(learning_rate, b1=0.9, b2=0.999, eps=1e-8)
return init, update, get_params
Construct optimizer triple for Adam.

  Inspired by the optimizer definitions in JAX
  (https://github.com/google/jax/blob/main/jax/experimental/optimizers.py),
  this implementation of Adam is fully functional (i.e., it maintains no hidden
  state) and so is compatible for use with an optimization-based meta-learner.

  Args:
    learning_rate: A positive scalar.
    b1: optional, a positive scalar value for beta_1, the exponential decay rate
      for the first moment estimates (default 0.9).
    b2: optional, a positive scalar value for beta_2, the exponential decay rate
      for the second moment estimates (default 0.999).
    eps: optional, a positive scalar value for epsilon, a small constant for
      numerical stability (default 1e-8).

  Returns:
    An (init, update, get_params) function triple.
Construct optimizer triple for Adam.
Construct optimizer triple for Adam .
def adam(learning_rate, b1=0.9, b2=0.999, eps=1e-8):
  """Construct optimizer triple for Adam.

  Inspired by the optimizer definitions in JAX
  (https://github.com/google/jax/blob/main/jax/experimental/optimizers.py),
  this implementation of Adam is fully functional (i.e., it maintains no hidden
  state) and so is compatible for use with an optimization-based meta-learner.

  Args:
    learning_rate: A positive scalar.
    b1: optional, a positive scalar value for beta_1, the exponential decay rate
      for the first moment estimates (default 0.9).
    b2: optional, a positive scalar value for beta_2, the exponential decay rate
      for the second moment estimates (default 0.999).
    eps: optional, a positive scalar value for epsilon, a small constant for
      numerical stability (default 1e-8).

  Returns:
    An (init, update, get_params) function triple.
  """

  def init(x0):
    m0 = tf.zeros_like(x0)
    v0 = tf.zeros_like(x0)
    return x0, m0, v0

  def update(i, grad, state):
    i = tf.cast(i, dtype=tf.float32)
    x, m, v = state
    m = (1. - b1) * grad + b1 * m  # First  moment estimate.
    v = (1. - b2) * (grad**2.) + b2 * v  # Second moment estimate.
    mhat = m / (1. - b1**(i + 1.))  # Bias correction.
    vhat = v / (1. - b2**(i + 1.))
    x = x - learning_rate * mhat / (tf.sqrt(vhat) + eps)
    return x, m, v

  def get_params(state):
    x, _, _ = state
    return x

  return init, update, get_params
def adam ( learning_rate , b1 = 0.9 , b2 = 0.999 , eps = 1e-8 ) : def init ( x0 ) : m0 = tf . zeros_like ( x0 ) v0 = tf . zeros_like ( x0 ) return x0 , m0 , v0 def update ( i , grad , state ) : i = tf . cast ( i , dtype = tf . float32 ) x , m , v = state m = ( 1. - b1 ) * grad + b1 * m # First  moment estimate. v = ( 1. - b2 ) * ( grad ** 2. ) + b2 * v # Second moment estimate. mhat = m / ( 1. - b1 ** ( i + 1. ) ) # Bias correction. vhat = v / ( 1. - b2 ** ( i + 1. ) ) x = x - learning_rate * mhat / ( tf . sqrt ( vhat ) + eps ) return x , m , v def get_params ( state ) : x , _ , _ = state return x return init , update , get_params