# Copyright 2018 The TensorFlow Authors. All Rights Reserved.
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# 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
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# http://www.apache.org/licenses/LICENSE-2.0
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# ==============================================================================
"""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.keras import backend_config
from tensorflow.python.keras.optimizer_v2 import optimizer_v2
from tensorflow.python.ops import array_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.training import training_ops
from tensorflow.python.util.tf_export import keras_export
@keras_export('keras.optimizers.Adam')
class Adam(optimizer_v2.OptimizerV2):
"""Optimizer that implements the Adam algorithm.
Adam optimization is a stochastic gradient descent method that is based on
adaptive estimation of first-order and second-order moments.
According to the paper
[Adam: A Method for Stochastic Optimization. Kingma et al.,
2014](http://arxiv.org/abs/1412.6980),
the method is "*computationally efficient, has little memory
requirement, invariant to diagonal rescaling of gradients, and is well suited
for problems that are large in terms of data/parameters*".
For AMSGrad see [On The Convergence Of Adam And Beyond.
Reddi et al., 5-8](https://openreview.net/pdf?id=ryQu7f-RZ).
"""
def __init__(self,
learning_rate=0.001,
beta_1=0.9,
beta_2=0.999,
epsilon=1e-7,
amsgrad=False,
name='Adam',
**kwargs):
r"""Construct a new Adam optimizer.
If amsgrad = False:
Initialization:
$$m_0 := 0 \text{(Initialize initial 1st moment vector)}$$
$$v_0 := 0 \text{(Initialize initial 2nd moment vector)}$$
$$t := 0 \text{(Initialize timestep)}$$
The update rule for `variable` with gradient `g` uses an optimization
described at the end of section 2 of the paper:
$$t := t + 1$$
$$lr_t := \text{learning\_rate} * \sqrt{1 - beta_2^t} / (1 - beta_1^t)$$
$$m_t := beta_1 * m_{t-1} + (1 - beta_1) * g$$
$$v_t := beta_2 * v_{t-1} + (1 - beta_2) * g * g$$
$$variable := variable - lr_t * m_t / (\sqrt{v_t} + \epsilon)$$
If amsgrad = True:
Initialization:
$$m_0 := 0 \text{(Initialize initial 1st moment vector)}$$
$$v_0 := 0 \text{(Initialize initial 2nd moment vector)}$$
$$v_hat_0 := 0 \text{(Initialize initial 2nd moment vector)}$$
$$t := 0 \text{(Initialize timestep)}$$
The update rule for `variable` with gradient `g` uses an optimization
described at the end of section 2 of the paper:
$$t := t + 1$$
$$lr_t := \text{learning\_rate} * \sqrt{1 - beta_2^t} / (1 - beta_1^t)$$
$$m_t := beta_1 * m_{t-1} + (1 - beta_1) * g$$
$$v_t := beta_2 * v_{t-1} + (1 - beta_2) * g * g$$
$$v_hat_t := max(v_hat_{t-1}, v_t)$$
$$variable := variable - lr_t * m_t / (\sqrt{v_hat_t} + \epsilon)$$
The default value of 1e-7 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. Note that since AdamOptimizer uses the
formulation just before Section 2.1 of the Kingma and Ba paper rather than
the formulation in Algorithm 1, the "epsilon" referred to here is "epsilon
hat" in the paper.
The sparse implementation of this algorithm (used when the gradient is an
IndexedSlices object, typically because of `tf.gather` or an embedding
lookup in the forward pass) does apply momentum to variable slices even if
they were not used in the forward pass (meaning they have a gradient equal
to zero). Momentum decay (beta1) is also applied to the entire momentum
accumulator. This means that the sparse behavior is equivalent to the dense
behavior (in contrast to some momentum implementations which ignore momentum
unless a variable slice was actually used).
Args:
learning_rate: A Tensor or a floating point value. The learning rate.
beta_1: A float value or a constant float tensor. The exponential decay
rate for the 1st moment estimates.
beta_2: A float value or a constant float tensor. The exponential decay
rate for the 2nd moment estimates.
epsilon: A small constant for numerical stability. This epsilon is
"epsilon hat" in the Kingma and Ba paper (in the formula just before
Section 2.1), not the epsilon in Algorithm 1 of the paper.
amsgrad: boolean. Whether to apply AMSGrad variant of this algorithm from
the paper "On the Convergence of Adam and beyond".
name: Optional name for the operations created when applying gradients.
Defaults to "Adam". @compatibility(eager) When eager execution is
enabled, `learning_rate`, `beta_1`, `beta_2`, and `epsilon` can each be
a callable that takes no arguments and returns the actual value to use.
This can be useful for changing these values across different
invocations of optimizer functions. @end_compatibility
**kwargs: keyword arguments. Allowed to be {`clipnorm`, `clipvalue`, `lr`,
`decay`}. `clipnorm` is clip gradients by norm; `clipvalue` is clip
gradients by value, `decay` is included for backward compatibility to
allow time inverse decay of learning rate. `lr` is included for backward
compatibility, recommended to use `learning_rate` instead.
"""
super(Adam, self).__init__(name, **kwargs)
self._set_hyper('learning_rate', kwargs.get('lr', learning_rate))
self._set_hyper('decay', self._initial_decay)
self._set_hyper('beta_1', beta_1)
self._set_hyper('beta_2', beta_2)
self.epsilon = epsilon or backend_config.epsilon()
self.amsgrad = amsgrad
def _create_slots(self, var_list):
# Create slots for the first and second moments.
# Separate for-loops to respect the ordering of slot variables from v1.
for var in var_list:
self.add_slot(var, 'm')
for var in var_list:
self.add_slot(var, 'v')
if self.amsgrad:
for var in var_list:
self.add_slot(var, 'vhat')
def _prepare_local(self, var_device, var_dtype, apply_state):
super(Adam, self)._prepare_local(var_device, var_dtype, apply_state)
local_step = math_ops.cast(self.iterations + 1, var_dtype)
beta_1_t = array_ops.identity(self._get_hyper('beta_1', var_dtype))
beta_2_t = array_ops.identity(self._get_hyper('beta_2', var_dtype))
beta_1_power = math_ops.pow(beta_1_t, local_step)
beta_2_power = math_ops.pow(beta_2_t, local_step)
lr = (apply_state[(var_device, var_dtype)]['lr_t'] *
(math_ops.sqrt(1 - beta_2_power) / (1 - beta_1_power)))
apply_state[(var_device, var_dtype)].update(dict(
lr=lr,
epsilon=ops.convert_to_tensor(self.epsilon, var_dtype),
beta_1_t=beta_1_t,
beta_1_power=beta_1_power,
one_minus_beta_1_t=1 - beta_1_t,
beta_2_t=beta_2_t,
beta_2_power=beta_2_power,
one_minus_beta_2_t=1 - beta_2_t
))
def set_weights(self, weights):
params = self.weights
# If the weights are generated by Keras V1 optimizer, it includes vhats
# even without amsgrad, i.e, V1 optimizer has 3x + 1 variables, while V2
# optimizer has 2x + 1 variables. Filter vhats out for compatibility.
num_vars = int((len(params) - 1) / 2)
if len(weights) == 3 * num_vars + 1:
weights = weights[:len(params)]
super(Adam, self).set_weights(weights)
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))
m = self.get_slot(var, 'm')
v = self.get_slot(var, 'v')
if not self.amsgrad:
return training_ops.resource_apply_adam(
var.handle,
m.handle,
v.handle,
coefficients['beta_1_power'],
coefficients['beta_2_power'],
coefficients['lr_t'],
coefficients['beta_1_t'],
coefficients['beta_2_t'],
coefficients['epsilon'],
grad,
use_locking=self._use_locking)
else:
vhat = self.get_slot(var, 'vhat')
return training_ops.resource_apply_adam_with_amsgrad(
var.handle,
m.handle,
v.handle,
vhat.handle,
coefficients['beta_1_power'],
coefficients['beta_2_power'],
coefficients['lr_t'],
coefficients['beta_1_t'],
coefficients['beta_2_t'],
coefficients['epsilon'],
grad,
use_locking=self._use_locking)
def _resource_apply_sparse(self, grad, var, indices, 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))
# m_t = beta1 * m + (1 - beta1) * g_t
m = self.get_slot(var, 'm')
m_scaled_g_values = grad * coefficients['one_minus_beta_1_t']
m_t = state_ops.assign(m, m * coefficients['beta_1_t'],
use_locking=self._use_locking)
with ops.control_dependencies([m_t]):
m_t = self._resource_scatter_add(m, indices, m_scaled_g_values)
# v_t = beta2 * v + (1 - beta2) * (g_t * g_t)
v = self.get_slot(var, 'v')
v_scaled_g_values = (grad * grad) * coefficients['one_minus_beta_2_t']
v_t = state_ops.assign(v, v * coefficients['beta_2_t'],
use_locking=self._use_locking)
with ops.control_dependencies([v_t]):
v_t = self._resource_scatter_add(v, indices, v_scaled_g_values)
if not self.amsgrad:
v_sqrt = math_ops.sqrt(v_t)
var_update = state_ops.assign_sub(
var, coefficients['lr'] * m_t / (v_sqrt + coefficients['epsilon']),
use_locking=self._use_locking)
return control_flow_ops.group(*[var_update, m_t, v_t])
else:
v_hat = self.get_slot(var, 'vhat')
v_hat_t = math_ops.maximum(v_hat, v_t)
with ops.control_dependencies([v_hat_t]):
v_hat_t = state_ops.assign(
v_hat, v_hat_t, use_locking=self._use_locking)
v_hat_sqrt = math_ops.sqrt(v_hat_t)
var_update = state_ops.assign_sub(
var,
coefficients['lr'] * m_t / (v_hat_sqrt + coefficients['epsilon']),
use_locking=self._use_locking)
return control_flow_ops.group(*[var_update, m_t, v_t, v_hat_t])
def get_config(self):
config = super(Adam, self).get_config()
config.update({
'learning_rate': self._serialize_hyperparameter('learning_rate'),
'decay': self._serialize_hyperparameter('decay'),
'beta_1': self._serialize_hyperparameter('beta_1'),
'beta_2': self._serialize_hyperparameter('beta_2'),
'epsilon': self.epsilon,
'amsgrad': self.amsgrad,
})
return config