
"clipnorm"
or"clipvalue"
."clipnorm"
(float) clips gradients by norm;"clipvalue"
(float) clips gradients by value.
Usage:
>>> opt = tf.keras.optimizers.SGD(learning_rate=0.1) >>> var = tf.Variable(1.0) >>> loss = lambda: (var ** 2)/2.0 # d(loss)/d(var1) = var1 >>> step_count = opt.minimize(loss, [var]).numpy() >>> # Step is `- learning_rate * grad` >>> var.numpy() 0.9
>>> opt = tf.keras.optimizers.SGD(learning_rate=0.1, momentum=0.9) >>> var = tf.Variable(1.0) >>> val0 = var.value() >>> loss = lambda: (var ** 2)/2.0 # d(loss)/d(var1) = var1 >>> # First step is `- learning_rate * grad` >>> step_count = opt.minimize(loss, [var]).numpy() >>> val1 = var.value() >>> (val0 - val1).numpy() 0.1 >>> # On later steps, step-size increases because of momentum >>> step_count = opt.minimize(loss, [var]).numpy() >>> val2 = var.value() >>> (val1 - val2).numpy() 0.18
Reference
- For
nesterov=True
, See Sutskever et al., 2013.
Create a new Optimizer.
This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.
This class is stateful and thread-compatible.
Example of custom gradient transformations:
def my_gradient_transformer(grads_and_vars): # Simple example, double the gradients. return [(2. * g, v) for g, v in grads_and_vars] optimizer = tf.keras.optimizers.SGD( 1e-3, gradient_transformers=[my_gradient_transformer])
Args
name
- String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
- The function to use to aggregate gradients across
devices (when using
tf.distribute.Strategy
). IfNone
, defaults to summing the gradients across devices. The function should accept and return a list of(gradient, variable)
tuples. gradient_transformers
- Optional. List of functions to use to transform
gradients before applying updates to Variables. The functions are
applied after
gradient_aggregator
. The functions should accept and return a list of(gradient, variable)
tuples. **kwargs
- keyword arguments. Allowed arguments are
clipvalue
,clipnorm
,global_clipnorm
. Ifclipvalue
(float) is set, the gradient of each weight is clipped to be no higher than this value. Ifclipnorm
(float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. Ifglobal_clipnorm
(float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.
Raises
ValueError
- in case of any invalid argument.
Expand source code
class SGD(optimizer_v2.OptimizerV2): r"""Gradient descent (with momentum) optimizer. Update rule for parameter `w` with gradient `g` when `momentum` is 0: ```python w = w - learning_rate * g ``` Update rule when `momentum` is larger than 0: ```python velocity = momentum * velocity - learning_rate * g w = w + velocity ``` When `nesterov=True`, this rule becomes: ```python velocity = momentum * velocity - learning_rate * g w = w + momentum * velocity - learning_rate * g ``` Args: learning_rate: A `Tensor`, floating point value, or a schedule that is a `tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable that takes no arguments and returns the actual value to use. The learning rate. Defaults to 0.01. momentum: float hyperparameter >= 0 that accelerates gradient descent in the relevant direction and dampens oscillations. Defaults to 0, i.e., vanilla gradient descent. nesterov: boolean. Whether to apply Nesterov momentum. Defaults to `False`. name: Optional name prefix for the operations created when applying gradients. Defaults to `"SGD"`. **kwargs: Keyword arguments. Allowed to be one of `"clipnorm"` or `"clipvalue"`. `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips gradients by value. Usage: >>> opt = tf.keras.optimizers.SGD(learning_rate=0.1) >>> var = tf.Variable(1.0) >>> loss = lambda: (var ** 2)/2.0 # d(loss)/d(var1) = var1 >>> step_count = opt.minimize(loss, [var]).numpy() >>> # Step is `- learning_rate * grad` >>> var.numpy() 0.9 >>> opt = tf.keras.optimizers.SGD(learning_rate=0.1, momentum=0.9) >>> var = tf.Variable(1.0) >>> val0 = var.value() >>> loss = lambda: (var ** 2)/2.0 # d(loss)/d(var1) = var1 >>> # First step is `- learning_rate * grad` >>> step_count = opt.minimize(loss, [var]).numpy() >>> val1 = var.value() >>> (val0 - val1).numpy() 0.1 >>> # On later steps, step-size increases because of momentum >>> step_count = opt.minimize(loss, [var]).numpy() >>> val2 = var.value() >>> (val1 - val2).numpy() 0.18 Reference: - For `nesterov=True`, See [Sutskever et al., 2013]( http://jmlr.org/proceedings/papers/v28/sutskever13.pdf). """ _HAS_AGGREGATE_GRAD = True def __init__(self, learning_rate=0.01, momentum=0.0, nesterov=False, name="SGD", **kwargs): super(SGD, self).__init__(name, **kwargs) self._set_hyper("learning_rate", kwargs.get("lr", learning_rate)) self._set_hyper("decay", self._initial_decay) self._momentum = False if isinstance(momentum, tf.Tensor) or callable(momentum) or momentum > 0: self._momentum = True if isinstance(momentum, (int, float)) and (momentum < 0 or momentum > 1): raise ValueError("`momentum` must be between [0, 1].") self._set_hyper("momentum", momentum) self.nesterov = nesterov def _create_slots(self, var_list): if self._momentum: for var in var_list: self.add_slot(var, "momentum") def _prepare_local(self, var_device, var_dtype, apply_state): super(SGD, self)._prepare_local(var_device, var_dtype, apply_state) apply_state[(var_device, var_dtype)]["momentum"] = tf.identity( self._get_hyper("momentum", var_dtype)) def _resource_apply_dense(self, grad, var, apply_state=None): var_device, var_dtype = var.device, var.dtype.base_dtype coefficients = ((apply_state or {}).get((var_device, var_dtype)) or self._fallback_apply_state(var_device, var_dtype)) if self._momentum: momentum_var = self.get_slot(var, "momentum") return tf.raw_ops.ResourceApplyKerasMomentum( var=var.handle, accum=momentum_var.handle, lr=coefficients["lr_t"], grad=grad, momentum=coefficients["momentum"], use_locking=self._use_locking, use_nesterov=self.nesterov) else: return tf.raw_ops.ResourceApplyGradientDescent( var=var.handle, alpha=coefficients["lr_t"], delta=grad, use_locking=self._use_locking) def _resource_apply_sparse_duplicate_indices(self, grad, var, indices, **kwargs): if self._momentum: return super(SGD, self)._resource_apply_sparse_duplicate_indices( grad, var, indices, **kwargs) else: var_device, var_dtype = var.device, var.dtype.base_dtype coefficients = (kwargs.get("apply_state", {}).get((var_device, var_dtype)) or self._fallback_apply_state(var_device, var_dtype)) return tf.raw_ops.ResourceScatterAdd( resource=var.handle, indices=indices, updates=-grad * coefficients["lr_t"]) def _resource_apply_sparse(self, grad, var, indices, apply_state=None): # This method is only needed for momentum optimization. var_device, var_dtype = var.device, var.dtype.base_dtype coefficients = ((apply_state or {}).get((var_device, var_dtype)) or self._fallback_apply_state(var_device, var_dtype)) momentum_var = self.get_slot(var, "momentum") return tf.raw_ops.ResourceSparseApplyKerasMomentum( var=var.handle, accum=momentum_var.handle, lr=coefficients["lr_t"], grad=grad, indices=indices, momentum=coefficients["momentum"], use_locking=self._use_locking, use_nesterov=self.nesterov) def get_config(self): config = super(SGD, self).get_config() config.update({ "learning_rate": self._serialize_hyperparameter("learning_rate"), "decay": self._initial_decay, "momentum": self._serialize_hyperparameter("momentum"), "nesterov": self.nesterov, }) return config
Ancestors
- OptimizerV2
- tensorflow.python.training.tracking.base.Trackable
Inherited members