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# Copyright 2015 The TensorFlow Authors. 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.
# ==============================================================================
"""Adam for TensorFlow."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.framework import ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import state_ops
from tensorflow.python.ops import variables
from tensorflow.python.training import optimizer
from tensorflow.python.training import training_ops
class AdamOptimizer(optimizer.Optimizer):
"""Optimizer that implements the Adam algorithm.
See [Kingma et. al., 2014](http://arxiv.org/abs/1412.6980)
([pdf](http://arxiv.org/pdf/1412.6980.pdf)).
@@__init__
"""
def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-8,
use_locking=False, name="Adam"):
"""Construct a new Adam optimizer.
Initialization:
```
m_0 <- 0 (Initialize initial 1st moment vector)
v_0 <- 0 (Initialize initial 2nd moment vector)
t <- 0 (Initialize timestep)
```
The update rule for `variable` with gradient `g` uses an optimization
described at the end of section2 of the paper:
```
t <- t + 1
lr_t <- learning_rate * sqrt(1 - beta2^t) / (1 - beta1^t)
m_t <- beta1 * m_{t-1} + (1 - beta1) * g
v_t <- beta2 * v_{t-1} + (1 - beta2) * g * g
variable <- variable - lr_t * m_t / (sqrt(v_t) + epsilon)
```
The default value of 1e-8 for epsilon might not be a good default in
general. For example, when training an Inception network on ImageNet a
current good choice is 1.0 or 0.1.
Args:
learning_rate: A Tensor or a floating point value. The learning rate.
beta1: A float value or a constant float tensor.
The exponential decay rate for the 1st moment estimates.
beta2: A float value or a constant float tensor.
The exponential decay rate for the 2nd moment estimates.
epsilon: A small constant for numerical stability.
use_locking: If True use locks for update operations.
name: Optional name for the operations created when applying gradients.
Defaults to "Adam".
"""
super(AdamOptimizer, self).__init__(use_locking, name)
self._lr = learning_rate
self._beta1 = beta1
self._beta2 = beta2
self._epsilon = epsilon
# Tensor versions of the constructor arguments, created in _prepare().
self._lr_t = None
self._beta1_t = None
self._beta2_t = None
self._epsilon_t = None
# Variables to accumulate the powers of the beta parameters.
# Created in _create_slots when we know the variables to optimize.
self._beta1_power = None
self._beta2_power = None
# Created in SparseApply if needed.
self._updated_lr = None
def _get_beta_accumulators(self):
return self._beta1_power, self._beta2_power
def _create_slots(self, var_list):
# Create the beta1 and beta2 accumulators on the same device as the first
# variable.
if self._beta1_power is None:
with ops.colocate_with(var_list[0]):
self._beta1_power = variables.Variable(self._beta1,
name="beta1_power",
trainable=False)
self._beta2_power = variables.Variable(self._beta2,
name="beta2_power",
trainable=False)
# Create slots for the first and second moments.
for v in var_list:
self._zeros_slot(v, "m", self._name)
self._zeros_slot(v, "v", self._name)
def _prepare(self):
self._lr_t = ops.convert_to_tensor(self._lr, name="learning_rate")
self._beta1_t = ops.convert_to_tensor(self._beta1, name="beta1")
self._beta2_t = ops.convert_to_tensor(self._beta2, name="beta2")
self._epsilon_t = ops.convert_to_tensor(self._epsilon, name="epsilon")
def _apply_dense(self, grad, var):
m = self.get_slot(var, "m")
v = self.get_slot(var, "v")
return training_ops.apply_adam(
var, m, v,
math_ops.cast(self._beta1_power, var.dtype.base_dtype),
math_ops.cast(self._beta2_power, var.dtype.base_dtype),
math_ops.cast(self._lr_t, var.dtype.base_dtype),
math_ops.cast(self._beta1_t, var.dtype.base_dtype),
math_ops.cast(self._beta2_t, var.dtype.base_dtype),
math_ops.cast(self._epsilon_t, var.dtype.base_dtype),
grad, use_locking=self._use_locking).op
def _apply_sparse(self, grad, var):
beta1_power = math_ops.cast(self._beta1_power, var.dtype.base_dtype)
beta2_power = math_ops.cast(self._beta2_power, var.dtype.base_dtype)
lr_t = math_ops.cast(self._lr_t, var.dtype.base_dtype)
beta1_t = math_ops.cast(self._beta1_t, var.dtype.base_dtype)
beta2_t = math_ops.cast(self._beta2_t, var.dtype.base_dtype)
epsilon_t = math_ops.cast(self._epsilon_t, var.dtype.base_dtype)
lr = (lr_t * math_ops.sqrt(1 - beta2_power) / (1 - beta1_power))
# m_t = beta1 * m + (1 - beta1) * g_t
m = self.get_slot(var, "m")
m_scaled_g_values = grad.values * (1 - beta1_t)
m_t = state_ops.assign(m, m * beta1_t,
use_locking=self._use_locking)
m_t = state_ops.scatter_add(m_t, grad.indices, m_scaled_g_values,
use_locking=self._use_locking)
# v_t = beta2 * v + (1 - beta2) * (g_t * g_t)
v = self.get_slot(var, "v")
v_scaled_g_values = (grad.values * grad.values) * (1 - beta2_t)
v_t = state_ops.assign(v, v * beta2_t, use_locking=self._use_locking)
v_t = state_ops.scatter_add(v_t, grad.indices, v_scaled_g_values,
use_locking=self._use_locking)
v_sqrt = math_ops.sqrt(v_t)
var_update = state_ops.assign_sub(var,
lr * m_t / (v_sqrt + epsilon_t),
use_locking=self._use_locking)
return control_flow_ops.group(*[var_update, m_t, v_t])
def _finish(self, update_ops, name_scope):
# Update the power accumulators.
with ops.control_dependencies(update_ops):
with ops.colocate_with(self._beta1_power):
update_beta1 = self._beta1_power.assign(
self._beta1_power * self._beta1_t,
use_locking=self._use_locking)
update_beta2 = self._beta2_power.assign(
self._beta2_power * self._beta2_t,
use_locking=self._use_locking)
return control_flow_ops.group(*update_ops + [update_beta1, update_beta2],
name=name_scope)
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