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# coding: utf-8
# pylint: disable=too-many-lines
"""Weight updating functions."""
import math
import pickle
import logging
import warnings
import numpy
from .base import py_str
from .ndarray import (NDArray, zeros, clip, sqrt, cast, maximum, abs as NDabs)
from .ndarray import (sgd_update, sgd_mom_update, adam_update, rmsprop_update, rmspropalex_update,
mp_sgd_update, mp_sgd_mom_update, square, ftrl_update)
from .ndarray import _internal
from .ndarray import op
from .ndarray import sparse
from .random import normal
[docs]class Optimizer(object):
"""The base class inherited by all optimizers.
Parameters
----------
rescale_grad : float, optional
Multiply the gradient with `rescale_grad` before updating. Often
choose to be ``1.0/batch_size``.
param_idx2name : dict from int to string, optional
A dictionary that maps int index to string name.
clip_gradient : float, optional
Clip the gradient by projecting onto the box ``[-clip_gradient, clip_gradient]``.
learning_rate : float, optional
The initial learning rate.
lr_scheduler : LRScheduler, optional
The learning rate scheduler.
wd : float, optional
The weight decay (or L2 regularization) coefficient. Modifies objective
by adding a penalty for having large weights.
sym: Symbol, optional
The Symbol this optimizer is applying to.
begin_num_update : int, optional
The initial number of updates.
multi_precision : bool, optional
Flag to control the internal precision of the optimizer.
``False`` results in using the same precision as the weights (default),
``True`` makes internal 32-bit copy of the weights and applies gradients
in 32-bit precision even if actual weights used in the model have lower precision.
Turning this on can improve convergence and accuracy when training with float16.
Properties
----------
learning_rate: float
The current learning rate of the optimizer. Given an Optimizer object
optimizer, its learning rate can be accessed as optimizer.learning_rate.
"""
def __init__(self, rescale_grad=1., param_idx2name=None, wd=0.,
clip_gradient=None, learning_rate=0.01,
lr_scheduler=None, sym=None, begin_num_update=0,
multi_precision=False, param_dict=None):
self.rescale_grad = rescale_grad
self.lr = learning_rate
self.lr_scheduler = lr_scheduler
if lr_scheduler is not None:
self.lr_scheduler.base_lr = learning_rate
self.wd = wd
self.lr_mult = {}
self.wd_mult = {}
self.begin_num_update = begin_num_update
self.num_update = begin_num_update
self._index_update_count = {}
self.clip_gradient = clip_gradient
self.multi_precision = multi_precision
if param_idx2name is None:
param_idx2name = {}
assert isinstance(param_idx2name, dict), \
'param_idx2name should be a dict of param indexes to names.'
self.idx2name = param_idx2name.copy()
self.sym_info = (sym.attr_dict(), sym.list_arguments()) if sym is not None else ()
self.param_dict = param_dict if param_dict else {}
self.set_lr_mult({})
self.set_wd_mult({})
opt_registry = {}
@staticmethod
[docs] def register(klass):
"""Registers a new optimizer.
Once an optimizer is registered, we can create an instance of this
optimizer with `create_optimizer` later.
Examples
--------
>>> @mx.optimizer.Optimizer.register
... class MyOptimizer(mx.optimizer.Optimizer):
... pass
>>> optim = mx.optimizer.Optimizer.create_optimizer('MyOptimizer')
>>> print(type(optim))
"""
assert(isinstance(klass, type))
name = klass.__name__.lower()
if name in Optimizer.opt_registry:
logging.warning('WARNING: New optimizer %s.%s is overriding '
'existing optimizer %s.%s',
klass.__module__, klass.__name__,
Optimizer.opt_registry[name].__module__,
Optimizer.opt_registry[name].__name__)
Optimizer.opt_registry[name] = klass
return klass
@staticmethod
[docs] def create_optimizer(name, **kwargs):
"""Instantiates an optimizer with a given name and kwargs.
.. note:: We can use the alias `create` for ``Optimizer.create_optimizer``.
Parameters
----------
name: str
Name of the optimizer. Should be the name
of a subclass of Optimizer. Case insensitive.
kwargs: dict
Parameters for the optimizer.
Returns
-------
Optimizer
An instantiated optimizer.
Examples
--------
>>> sgd = mx.optimizer.Optimizer.create_optimizer('sgd')
>>> type(sgd)
>>> adam = mx.optimizer.create('adam', learning_rate=.1)
>>> type(adam)
"""
if name.lower() in Optimizer.opt_registry:
return Optimizer.opt_registry[name.lower()](**kwargs)
else:
raise ValueError('Cannot find optimizer %s' % name)
@property
def learning_rate(self):
if self.lr_scheduler is not None:
return self.lr_scheduler(self.num_update)
else:
return self.lr
[docs] def create_state(self, index, weight):
"""Creates auxiliary state for a given weight.
Some optimizers require additional states, e.g. as momentum, in addition
to gradients in order to update weights. This function creates state
for a given weight which will be used in `update`. This function is
called only once for each weight.
Parameters
----------
index : int
An unique index to identify the weight.
weight : NDArray
The weight.
Returns
-------
state : any obj
The state associated with the weight.
"""
[docs] def create_state_multi_precision(self, index, weight):
"""Creates auxiliary state for a given weight, including FP32 high
precision copy if original weight is FP16.
This method is provided to perform automatic mixed precision training
for optimizers that do not support it themselves.
Parameters
----------
index : int
An unique index to identify the weight.
weight : NDArray
The weight.
Returns
-------
state : any obj
The state associated with the weight.
"""
weight_master_copy = None
if self.multi_precision and weight.dtype == numpy.float16:
weight_master_copy = weight.astype(numpy.float32)
return (weight_master_copy,) + (self.create_state(index, weight_master_copy),)
if weight.dtype == numpy.float16 and not self.multi_precision:
warnings.warn("Accumulating with float16 in optimizer can lead to "
"poor accuracy or slow convergence. "
"Consider using multi_precision=True option of the "
"optimizer")
return self.create_state(index, weight)
[docs] def update(self, index, weight, grad, state):
"""Updates the given parameter using the corresponding gradient and state.
Parameters
----------
index : int
The unique index of the parameter into the individual learning
rates and weight decays. Learning rates and weight decay
may be set via `set_lr_mult()` and `set_wd_mult()`, respectively.
weight : NDArray
The parameter to be updated.
grad : NDArray
The gradient of the objective with respect to this parameter.
state : any obj
The state returned by `create_state()`.
"""
raise NotImplementedError()
[docs] def update_multi_precision(self, index, weight, grad, state):
"""Updates the given parameter using the corresponding gradient and state.
Mixed precision version.
Parameters
----------
index : int
The unique index of the parameter into the individual learning
rates and weight decays. Learning rates and weight decay
may be set via `set_lr_mult()` and `set_wd_mult()`, respectively.
weight : NDArray
The parameter to be updated.
grad : NDArray
The gradient of the objective with respect to this parameter.
state : any obj
The state returned by `create_state()`.
"""
if self.multi_precision and weight.dtype == numpy.float16:
# Wrapper for mixed precision
weight_master_copy = state[0]
original_state = state[1]
grad32 = grad.astype(numpy.float32)
self.update(index, weight_master_copy, grad32, original_state)
cast(weight_master_copy, dtype=weight.dtype, out=weight)
else:
self.update(index, weight, grad, state)
[docs] def set_learning_rate(self, lr):
"""Sets a new learning rate of the optimizer.
Parameters
----------
lr : float
The new learning rate of the optimizer.
"""
if self.lr_scheduler is not None:
raise UserWarning("LRScheduler of the optimizer has already been "
"defined. Note that set_learning_rate can mutate "
"the value of the learning rate of the optimizer "
"only when the LRScheduler of the optimizer is "
"undefined.")
else:
self.lr = lr
[docs] def set_lr_scale(self, args_lrscale): # pylint: disable=unused-argument
"""[DEPRECATED] Sets lr scale. Use set_lr_mult instead."""
raise DeprecationWarning
[docs] def set_lr_mult(self, args_lr_mult):
"""Sets an individual learning rate multiplier for each parameter.
If you specify a learning rate multiplier for a parameter, then
the learning rate for the parameter will be set as the product of
the global learning rate `self.lr` and its multiplier.
.. note:: The default learning rate multiplier of a `Variable`
can be set with `lr_mult` argument in the constructor.
Parameters
----------
args_lr_mult : dict of str/int to float
For each of its key-value entries, the learning rate multipler for the
parameter specified in the key will be set as the given value.
You can specify the parameter with either its name or its index.
If you use the name, you should pass `sym` in the constructor,
and the name you specified in the key of `args_lr_mult` should match
the name of the parameter in `sym`. If you use the index, it should
correspond to the index of the parameter used in the `update` method.
Specifying a parameter by its index is only supported for backward
compatibility, and we recommend to use the name instead.
"""
self.lr_mult = {}
if self.sym_info:
attr, arg_names = self.sym_info
for name in arg_names:
if name in attr and '__lr_mult__' in attr[name]:
self.lr_mult[name] = float(attr[name]['__lr_mult__'])
self.lr_mult.update(args_lr_mult)
[docs] def set_wd_mult(self, args_wd_mult):
"""Sets an individual weight decay multiplier for each parameter.
By default, if `param_idx2name` was provided in the
constructor, the weight decay multipler is set as 0 for all
parameters whose name don't end with ``_weight`` or
``_gamma``.
.. note:: The default weight decay multiplier for a `Variable`
can be set with its `wd_mult` argument in the constructor.
Parameters
----------
args_wd_mult : dict of string/int to float
For each of its key-value entries, the weight decay multipler for the
parameter specified in the key will be set as the given value.
You can specify the parameter with either its name or its index.
If you use the name, you should pass `sym` in the constructor,
and the name you specified in the key of `args_lr_mult` should match
the name of the parameter in `sym`. If you use the index, it should
correspond to the index of the parameter used in the `update` method.
Specifying a parameter by its index is only supported for backward
compatibility, and we recommend to use the name instead.
"""
self.wd_mult = {}
for n in self.idx2name.values():
if not (n.endswith('_weight') or n.endswith('_gamma')):
self.wd_mult[n] = 0.0
if self.sym_info:
attr, arg_names = self.sym_info
for name in arg_names:
if name in attr and '__wd_mult__' in attr[name]:
self.wd_mult[name] = float(attr[name]['__wd_mult__'])
self.wd_mult.update(args_wd_mult)
def _update_count(self, index):
"""Updates num_update.
Parameters
----------
index : int
The index to be updated.
"""
if index not in self._index_update_count:
self._index_update_count[index] = self.begin_num_update
self._index_update_count[index] += 1
self.num_update = max(self._index_update_count[index], self.num_update)
def _get_lr(self, index):
"""Gets the learning rate given the index of the weight.
Parameters
----------
index : int
The index corresponding to the weight.
Returns
-------
lr : float
Learning rate for this index.
"""
if self.lr_scheduler is not None:
lr = self.lr_scheduler(self.num_update)
else:
lr = self.lr
if index in self.param_dict:
lr *= self.param_dict[index].lr_mult
elif index in self.lr_mult:
lr *= self.lr_mult[index]
elif index in self.idx2name:
lr *= self.lr_mult.get(self.idx2name[index], 1.0)
return lr
def _get_wd(self, index):
"""Gets weight decay for index.
Returns 0 for non-weights if the name of weights are provided for `__init__`.
Parameters
----------
index : int
The index for weight.
Returns
-------
wd : float
Weight decay for this index.
"""
wd = self.wd
if index in self.param_dict:
wd *= self.param_dict[index].wd_mult
elif index in self.wd_mult:
wd *= self.wd_mult[index]
elif index in self.idx2name:
wd *= self.wd_mult.get(self.idx2name[index], 1.0)
return wd
# convenience wrapper for Optimizer.Register
register = Optimizer.register # pylint: disable=invalid-name
# pylint: disable=line-too-long
@register
[docs]class SGD(Optimizer):
"""The SGD optimizer with momentum and weight decay.
The optimizer updates the weight by::
rescaled_grad = lr * rescale_grad * clip(grad, clip_gradient) + wd * weight
state = momentum * state + rescaled_grad
weight = weight - state
If the storage types of weight, state and grad are all ``row_sparse``, \
**sparse updates** are applied by::
for row in grad.indices:
rescaled_grad[row] = lr * rescale_grad * clip(grad[row], clip_gradient) + wd * weight[row]
state[row] = momentum[row] * state[row] + rescaled_grad[row]
weight[row] = weight[row] - state[row]
The sparse update only updates the momentum for the weights whose row_sparse
gradient indices appear in the current batch, rather than updating it for all
indices. Compared with the original update, it can provide large
improvements in model training throughput for some applications. However, it
provides slightly different semantics than the original update, and
may lead to different empirical results.
For details of the update algorithm see
:class:`~mxnet.ndarray.sgd_update` and :class:`~mxnet.ndarray.sgd_mom_update`.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
momentum : float, optional
The momentum value.
multi_precision: bool, optional
Flag to control the internal precision of the optimizer.
``False`` results in using the same precision as the weights (default),
``True`` makes internal 32-bit copy of the weights and applies gradients \
in 32-bit precision even if actual weights used in the model have lower precision.\
Turning this on can improve convergence and accuracy when training with float16.
"""
def __init__(self, momentum=0.0, **kwargs):
super(SGD, self).__init__(**kwargs)
self.momentum = momentum
def create_state_multi_precision(self, index, weight):
weight_master_copy = None
if self.multi_precision and weight.dtype == numpy.float16:
weight_master_copy = weight.astype(numpy.float32)
return (self.create_state(index, weight_master_copy), weight_master_copy)
if weight.dtype == numpy.float16 and not self.multi_precision:
warnings.warn("Accumulating with float16 in optimizer can lead to "
"poor accuracy or slow convergence. "
"Consider using multi_precision=True option of the "
"SGD optimizer")
return self.create_state(index, weight)
def create_state(self, index, weight):
momentum = None
if self.momentum != 0.0:
momentum = zeros(weight.shape, weight.context, dtype=weight.dtype, stype=weight.stype)
return momentum
def _update_impl(self, index, weight, grad, state, multi_precision=False):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
kwargs = {'rescale_grad': self.rescale_grad}
if self.momentum > 0:
kwargs['momentum'] = self.momentum
if self.clip_gradient:
kwargs['clip_gradient'] = self.clip_gradient
if not multi_precision:
if state is not None:
sgd_mom_update(weight, grad, state, out=weight,
lr=lr, wd=wd, **kwargs)
else:
sgd_update(weight, grad, out=weight,
lr=lr, wd=wd, **kwargs)
else:
if state[0] is not None:
mp_sgd_mom_update(weight, grad, state[0], state[1], out=weight,
lr=lr, wd=wd, **kwargs)
else:
mp_sgd_update(weight, grad, state[1], out=weight,
lr=lr, wd=wd, **kwargs)
def update(self, index, weight, grad, state):
self._update_impl(index, weight, grad, state, multi_precision=False)
def update_multi_precision(self, index, weight, grad, state):
use_multi_precision = self.multi_precision and weight.dtype == numpy.float16
self._update_impl(index, weight, grad, state,
multi_precision=use_multi_precision)
# pylint: enable=line-too-long
@register
[docs]class DCASGD(Optimizer):
"""The DCASGD optimizer.
This class implements the optimizer described in *Asynchronous Stochastic Gradient Descent
with Delay Compensation for Distributed Deep Learning*,
available at https://arxiv.org/abs/1609.08326.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
momentum : float, optional
The momentum value.
lamda : float, optional
Scale DC value.
"""
def __init__(self, momentum=0.0, lamda=0.04, **kwargs):
super(DCASGD, self).__init__(**kwargs)
self.momentum = momentum
self.weight_previous = {}
self.lamda = lamda
def create_state(self, index, weight):
if self.momentum == 0.0:
return (None,
weight.copy()) # previous weight
else:
return (zeros(weight.shape, weight.context, dtype=weight.dtype), # momentum
weight.copy()) # previous weight
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
grad = grad * self.rescale_grad
if self.clip_gradient is not None:
grad = clip(grad, -self.clip_gradient, self.clip_gradient)
mom, previous_weight = state
if mom:
mom[:] *= self.momentum
mom[:] += -lr * (grad + wd * weight + self.lamda \
* grad * grad * (weight - previous_weight))
else:
assert(self.momentum == 0.0)
mom = -lr * (grad + wd * weight + self.lamda \
* grad * grad * (weight - previous_weight))
previous_weight[:] = weight
weight[:] += mom
@register
[docs]class NAG(SGD):
"""Nesterov accelerated SGD.
This optimizer updates each weight by::
state = momentum * state + grad + wd * weight
weight = weight - (lr * (grad + momentum * state))
This optimizer accepts the same arguments as :class:`.SGD`.
"""
def __init__(self, **kwargs):
super(NAG, self).__init__(**kwargs)
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
grad = grad * self.rescale_grad
if self.clip_gradient is not None:
grad = clip(grad, -self.clip_gradient, self.clip_gradient)
if state is not None:
mom = state
mom[:] *= self.momentum
grad += wd * weight
mom[:] += grad
grad[:] += self.momentum * mom
weight[:] += -lr * grad
else:
assert self.momentum == 0.0
weight[:] += -lr * (grad + wd * weight)
@register
[docs]class SGLD(Optimizer):
"""Stochastic Gradient Riemannian Langevin Dynamics.
This class implements the optimizer described in the paper *Stochastic Gradient
Riemannian Langevin Dynamics on the Probability Simplex*, available at
https://papers.nips.cc/paper/4883-stochastic-gradient-riemannian-langevin-dynamics-on-the-probability-simplex.pdf.
"""
def __init__(self, **kwargs):
super(SGLD, self).__init__(**kwargs)
def create_state(self, index, weight):
return None
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
grad = grad * self.rescale_grad
if self.clip_gradient is not None:
grad = clip(grad, -self.clip_gradient, self.clip_gradient)
weight[:] += - lr/2 * (grad + wd * weight) + normal(0, math.sqrt(lr),
shape=weight.shape,
ctx=weight.context)
@register # pylint: disable=invalid-name
[docs]class ccSGD(SGD):
"""[DEPRECATED] Same as `SGD`. Left here for backward compatibility."""
def __init__(self, *args, **kwargs):
super(ccSGD, self).__init__(*args, **kwargs)
@register
[docs]class Adam(Optimizer):
"""The Adam optimizer.
This class implements the optimizer described in *Adam: A Method for
Stochastic Optimization*, available at http://arxiv.org/abs/1412.6980.
The optimizer updates the weight by::
rescaled_grad = clip(grad * rescale_grad + wd * weight, clip_gradient)
m = beta1 * m + (1 - beta1) * rescaled_grad
v = beta2 * v + (1 - beta2) * (rescaled_grad**2)
w = w - learning_rate * m / (sqrt(v) + epsilon)
If the storage types of weight, state and grad are all ``row_sparse``, \
**sparse updates** are applied by::
for row in grad.indices:
rescaled_grad[row] = clip(grad[row] * rescale_grad + wd * weight[row], clip_gradient)
m[row] = beta1 * m[row] + (1 - beta1) * rescaled_grad[row]
v[row] = beta2 * v[row] + (1 - beta2) * (rescaled_grad[row]**2)
w[row] = w[row] - learning_rate * m[row] / (sqrt(v[row]) + epsilon)
The sparse update only updates the mean and var for the weights whose row_sparse
gradient indices appear in the current batch, rather than updating it for all indices.
Compared with the original update, it can provide large improvements in model training
throughput for some applications. However, it provides slightly different semantics than
the original update, and may lead to different empirical results.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
For details of the update algorithm, see :class:`~mxnet.ndarray.adam_update`.
Parameters
----------
beta1 : float, optional
Exponential decay rate for the first moment estimates.
beta2 : float, optional
Exponential decay rate for the second moment estimates.
epsilon : float, optional
Small value to avoid division by 0.
"""
def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-8,
**kwargs):
super(Adam, self).__init__(learning_rate=learning_rate, **kwargs)
self.beta1 = beta1
self.beta2 = beta2
self.epsilon = epsilon
def create_state(self, index, weight):
return (zeros(weight.shape, weight.context, dtype=weight.dtype,
stype=weight.stype), # mean
zeros(weight.shape, weight.context, dtype=weight.dtype,
stype=weight.stype)) # variance
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
t = self._index_update_count[index]
coef1 = 1. - self.beta1**t
coef2 = 1. - self.beta2**t
lr *= math.sqrt(coef2)/coef1
kwargs = {'beta1': self.beta1, 'beta2': self.beta2, 'epsilon': self.epsilon,
'rescale_grad': self.rescale_grad}
if self.clip_gradient:
kwargs['clip_gradient'] = self.clip_gradient
mean, var = state
adam_update(weight, grad, mean, var, out=weight,
lr=lr, wd=wd, **kwargs)
@register
[docs]class AdaGrad(Optimizer):
"""AdaGrad optimizer.
This class implements the AdaGrad optimizer described in *Adaptive Subgradient
Methods for Online Learning and Stochastic Optimization*, and available at
http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
eps: float, optional
Small value to avoid division by 0.
"""
def __init__(self, eps=1e-7, **kwargs):
super(AdaGrad, self).__init__(**kwargs)
self.float_stable_eps = eps
def create_state(self, index, weight):
return zeros(weight.shape, weight.context, stype=weight.stype) # history
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
is_sparse = True if weight.stype == 'row_sparse' and grad.stype == 'row_sparse' else False
if is_sparse is True:
grad_indices_count = len(grad.indices)
grad = grad * self.rescale_grad
if is_sparse is True:
grad_indices = grad.indices
# Make sure that the scalar multiply still has a sparse result
assert grad_indices_count == len(grad_indices)
if self.clip_gradient is not None:
grad = clip(grad, -self.clip_gradient, self.clip_gradient)
history = state
save_history_stype = history.stype
if is_sparse:
history[:] = sparse.elemwise_add(sparse.square(grad),
sparse.retain(history, grad_indices))
history_indices = history.indices
assert len(history_indices) == grad_indices_count
adjusted_add = _internal._scatter_plus_scalar(history, self.float_stable_eps)
srt = op.sqrt(adjusted_add)
div = _internal._scatter_elemwise_div(grad, srt)
retained_weight = sparse.retain(weight, grad.indices)
to_add = sparse.elemwise_add(div, _internal._mul_scalar(retained_weight, float(wd)))
assert len(to_add.indices) == grad_indices_count
weight[:] = sparse.elemwise_add(weight, _internal._mul_scalar(to_add, float(-lr)))
state[:] = history
assert state.stype == save_history_stype
assert len(history_indices) == grad_indices_count
else:
history[:] += square(grad)
div = grad / sqrt(history + self.float_stable_eps)
weight[:] += (div + weight * wd) * -lr
@register
[docs]class RMSProp(Optimizer):
"""The RMSProp optimizer.
Two versions of RMSProp are implemented:
If ``centered=False``, we follow
http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf by
Tieleman & Hinton, 2012.
For details of the update algorithm see :class:`~mxnet.ndarray.rmsprop_update`.
If ``centered=True``, we follow http://arxiv.org/pdf/1308.0850v5.pdf (38)-(45)
by Alex Graves, 2013.
For details of the update algorithm see :class:`~mxnet.ndarray.rmspropalex_update`.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
gamma1: float, optional
A decay factor of moving average over past squared gradient.
gamma2: float, optional
A "momentum" factor. Only used if `centered`=``True``.
epsilon : float, optional
Small value to avoid division by 0.
centered : bool, optional
Flag to control which version of RMSProp to use.
``True`` will use Graves's version of `RMSProp`,
``False`` will use Tieleman & Hinton's version of `RMSProp`.
clip_weights : float, optional
Clips weights into range ``[-clip_weights, clip_weights]``.
"""
def __init__(self, learning_rate=0.001, gamma1=0.9, gamma2=0.9,
epsilon=1e-8, centered=False, clip_weights=None, **kwargs):
super(RMSProp, self).__init__(learning_rate=learning_rate, **kwargs)
self.gamma1 = gamma1
self.gamma2 = gamma2
self.centered = centered
self.epsilon = epsilon
self.clip_weights = clip_weights
def create_state(self, index, weight):
if self.centered:
return (
zeros(weight.shape, weight.context, stype=weight.stype), # n
zeros(weight.shape, weight.context, stype=weight.stype), # g
zeros(weight.shape, weight.context, stype=weight.stype)) # delta
else:
return (zeros(weight.shape, weight.context, stype=weight.stype),) # n
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
kwargs = {'gamma1': self.gamma1, 'epsilon': self.epsilon,
'rescale_grad': self.rescale_grad}
if self.centered:
kwargs['gamma2'] = self.gamma2
if self.clip_gradient:
kwargs['clip_gradient'] = self.clip_gradient
if self.clip_weights:
kwargs['clip_weights'] = self.clip_weights
if not self.centered:
(n, ) = state
rmsprop_update(
weight, grad, n, out=weight, lr=lr, wd=wd, **kwargs)
else:
n, g, delta = state
rmspropalex_update(weight, grad, n, g, delta, out=weight,
lr=lr, wd=wd, **kwargs)
@register
[docs]class AdaDelta(Optimizer):
"""The AdaDelta optimizer.
This class implements AdaDelta, an optimizer described in *ADADELTA: An adaptive
learning rate method*, available at https://arxiv.org/abs/1212.5701.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
rho: float
Decay rate for both squared gradients and delta.
epsilon : float
Small value to avoid division by 0.
"""
def __init__(self, rho=0.90, epsilon=1e-5, **kwargs):
super(AdaDelta, self).__init__(**kwargs)
self.rho = rho
self.epsilon = epsilon
def create_state(self, index, weight):
return (zeros(weight.shape, weight.context), # accumulated g
zeros(weight.shape, weight.context)) # accumulated delta
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
wd = self._get_wd(index)
self._update_count(index)
# preprocess grad
grad *= self.rescale_grad
if self.clip_gradient is not None:
grad = clip(grad, -self.clip_gradient, self.clip_gradient)
# accumulated g and delta initlization
acc_g, acc_delta = state
# update g, delta
acc_g[:] = self.rho * acc_g + (1. - self.rho) * grad * grad
current_delta = sqrt(acc_delta + self.epsilon) / sqrt(acc_g + self.epsilon) * grad
acc_delta[:] = self.rho * acc_delta + (1. - self.rho) * current_delta * current_delta
# update weight
weight[:] -= current_delta + wd * weight
#pylint: disable=invalid-name
#pylint: disable=line-too-long
@register
[docs]class Ftrl(Optimizer):
"""The Ftrl optimizer.
Referenced from *Ad Click Prediction: a View from the Trenches*, available at
http://dl.acm.org/citation.cfm?id=2488200.
eta :
.. math::
\\eta_{t,i} = \\frac{learningrate}{\\beta+\\sqrt{\\sum_{s=1}^tg_{s,i}^2}}
The optimizer updates the weight by::
rescaled_grad = clip(grad * rescale_grad, clip_gradient)
z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
n += rescaled_grad**2
w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)
If the storage types of weight, state and grad are all ``row_sparse``, \
**sparse updates** are applied by::
for row in grad.indices:
rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient)
z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
n[row] += rescaled_grad[row]**2
w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)
The sparse update only updates the z and n for the weights whose row_sparse
gradient indices appear in the current batch, rather than updating it for all
indices. Compared with the original update, it can provide large
improvements in model training throughput for some applications. However, it
provides slightly different semantics than the original update, and
may lead to different empirical results.
For details of the update algorithm, see :class:`~mxnet.ndarray.ftrl_update`.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
lamda1 : float, optional
L1 regularization coefficient.
learning_rate : float, optional
The initial learning rate.
beta : float, optional
Per-coordinate learning rate correlation parameter.
"""
def __init__(self, lamda1=0.01, learning_rate=0.1, beta=1, **kwargs):
super(Ftrl, self).__init__(**kwargs)
self.lamda1 = lamda1
self.beta = beta
self.lr = learning_rate
def create_state(self, index, weight):
return (zeros(weight.shape, weight.context, stype=weight.stype), # z
zeros(weight.shape, weight.context, stype=weight.stype)) # n
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
wd = self._get_wd(index)
lr = self._get_lr(index)
kwargs = {'lamda1': self.lamda1, 'beta': self.beta, 'rescale_grad': self.rescale_grad}
if self.clip_gradient:
kwargs['clip_gradient'] = self.clip_gradient
# accumulated g and delta initialization
z, n = state
ftrl_update(weight, grad, z, n, out=weight,
lr=lr, wd=wd, **kwargs)
# pylint: enable=line-too-long
@register
[docs]class Adamax(Optimizer):
"""The AdaMax optimizer.
It is a variant of Adam based on the infinity norm
available at http://arxiv.org/abs/1412.6980 Section 7.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
beta1 : float, optional
Exponential decay rate for the first moment estimates.
beta2 : float, optional
Exponential decay rate for the second moment estimates.
"""
def __init__(self, learning_rate=0.002, beta1=0.9, beta2=0.999, **kwargs):
super(Adamax, self).__init__(learning_rate=learning_rate, **kwargs)
self.beta1 = beta1
self.beta2 = beta2
def create_state(self, index, weight):
return (zeros(weight.shape, weight.context, dtype=weight.dtype), # mean
zeros(weight.shape, weight.context, dtype=weight.dtype)) # variance
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
t = self._index_update_count[index]
lr /= (1. - self.beta1**t)
# preprocess grad
grad = grad * self.rescale_grad + wd * weight
if self.clip_gradient is not None:
grad = clip(grad, -self.clip_gradient, self.clip_gradient)
# update m_t and u_t
m_t, u_t = state
m_t[:] = self.beta1 * m_t + (1. - self.beta1) * grad
u_t[:] = maximum(self.beta2 * u_t, NDabs(grad))
# update weight
weight[:] -= lr * m_t / u_t
@register
[docs]class Nadam(Optimizer):
"""The Nesterov Adam optimizer.
Much like Adam is essentially RMSprop with momentum,
Nadam is Adam RMSprop with Nesterov momentum available
at http://cs229.stanford.edu/proj2015/054_report.pdf.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
beta1 : float, optional
Exponential decay rate for the first moment estimates.
beta2 : float, optional
Exponential decay rate for the second moment estimates.
epsilon : float, optional
Small value to avoid division by 0.
schedule_decay : float, optional
Exponential decay rate for the momentum schedule
"""
def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-8,
schedule_decay=0.004, **kwargs):
super(Nadam, self).__init__(learning_rate=learning_rate, **kwargs)
self.beta1 = beta1
self.beta2 = beta2
self.epsilon = epsilon
self.schedule_decay = schedule_decay
self.m_schedule = 1.
def create_state(self, index, weight):
return (zeros(weight.shape, weight.context, dtype=weight.dtype), # mean
zeros(weight.shape, weight.context, dtype=weight.dtype)) # variance
def update(self, index, weight, grad, state):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
t = self._index_update_count[index]
# preprocess grad
grad = grad * self.rescale_grad + wd * weight
if self.clip_gradient is not None:
grad = clip(grad, -self.clip_gradient, self.clip_gradient)
# warming momentum schedule
momentum_t = self.beta1 * (1. - 0.5 * (pow(0.96, t * self.schedule_decay)))
momentum_t_1 = self.beta1 * (1. - 0.5 * (pow(0.96, (t + 1) * self.schedule_decay)))
self.m_schedule = self.m_schedule * momentum_t
m_schedule_next = self.m_schedule * momentum_t_1
# update m_t and v_t
m_t, v_t = state
m_t[:] = self.beta1 * m_t + (1. - self.beta1) * grad
v_t[:] = self.beta2 * v_t + (1. - self.beta2) * grad * grad
grad_prime = grad / (1. - self.m_schedule)
m_t_prime = m_t / (1. - m_schedule_next)
v_t_prime = v_t / (1. - pow(self.beta2, t))
m_t_bar = (1. - momentum_t) * grad_prime + momentum_t_1 * m_t_prime
# update weight
weight[:] -= lr * m_t_bar / (sqrt(v_t_prime) + self.epsilon)
@register
[docs]class Test(Optimizer):
"""The Test optimizer"""
def __init__(self, **kwargs):
super(Test, self).__init__(**kwargs)
[docs] def create_state(self, index, weight):
"""Creates a state to duplicate weight."""
return zeros(weight.shape, weight.context)
[docs] def update(self, index, weight, grad, state):
"""Performs w += rescale_grad * grad."""
weight[:] += grad * self.rescale_grad
state[:] = weight
# backward compatibility wrapper for Optimizer.CreateOptimizer
create = Optimizer.create_optimizer # pylint: disable=invalid-name
[docs]class Updater(object):
"""Updater for kvstore."""
def __init__(self, optimizer):
self.optimizer = optimizer
self.states = {}
self.states_synced = {}
def __call__(self, index, grad, weight):
"""Updates weight given gradient and index."""
# convert ctypes.char_p.value back to python str if needed
if isinstance(index, bytes):
index = py_str(index)
if index not in self.states:
self.states[index] = self.optimizer.create_state_multi_precision(index, weight)
self.states_synced[index] = True
elif not self.states_synced[index]:
self.states[index] = \
self.sync_state_context(self.states[index], weight.context)
self.states_synced[index] = True
self.optimizer.update_multi_precision(index, weight, grad, self.states[index])
def sync_state_context(self, state, context):
if isinstance(state, NDArray):
return state.as_in_context(context)
elif isinstance(state, (tuple, list)):
synced_state = (self.sync_state_context(i, context) for i in state)
if isinstance(state, tuple):
return tuple(synced_state)
else:
return list(synced_state)
else:
return state
[docs] def set_states(self, states):
"""Sets updater states."""
states = pickle.loads(states)
if isinstance(states, tuple) and len(states) == 2:
self.states, self.optimizer = states
else:
self.states = states
self.states_synced = dict.fromkeys(self.states.keys(), False)
[docs] def get_states(self, dump_optimizer=False):
"""Gets updater states.
Parameters
----------
dump_optimizer : bool, default False
Whether to also save the optimizer itself. This would also save optimizer
information such as learning rate and weight decay schedules.
"""
return pickle.dumps((self.states, self.optimizer) if dump_optimizer else self.states)
[docs]def get_updater(optimizer):
"""Returns a closure of the updater needed for kvstore.
Parameters
----------
optimizer: Optimizer
The optimizer.
Returns
-------
updater: function
The closure of the updater.
"""
return Updater(optimizer)
