sparse_adam_optimizer.py

# Copyright 2017 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.
# ==============================================================================
"""
Variant of the Adam optimizer that handles sparse updates more efficiently and
convergence is close to Adam.

Compared with the original Adam optimizer, the one in this file can provide a
large improvement in model training throughput for some applications.
The semantics of Sparse Adam is close to the original Adam algorithm, and the
convergence is also close to Adam.

A detailed description of SparseAdam.
- maintain a timestamp variable (pre_step) for each weight
- count the skipped steps for each weight
- skipped_step = global_step - pre_step
- adapt the Adam learning rate based on skipped_step
- For each time step, SparseAdam updates weight first, then update momentum (m)
and momentum (v)

lr = extlearningrate * sqrt(1 - beta2 ** pre_step) / (1 - beta1 ** pre_step) *
    (1 - beta1 ** skipped_step) / (1 - beta1)
variable = variable - lr * m / sqrt(v + epsilon)
m = m * beta1 ** skipped_step + (1 - beta1) * gradient
v = v * beta2 ** skipped_step + (1 - beta2) * gradient ** 2
"""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

from tensorflow.python.eager import context
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 resource_variable_ops
from tensorflow.python.ops import state_ops
from tensorflow.python.training import adam
from tensorflow.python.framework import ops
from tensorflow.python.framework import constant_op


class SparseAdamOptimizer(adam.AdamOptimizer):
  """Variant of the Adam optimizer that handles sparse updates more efficiently.

  The original Adam algorithm maintains two moving-average accumulators for
  each trainable variable; the accumulators are updated at every step.
  The same as Lazy Adam, this class provides lazier handling of gradient
  updates for sparse variables. It only updates moving-average accumulators
  for sparse variable indices that appear in the current batch, rather than
  updating the accumulators for all indices. Compared with the original
  Adam optimizer, it can provide large improvements in model training
  throughput for some applications. Compared with Lazy Adam, the sementics of
  Spare Adam is close to original Adam optimizer, and the convergence is also
  close to original Adam.
  """

  def _create_slots(self, var_list):
    #Create the beta1 and beta2 accumulators on the same device as the first
    #variable.Sort the var_list to make sure this device is consistent across
    #workers(these need to go on the same PS, otherwise some updates are
    #silently ignored).
    first_var = min(var_list, key=lambda x: x.name)
    self._create_non_slot_variable(
        initial_value=self._beta1, name="beta1_power", colocate_with=first_var)
    self._create_non_slot_variable(
        initial_value=self._beta2, name="beta2_power", colocate_with=first_var)
    self._create_non_slot_variable(
        initial_value=1.0, name="global_step", colocate_with=first_var)

    #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)
      self._get_or_make_slot(
          v,
          constant_op.constant(
              1.0, dtype=v.dtype.base_dtype, shape=v.get_shape()), "pre_step",
          self._name)

  def _get_step_accumulators(self):
    with ops.init_scope():
      if context.executing_eagerly():
        graph = None
      else:
        graph = ops.get_default_graph()
      return self._get_non_slot_variable("global_step", graph=graph)

  def _finish(self, update_ops, name_scope):
    #Update the power accumulators.
    with ops.control_dependencies(update_ops):
      beta1_power, beta2_power = self._get_beta_accumulators()
      global_step = self._get_step_accumulators()
      with ops.colocate_with(beta1_power):
        update_beta1 = beta1_power.assign(
            beta1_power * self._beta1_t, use_locking=self._use_locking)
        update_beta2 = beta2_power.assign(
            beta2_power * self._beta2_t, use_locking=self._use_locking)
        update_step = global_step.assign(
            global_step + 1, use_locking=self._use_locking)
    return control_flow_ops.group(
        *update_ops + [update_beta1, update_beta2, update_step],
        name=name_scope)

  def _apply_sparse(self, grad, var):
    beta1_power, beta2_power = self._get_beta_accumulators()
    beta1_power = math_ops.cast(beta1_power, var.dtype.base_dtype)
    beta2_power = math_ops.cast(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)
    global_step = self._get_step_accumulators()
    global_step = math_ops.cast(global_step, var.dtype.base_dtype)
    pre_step = self.get_slot(var, "pre_step")

    indices = grad.indices
    pre_step_slice = array_ops.gather(pre_step, indices)
    skipped_steps = global_step - pre_step_slice

    m = self.get_slot(var, "m")
    m_slice = array_ops.gather(m, indices)
    v = self.get_slot(var, "v")
    v_slice = array_ops.gather(v, indices)
    # for performance reason, here use math_ops.exp(a* math_ops.log(b)) to
    # replace math_ops.pow(b, a)
    # \\(lr : = extlearningrate * sqrt(1 - beta2 * * pre_step) /
    #           (1 - beta1 * * pre_step) *(1 - beta1 * * skipped_step) /
    #           (1 - beta1)\\)
    lr = ((lr_t * math_ops.sqrt(
        1 - math_ops.exp(pre_step_slice * math_ops.log(beta2_t))) /
           (1 - math_ops.exp(pre_step_slice * math_ops.log(beta1_t)))) *
          (1 - math_ops.exp(math_ops.log(beta1_t) * skipped_steps)) /
          (1 - beta1_t))
    # \\(variable -= learning_rate * m /(epsilon + sqrt(v))\\)
    var_slice = lr * m_slice / (math_ops.sqrt(v_slice) + epsilon_t)
    var_update_op = state_ops.scatter_sub(
        var, indices, var_slice, use_locking=self._use_locking)

    with ops.control_dependencies([var_update_op]):
      # \\(m : = m * beta1 * * skipped_step +(1 - beta1) * g_t\\)
      # for performance reason, here use math_ops.exp(a* math_ops.log(b)) to
      # replace math_ops.pow(b, a)
      m_t_slice = (
          math_ops.exp(math_ops.log(beta1_t) * skipped_steps) * m_slice +
          (1 - beta1_t) * grad)
      m_update_op = state_ops.scatter_update(
          m, indices, m_t_slice, use_locking=self._use_locking)

      # \\(v : = v * beta2 * * skipped_step +(1 - beta2) *(g_t * g_t)\\)
      # for performance reason, here use math_ops.exp(a* math_ops.log(b)) to
      # replace math_ops.pow(b, a)
      v_t_slice = (
          math_ops.exp(math_ops.log(beta2_t) * skipped_steps) * v_slice +
          (1 - beta2_t) * math_ops.square(grad))
      v_update_op = state_ops.scatter_update(
          v, indices, v_t_slice, use_locking=self._use_locking)

    with ops.control_dependencies([m_update_op, v_update_op]):
      pre_step_update_op = state_ops.scatter_update(
          pre_step, indices, global_step, use_locking=self._use_locking)

    return control_flow_ops.group(var_update_op, m_update_op, v_update_op,
                                  pre_step_update_op)

  def _resource_apply_sparse(self, grad, var, indices):
    beta1_power, beta2_power = self._get_beta_accumulators()
    beta1_power = math_ops.cast(beta1_power, var.dtype.base_dtype)
    beta2_power = math_ops.cast(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)
    global_step = self._get_step_accumulators()
    global_step = math_ops.cast(global_step, var.dtype.base_dtype)
    pre_step = self.get_slot(var, "pre_step")

    pre_step_slice = array_ops.gather(pre_step, indices)
    skipped_steps = global_step - pre_step_slice

    m = self.get_slot(var, "m")
    m_slice = array_ops.gather(m, indices)
    v = self.get_slot(var, "v")
    v_slice = array_ops.gather(v, indices)

    # for performance reason, here use math_ops.exp(a* math_ops.log(b)) to
    # replace math_ops.pow(b, a)
    # \\(lr : = extlearningrate * sqrt(1 - beta2 * * pre_step) /
    #           (1 - beta1 * * pre_step) *(1 - beta1 * * skipped_step) /
    #           (1 - beta1)\\)
    lr = ((lr_t * math_ops.sqrt(
        1 - math_ops.exp(pre_step_slice * math_ops.log(beta2_t))) /
           (1 - math_ops.exp(pre_step_slice * math_ops.log(beta1_t)))) *
          (1 - math_ops.exp(math_ops.log(beta1_t) * skipped_steps)) /
          (1 - beta1_t))
    # \\(variable -= learning_rate * m /(epsilon + sqrt(v))\\)
    var_slice = lr * m_slice / (math_ops.sqrt(v_slice) + epsilon_t)
    var_update_op = resource_variable_ops.resource_scatter_sub(
        var.handle, indices, var_slice)

    with ops.control_dependencies([var_update_op]):
      # \\(m : = m * beta1 * * skipped_step +(1 - beta1) * g_t\\)
      # for performance reason, here use math_ops.exp(a* math_ops.log(b)) to
      # replace math_ops.pow(b, a)
      m_t_slice = (
          math_ops.exp(math_ops.log(beta1_t) * skipped_steps) * m_slice +
          (1 - beta1_t) * grad)
      m_update_op = resource_variable_ops.resource_scatter_update(
          m.handle, indices, m_t_slice)

      # \\(v : = v * beta2 * * skipped_step +(1 - beta2) *(g_t * g_t)\\)
      # for performance reason, here use math_ops.exp(a* math_ops.log(b)) to
      # replace math_ops.pow(b, a)
      v_t_slice = (
          math_ops.exp(math_ops.log(beta2_t) * skipped_steps) * v_slice +
          (1 - beta2_t) * math_ops.square(grad))
      v_update_op = resource_variable_ops.resource_scatter_update(
          v.handle, indices, v_t_slice)

    with ops.control_dependencies([m_update_op, v_update_op]):
      pre_step_update_op = resource_variable_ops.resource_scatter_update(
          pre_step.handle, indices, global_step)

    return control_flow_ops.group(var_update_op, m_update_op, v_update_op,
                                  pre_step_update_op)