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optimizers.py
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optimizers.py
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import numpy as np
import tensorflow as tf
def create_train_op(loss, params):
lr = params["lr"]
if "warmup_steps" in params.keys():
lr = cosine_decay_with_warmup(tf.train.get_global_step(), lr,
params["max_steps"], warmup_steps=params["warmup_steps"])
if params["opt_name"] == "adam":
if not "weight_decay" in params.keys():
optimizer = tf.train.AdamOptimizer(
learning_rate=lr,
beta1=params["beta1"],
beta2=params["beta2"],
epsilon=params["epsilon"])
else:
optimizer = tf.contrib.opt.AdamWOptimizer(
learning_rate=lr,
weight_decay=lr*params["weight_decay"],
beta1=params["beta1"],
beta2=params["beta2"],
epsilon=params["epsilon"])
elif params["opt_name"] == "adafactor":
if params["decay_type"] == "adam":
decay_rate = adafactor_decay_rate_adam(params["beta2"])
elif params["decay_type"] == "pow":
decay_rate = adafactor_decay_rate_pow(params["decay_exponent"])
else:
raise ValueError("unknown optimizer_adafactor_decay_type")
if not "weight_decay" in params.keys():
optimizer = AdafactorOptimizer(
learning_rate=lr,
decay_rate=decay_rate,
beta1=params["beta1"],
name="Adafactor")
else:
AdafactorWOptimizer = tf.contrib.opt.extend_with_decoupled_weight_decay(AdafactorOptimizer)
optimizer = AdafactorWOptimizer(
weight_decay=params["weight_decay"] * lr,
learning_rate=lr,
decay_rate=decay_rate,
beta1=params["beta1"],
name="AdafactorW")
else:
raise ValueError("Unknown optimizer type!")
if params["use_tpu"]:
optimizer = tf.contrib.tpu.CrossShardOptimizer(optimizer)
update_ops = tf.get_collection(tf.GraphKeys.UPDATE_OPS) # To update batchnorm, if present
train_op = optimizer.minimize(loss, global_step=tf.train.get_global_step())
train_op = tf.group([train_op, update_ops])
return train_op
def cosine_decay_with_warmup(global_step,
learning_rate_base,
total_steps,
warmup_learning_rate=0.0,
warmup_steps=0,
hold_base_rate_steps=0,
name="learning_rate"):
if total_steps < warmup_steps:
raise ValueError('total_steps must be larger or equal to '
'warmup_steps.')
learning_rate = 0.5 * learning_rate_base * (1 + tf.cos(
np.pi *
(tf.cast(global_step, tf.float32) - warmup_steps - hold_base_rate_steps
) / float(total_steps - warmup_steps - hold_base_rate_steps)))
if hold_base_rate_steps > 0:
learning_rate = tf.where(global_step > warmup_steps + hold_base_rate_steps,
learning_rate, learning_rate_base)
if warmup_steps > 0:
if learning_rate_base < warmup_learning_rate:
raise ValueError('learning_rate_base must be larger or equal to '
'warmup_learning_rate.')
slope = (learning_rate_base - warmup_learning_rate) / warmup_steps
warmup_rate = slope * tf.cast(global_step,
tf.float32) + warmup_learning_rate
learning_rate = tf.where(global_step < warmup_steps, warmup_rate,
learning_rate)
return tf.where(global_step > total_steps, 0.0, learning_rate,
name=name)
# Adafactor from tensor2tensor -------------------------------------------------------------
class AdafactorOptimizer(tf.train.Optimizer):
"""Optimizer that implements the Adafactor algorithm.
Adafactor is described in https://arxiv.org/abs/1804.04235.
Adafactor is most similar to Adam (Kingma and Ba), the major differences are:
1. For a two-dimensional AxB weight matrix, Adafactor uses only A+B auxiliary
parameters to maintain the second-moment estimator, instead of AB.
This is advantageous on memory-limited systems. In addition, beta1
(momentum) is set to zero by default, saving an additional auxiliary
parameter per weight. Variables with >=3 dimensions are treated as
collections of two-dimensional matrices - factorization is over the final
two dimensions.
2. Adafactor incorporates "update-clipping" - a scale-invariant analog of
gradient clipping. This adds stability
3. Adafactor does not require an external "learning rate". By default, it
incorporates a relative-update-scale schedule, corresponding to
inverse-square-root learning-rate-decay in ADAM. We hope this works well
for most applications.
ALGORITHM:
parameter -= absolute_update_scale * clip(grad / grad_scale)
where:
absolute_update_scale := relative_update_scale * parameter_scale
relative_update_scale := min((step_num + 1)**-0.5, 1e-2)
parameter_scale := max(rms(var)), epsilon2)
clip(x) := x / max(1.0, rms(x))
grad_scale := tf.sqrt(v) (v is the second-moment estimator)
The second-moment estimator v is maintained in a manner similar to Adam:
We initialize
```
if var is 2-dimensional:
v_r <- zeros([num_rows])
v_c <- zeros([num_cols])
if var is 0-dimensional or 1-dimensional:
v <- zeros(shape(var))
```
The update rule is as follows:
```
decay_rate = 1 - (step_num + 1) ^ -0.8
grad_squared = tf.square(grad) + epsilon1
if var is 2-dimensional:
v_r <- decay_rate * v_r + (1 - decay_rate) * reduce_mean(grad_squared, 1)
v_c <- decay_rate * v_c + (1 - decay_rate) * reduce_mean(grad_squared, 0)
v = outer_prod(v_r, v_c) / reduce_mean(v_r)
if var is 0-dimensional or 1-dimensional:
v <- decay_rate * v + (1 - decay_rate) * grad_squared
```
For variables with >=3 dimensions, we factorize the second-moment accumulator
over the final 2 dimensions. See the code for details.
Several parts of this algorithm are configurable from the initializer.
multiply_by_parameter_scale: If True, then compute absolute_update_scale
as described above. If False, let absolute_update_scale be the externally
supplied learning_rate.
learning_rate: represents relative_update_scale if
multiply_by_parameter_scale==True, or absolute_update_scale if
multiply_by_parameter_scale==False.
decay_rate: Decay rate of the second moment estimator (varies by step_num).
This should be set to a function such that:
1-1/(step_num + 1) <= decay_rate(step_num) < 1.0
beta1: enables momentum, as in Adam. Uses extra memory if nonzero.
clipping_threshold: should be >=1.0 or None for no update clipping
factored: whether to factor the second-moment estimator. True means
less memory usage.
"""
def __init__(self,
multiply_by_parameter_scale=True,
learning_rate=None,
decay_rate=None,
beta1=0.0,
clipping_threshold=1.0,
factored=True,
use_locking=False,
name="Adafactor",
epsilon1=1e-30,
epsilon2=1e-3):
"""Construct a new Adafactor optimizer.
See class comment.
Args:
multiply_by_parameter_scale: a boolean
learning_rate: an optional Scalar.
decay_rate: an optional Scalar.
beta1: a float value between 0 and 1
clipping_threshold: an optional float >= 1
factored: a boolean - whether to use factored second-moment estimator
for 2d variables
use_locking: If True use locks for update operations.
name: Optional name for the operations created when applying gradients.
Defaults to "AdafactorOptimizer".
epsilon1: Regularization constant for squared gradient.
epsilon2: Regularization constant for parameter scale.
Raises:
ValueError: if absolute_update_scale and relative_update_scale_fn are both
present or both absent.
"""
super(AdafactorOptimizer, self).__init__(use_locking, name)
self._multiply_by_parameter_scale = multiply_by_parameter_scale
if learning_rate is None:
learning_rate = self._learning_rate_default(multiply_by_parameter_scale)
self._learning_rate = learning_rate
if decay_rate is None:
decay_rate = self._decay_rate_default()
self._decay_rate = decay_rate
self._beta1 = beta1
self._clipping_threshold = clipping_threshold
self._factored = factored
self._epsilon1 = epsilon1
self._epsilon2 = epsilon2
def _should_use_factored_second_moment_estimate(self, shape):
"""Should we use a factored second moment estimator.
Based on the shape of the variable.
Args:
shape: a list of integers
Returns:
a boolean
"""
return self._factored and len(shape) >= 2
def _create_slots(self, var_list):
for var in var_list:
shape = var.get_shape().as_list()
if self._beta1:
self._zeros_slot(var, "m", self._name)
if self._should_use_factored_second_moment_estimate(shape):
r_val = tf.zeros(shape[:-1], dtype=tf.float32)
c_val = tf.zeros(shape[:-2] + shape[-1:], dtype=tf.float32)
self._get_or_make_slot(var, r_val, "vr", self._name)
self._get_or_make_slot(var, c_val, "vc", self._name)
else:
v_val = tf.zeros(shape, dtype=tf.float32)
self._get_or_make_slot(var, v_val, "v", self._name)
def _apply_dense(self, grad, var):
return self._resource_apply_dense(grad, var)
def _apply_sparse(self, grad, var):
return self._apply_dense(tf.convert_to_tensor(grad), var)
def _resource_apply_sparse(self, grad, handle, indices):
return self._resource_apply_dense(
tf.convert_to_tensor(tf.IndexedSlices(grad, indices, tf.shape(handle))),
handle)
def _parameter_scale(self, var):
"""Estimate the scale of the parameters from the current values.
We include a minimum value of 0.001 to give it a chance to escape 0
if it was zero-initialized.
Instead of using the value, we could impute the scale from the shape,
as initializers do.
Args:
var: a variable or Tensor.
Returns:
a Scalar
"""
return tf.maximum(reduce_rms(var), self._epsilon2)
def _resource_apply_dense(self, grad, handle):
var = handle
grad = tf.to_float(grad)
grad_squared = tf.square(grad) + self._epsilon1
grad_squared_mean = tf.reduce_mean(grad_squared)
decay_rate = self._decay_rate
update_scale = self._learning_rate
old_val = var
if var.dtype.base_dtype == tf.bfloat16:
old_val = tf.to_float(self._parameter_encoding.decode(old_val))
if self._multiply_by_parameter_scale:
update_scale *= tf.to_float(self._parameter_scale(old_val))
# HACK: Make things dependent on grad.
# This confounds the XLA rewriter and keeps it from fusing computations
# across different variables. This fusion is a bad for HBM usage, since
# it causes the gradients to persist in memory.
decay_rate += grad_squared_mean * 1e-30
update_scale += grad_squared_mean * 1e-30
# END HACK
mixing_rate = 1.0 - decay_rate
shape = var.get_shape().as_list()
updates = []
if self._should_use_factored_second_moment_estimate(shape):
grad_squared_row_mean = tf.reduce_mean(grad_squared, -1)
grad_squared_col_mean = tf.reduce_mean(grad_squared, -2)
vr = self.get_slot(var, "vr")
new_vr = (decay_rate * vr + mixing_rate * grad_squared_row_mean)
vc = self.get_slot(var, "vc")
new_vc = (decay_rate * vc + mixing_rate * grad_squared_col_mean)
vr_update = tf.assign(vr, new_vr, use_locking=self._use_locking)
vc_update = tf.assign(vc, new_vc, use_locking=self._use_locking)
updates = [vr_update, vc_update]
long_term_mean = tf.reduce_mean(new_vr, -1, keepdims=True)
r_factor = tf.rsqrt(new_vr / long_term_mean)
c_factor = tf.rsqrt(new_vc)
x = grad * tf.expand_dims(r_factor, -1) * tf.expand_dims(c_factor, -2)
else:
v = self.get_slot(var, "v")
new_v = decay_rate * v + mixing_rate * grad_squared
v_update = tf.assign(v, new_v, use_locking=self._use_locking)
updates = [v_update]
x = grad * tf.rsqrt(new_v)
if self._clipping_threshold is not None:
clipping_denom = tf.maximum(1.0, reduce_rms(x) / self._clipping_threshold)
x /= clipping_denom
subtrahend = update_scale * x
if self._beta1:
m = self.get_slot(var, "m")
new_m = self._beta1 * tf.to_float(m) + (1.0 - self._beta1) * subtrahend
subtrahend = new_m
new_m = cast_like(new_m, var)
updates.append(tf.assign(m, new_m, use_locking=self._use_locking))
new_val = tf.to_float(old_val) - subtrahend
var_update = tf.assign(var, new_val, use_locking=self._use_locking)
updates = [var_update] + updates
return tf.group(*updates)
def _decay_rate_default(self):
return adafactor_decay_rate_pow(0.8)
def _learning_rate_default(self, multiply_by_parameter_scale):
learning_rate = tf.minimum(tf.rsqrt(step_num() + 1.0), 0.01)
if not multiply_by_parameter_scale:
learning_rate *= 0.05
return learning_rate
def adafactor_decay_rate_adam(beta2):
t = tf.to_float(tf.train.get_or_create_global_step()) + 1.0
decay = beta2 * (1.0 - tf.pow(beta2, t - 1.0)) / (1.0 - tf.pow(beta2, t))
# decay = tf.cond(tf.equal(t, 1.0), lambda: beta2, lambda: decay)
return decay
def adafactor_decay_rate_pow(exponent):
return 1.0 - tf.pow((step_num() + 1.0), -exponent)
def step_num():
return tf.to_float(tf.train.get_or_create_global_step())
def reduce_rms(x):
return tf.sqrt(tf.reduce_mean(tf.square(x)))
def cast_like(x, y):
"""Cast x to y's dtype, if necessary."""
x = tf.convert_to_tensor(x)
y = tf.convert_to_tensor(y)
if x.dtype.base_dtype == y.dtype.base_dtype:
return x
cast_x = tf.cast(x, y.dtype)
if cast_x.device != x.device:
x_name = "(eager Tensor)"
try:
x_name = x.name
except AttributeError:
pass
tf.logging.warning("Cast for %s may induce copy from '%s' to '%s'", x_name,
x.device, cast_x.device)
return cast_x