# Copyright 2018 The TensorFlow Probability Authors.
#
# 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,
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# ============================================================================
"""An optimizer module for constant stochastic gradient descent."""

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

import tensorflow as tf

from tensorflow_probability.python.internal import distribution_util
from tensorflow_probability.python.internal import dtype_util
from tensorflow.python.training import training_ops


__all__ = [
    'VariationalSGD',
]


class VariationalSGD(tf.compat.v2.optimizers.Optimizer):
  """An optimizer module for constant stochastic gradient descent.

  This implements an optimizer module for the constant stochastic gradient
  descent algorithm [(Mandt et al., 2017)][1]. The optimization variable is
  regarded as an approximate sample from the posterior .

  Note: If a prior is included in the loss, it should be scaled by
  `1/num_pseudo_batches`, where num_pseudo_batches is the number of minibatches
  in the data.  I.e., it should be divided by the `num_pseudo_batches` term
  described below.

  Args:
    batch_size: Scalar `int`-like `Tensor`. The number of examples in a
      minibatch in the data set. Note: Assumes the loss is taken as the mean
      over a minibatch. Otherwise if the sum was taken set this to 1.
    total_num_examples: Scalar `int`-like `Tensor`. The total number of examples
      in the data set.
    max_learning_rate: Scalar `float`-like `Tensor`. A maximum allowable
      effective coordinate-wise learning rate. The algorithm scales down any
      effective learning rate (i.e. after preconditioning) that is larger than
      this. (Default: `1`)
    preconditioner_decay_rate: Scalar `float`-like `Tensor`. The exponential
      decay rate of the rescaling of the preconditioner (RMSprop). (This is
      "alpha" in Mandt et al. (2017)). Should be smaller than but nearly `1` to
      approximate sampling from the posterior. (Default: `0.95`)
    burnin: Scalar `int`-like `Tensor`. The number of iterations to collect
      gradient statistics to update the preconditioner before starting to draw
      noisy samples. (Default: `25`)
    burnin_max_learning_rate: Scalar `float`-like `Tensor`. Maximum learning
      rate to use during the burnin period.
      (Default: `1e-8`)
    use_single_learning_rate: Boolean Indicates whether one single learning
      rate is used or coordinate_wise learning rates are used.
      (Default: `False`)
    name: Python `str` describing ops managed by this function.
      (Default: `"VariationalSGD"`)

  Raises:
    InvalidArgumentError: If preconditioner_decay_rate is a `Tensor` not in
      `(0,1]`.

  #### References

  [1]: Stephan Mandt, Matthew D. Hoffman, and David M. Blei. Stochastic
       Gradient Descent as Approximate Bayesian Inference. _arXiv preprint
       arXiv:1704.04289_, 2017. https://arxiv.org/abs/1704.04289
  """

  def __init__(self,
               batch_size,
               total_num_examples,
               max_learning_rate=1.,
               preconditioner_decay_rate=0.95,
               burnin=25,
               burnin_max_learning_rate=1e-6,
               use_single_learning_rate=False,
               name=None):
    default_name = 'VariationalSGD'
    with tf.compat.v1.name_scope(name, default_name, [
        max_learning_rate, preconditioner_decay_rate, batch_size, burnin,
        burnin_max_learning_rate
    ]):
      self._preconditioner_decay_rate = tf.convert_to_tensor(
          value=preconditioner_decay_rate, name='preconditioner_decay_rate')
      self._batch_size = tf.convert_to_tensor(
          value=batch_size, name='batch_size')
      self._total_num_examples = tf.convert_to_tensor(
          value=total_num_examples, name='total_num_examples')

      self._burnin = tf.convert_to_tensor(
          value=burnin,
          name='burnin',
          dtype=dtype_util.common_dtype([burnin], preferred_dtype=tf.int64))
      self._burnin_max_learning_rate = tf.convert_to_tensor(
          value=burnin_max_learning_rate, name='burnin_max_learning_rate')
      self._max_learning_rate = tf.convert_to_tensor(
          value=max_learning_rate, name='max_learning_rate')
      self._use_single_learning_rate = use_single_learning_rate

      self._preconditioner_decay_rate = distribution_util.with_dependencies([
          tf.compat.v1.assert_non_negative(
              self._preconditioner_decay_rate,
              message='`preconditioner_decay_rate` must be non-negative'),
          tf.compat.v1.assert_less_equal(
              self._preconditioner_decay_rate,
              1.,
              message='`preconditioner_decay_rate` must be at most 1.'),
      ], self._preconditioner_decay_rate)

      self._batch_size = distribution_util.with_dependencies([
          tf.compat.v1.assert_greater(
              self._batch_size,
              0,
              message='`batch_size` must be greater than zero')
      ], self._batch_size)

      self._total_num_examples = distribution_util.with_dependencies([
          tf.compat.v1.assert_greater(
              self._total_num_examples,
              0,
              message='`total_num_examples` must be greater than zero')
      ], self._total_num_examples)

      self._burnin = distribution_util.with_dependencies([
          tf.compat.v1.assert_non_negative(
              self._burnin, message='`burnin` must be non-negative'),
          tf.compat.v1.assert_integer(
              self._burnin, message='`burnin` must be an integer')
      ], self._burnin)

      self._burnin_max_learning_rate = distribution_util.with_dependencies([
          tf.compat.v1.assert_non_negative(
              self._burnin_max_learning_rate,
              message='`burnin_max_learning_rate` must be non-negative')
      ], self._burnin_max_learning_rate)

      self._max_learning_rate = distribution_util.with_dependencies([
          tf.compat.v1.assert_non_negative(
              self._max_learning_rate,
              message='`max_learning_rate` must be non-negative')
      ], self._max_learning_rate)

      super(VariationalSGD, self).__init__(name=name or default_name)

  def get_config(self):
    # TODO(b/124800185): Consider migrating `max_learning_rate`, `burnin`,
    # `preconditioner_decay_rate` and other properties into optimizer
    # hyperparameters.
    pass

  def _create_slots(self, var_list):
    for var in var_list:
      self.add_slot(var, 'first_moment', 'zeros')
      self.add_slot(var, 'second_moment', 'zeros')

  def _prepare(self, var_list):
    self._decay_tensor = tf.convert_to_tensor(
        value=self._preconditioner_decay_rate, name='preconditioner_decay_rate')
    self._batch_size_tensor = tf.convert_to_tensor(
        value=self._batch_size, name='batch_size_tensor')

    super(VariationalSGD, self)._prepare(var_list)

  def _get_coordinatewise_learning_rate(self, grad, var):
    # Compute the learning rate using a moving average for the diagonal of BB^T
    avg_first = self.get_slot(var, 'first_moment')
    avg_second = self.get_slot(var, 'second_moment')
    decay_tensor = tf.cast(self._decay_tensor, var.dtype)
    batch_size = tf.cast(self._batch_size_tensor, var.dtype)

    # Create an estimator for the moving average of gradient mean and variance
    # via Welford's algorithm
    if isinstance(grad, tf.Tensor):
      delta = grad - avg_first
      first_moment_update = avg_first.assign_add(delta * tf.compat.v1.where(
          self.iterations < 1, tf.cast(1, var.dtype), 1. - decay_tensor))

      with tf.control_dependencies([first_moment_update]):
        second_moment_update = avg_second.assign_add(
            tf.cast(self.iterations < 1, var.dtype) * -(1. - decay_tensor) *
            (avg_second - decay_tensor * tf.square(delta)))
      diag_preconditioner = distribution_util.with_dependencies(
          [second_moment_update],
          tf.clip_by_value(avg_second, 1e-12, 1e12))
    elif isinstance(grad, tf.IndexedSlices):
      delta = grad.values - tf.gather_nd(avg_first, grad.indices)
      first_moment_update = tf.compat.v1.scatter_add(
          avg_first, grad.indices,
          delta * tf.compat.v1.where(self.iterations < 1, tf.cast(
              1., var.dtype), 1. - decay_tensor))

      with tf.control_dependencies([first_moment_update]):
        avg_second = tf.compat.v1.scatter_add(
            avg_second, grad.indices,
            tf.cast(self.iterations < 1, var.dtype) * -(1. - decay_tensor) *
            (tf.gather_nd(avg_second, grad.indices) -
             decay_tensor * tf.square(delta)))
        avg_second = tf.gather_nd(avg_second, grad.indices)
        # TODO(b/70783772): Needs dtype specific clipping.
        diag_preconditioner = tf.clip_by_value(avg_second, 1e-12, 1e12)
    else:
      raise tf.errors.InvalidArgumentError(
          None, None, 'grad must of type Tensor or IndexedSlice')

    diag_preconditioner *= batch_size

    if self._use_single_learning_rate:
      diag_preconditioner = tf.reduce_mean(input_tensor=diag_preconditioner)

    # From Theorem 2 Corollary 1 of Mandt et al. 2017
    return 2. * batch_size / (
        tf.cast(self._total_num_examples, var.dtype.base_dtype) *
        diag_preconditioner)

  def _resource_apply_dense(self, grad, var):
    max_learning_rate = tf.compat.v1.where(
        self.iterations < tf.cast(self._burnin, tf.int64),
        self._burnin_max_learning_rate, self._max_learning_rate)

    learn_rates = tf.clip_by_value(
        self._get_coordinatewise_learning_rate(grad, var), 0.,
        tf.cast(max_learning_rate, var.dtype.base_dtype))

    newgrad = grad * learn_rates
    return training_ops.resource_apply_gradient_descent(
        var.handle,
        tf.cast(1., var.dtype),
        newgrad,
        use_locking=self._use_locking)

  def _resource_apply_sparse(self, grad, var, indices):
    max_learning_rate = tf.compat.v1.where(
        self.iterations < tf.cast(self._burnin, tf.int64),
        self._burnin_max_learning_rate, self._max_learning_rate)

    learn_rate = tf.clip_by_value(
        self._get_coordinatewise_learning_rate(grad, var), 0.,
        tf.cast(max_learning_rate, var.dtype))
    delta = grad * learn_rate

    return self._resource_scatter_add(var, indices, -delta)
