Source code for mxnet.optimizer.optimizer
# coding: utf-8
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# pylint: disable=too-many-lines
"""Weight updating functions."""
from __future__ import absolute_import
import logging
import math
import pickle
import warnings
import os
import numpy
from ..base import py_str
from ..ndarray import (NDArray, zeros, clip, sqrt, cast, maximum, abs as NDabs, array, multiply,
multi_sum_sq, multi_lars, norm as NDnorm)
from ..ndarray import (sgd_update, sgd_mom_update, adam_update, rmsprop_update, rmspropalex_update,
mp_sgd_update, mp_sgd_mom_update, square, ftrl_update, ftml_update,
signsgd_update, signum_update, nag_mom_update, mp_nag_mom_update,
multi_sgd_update, multi_sgd_mom_update, multi_mp_sgd_update,
multi_mp_sgd_mom_update, preloaded_multi_sgd_update,
preloaded_multi_sgd_mom_update, preloaded_multi_mp_sgd_update,
preloaded_multi_mp_sgd_mom_update, lamb_update_phase1, lamb_update_phase2,
mp_lamb_update_phase1, mp_lamb_update_phase2)
from ..ndarray import sparse
from ..random import normal
from ..util import is_np_array
__all__ = [
'AdaDelta', 'AdaGrad', 'Adam', 'Adamax', 'DCASGD', 'FTML', 'Ftrl', 'LARS', 'LBSGD',
'NAG', 'NDabs', 'Nadam', 'Optimizer', 'RMSProp', 'SGD', 'SGLD', 'Signum', 'LAMB',
'Test', 'Updater', 'ccSGD', 'create', 'get_updater', 'register'
]
def _flatten_list(nested_list):
return [item for sublist in nested_list for item in sublist]
[docs]class Optimizer(object):
"""The base class inherited by all optimizers.
Parameters
----------
rescale_grad : float, optional, default 1.0
Multiply the gradient with `rescale_grad` before updating. Often
choose to be ``1.0/batch_size``.
param_idx2name : dict from int to string, optional, default None
A dictionary that maps int index to string name.
clip_gradient : float, optional, default None
Clip the gradient by projecting onto the box ``[-clip_gradient, clip_gradient]``.
learning_rate : float, optional, default None
The initial learning rate. If None, the optimization will use the
learning rate from ``lr_scheduler``. If not None, it will overwrite
the learning rate in ``lr_scheduler``. If None and ``lr_scheduler``
is also None, then it will be set to 0.01 by default.
lr_scheduler : LRScheduler, optional, default None
The learning rate scheduler.
wd : float, optional, default 0.0
The weight decay (or L2 regularization) coefficient. Modifies objective
by adding a penalty for having large weights.
sym: Symbol, optional, default None
The Symbol this optimizer is applying to.
begin_num_update : int, optional, default 0
The initial number of updates.
multi_precision : bool, optional, default False
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.
param_dict : dict of int -> gluon.Parameter, default None
Dictionary of parameter index to gluon.Parameter, used to lookup parameter attributes
such as lr_mult, wd_mult, etc. param_dict shall not be deep copied.
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=None,
lr_scheduler=None, sym=None, begin_num_update=0,
multi_precision=False, param_dict=None):
self.rescale_grad = rescale_grad
self.lr_scheduler = lr_scheduler
if self.lr_scheduler is None and learning_rate is None:
learning_rate = 0.01
self.lr = learning_rate
if self.lr_scheduler is not None and learning_rate is not None:
if self.lr_scheduler.base_lr != learning_rate:
print(UserWarning("learning rate from ``lr_scheduler`` has been "
"overwritten by ``learning_rate`` in optimizer."))
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._all_index_update_counts = {0 : {}}
self._index_update_count = self._all_index_update_counts[0]
self.clip_gradient = clip_gradient
self.multi_precision = multi_precision
self.aggregate_num = 0
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.allow_np_array = is_np_array()
self.set_lr_mult({})
self.set_wd_mult({})
opt_registry = {}
[docs] @staticmethod
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))
<class '__main__.MyOptimizer'>
"""
assert(isinstance(klass, type))
name = klass.__name__.lower()
if name in Optimizer.opt_registry:
warnings.warn('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
[docs] @staticmethod
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)
<class 'mxnet.optimizer.SGD'>
>>> adam = mx.optimizer.create('adam', learning_rate=.1)
>>> type(adam)
<class 'mxnet.optimizer.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: # pylint: disable=no-else-raise
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 _set_current_context(self, device_id):
"""Sets the number of the currently handled device.
Parameters
----------
device_id : int
The number of current device.
"""
if device_id not in self._all_index_update_counts:
self._all_index_update_counts[device_id] = {}
self._index_update_count = self._all_index_update_counts[device_id]
def _update_count(self, index):
"""Updates num_update.
Parameters
----------
index : int or list of int
The index to be updated.
"""
if not isinstance(index, (list, tuple)):
index = [index]
for idx in index:
if idx not in self._index_update_count:
self._index_update_count[idx] = self.begin_num_update
self._index_update_count[idx] += 1
self.num_update = max(self._index_update_count[idx], self.num_update)
def _get_lrs(self, indices):
"""Gets the learning rates given the indices of the weights.
Parameters
----------
indices : list of int
Indices corresponding to weights.
Returns
-------
lrs : list of float
Learning rates for those indices.
"""
if self.lr_scheduler is not None:
lr = self.lr_scheduler(self.num_update)
else:
lr = self.lr
lrs = [lr for _ in indices]
for i, index in enumerate(indices):
if index in self.param_dict:
lrs[i] *= self.param_dict[index].lr_mult
elif index in self.lr_mult:
lrs[i] *= self.lr_mult[index]
elif index in self.idx2name:
lrs[i] *= self.lr_mult.get(self.idx2name[index], 1.0)
return lrs
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.
"""
return self._get_lrs([index])[0]
def _get_wds(self, indices):
"""Gets weight decays for indices.
Returns 0 for non-weights if the name of weights are provided for `__init__`.
Parameters
----------
indices : list of int
Indices of weights.
Returns
-------
wds : list of float
Weight decays for those indices.
"""
wds = [self.wd for _ in indices]
for i, index in enumerate(indices):
if index in self.param_dict:
wds[i] *= self.param_dict[index].wd_mult
elif index in self.wd_mult:
wds[i] *= self.wd_mult[index]
elif index in self.idx2name:
wds[i] *= self.wd_mult.get(self.idx2name[index], 1.0)
return wds
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 of weight.
Returns
-------
wd : float
Weight decay for this index.
"""
return self._get_wds([index])[0]
def __getstate__(self):
ret = self.__dict__.copy()
# do not include param_dict in the state
del ret['param_dict']
return ret
def __setstate__(self, state):
self.__dict__ = state
# param_dict needs to be explicitly set by the trainer
self.param_dict = {}
# convenience wrapper for Optimizer.Register
register = Optimizer.register # pylint: disable=invalid-name
# pylint: disable=line-too-long
[docs]@register
class SGD(Optimizer):
"""The SGD optimizer with momentum and weight decay.
If the storage types of grad is ``row_sparse`` and ``lazy_update`` is True, \
**lazy 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.
In the case when ``update_on_kvstore`` is set to False (either globally via
MXNET_UPDATE_ON_KVSTORE=0 environment variable or as a parameter in
:class:`~mxnet.gluon.Trainer`) SGD optimizer can perform aggregated update
of parameters, which may lead to improved performance. The aggregation size
is controlled by MXNET_OPTIMIZER_AGGREGATION_SIZE environment variable and
defaults to 4.
Otherwise, **standard updates** are applied by::
rescaled_grad = lr * (rescale_grad * clip(grad, clip_gradient) + wd * weight)
state = momentum * state + rescaled_grad
weight = weight - state
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.
lazy_update : bool, optional
Default is True. If True, lazy updates are applied \
if the storage types of weight and grad are both ``row_sparse``.
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, lazy_update=True, **kwargs):
super(SGD, self).__init__(**kwargs)
self.momentum = momentum
self.lazy_update = lazy_update
self.aggregate_num = int(os.getenv('MXNET_OPTIMIZER_AGGREGATION_SIZE', "4"))
[docs] 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)
[docs] def create_state(self, index, weight):
momentum = None
if self.momentum != 0.0:
stype = weight.stype if self.lazy_update else 'default'
momentum = zeros(weight.shape, weight.context, dtype=weight.dtype, stype=stype)
return momentum
def _update_impl(self, indices, weights, grads, states, multi_precision=False):
aggregate = True
if not isinstance(indices, (tuple, list)):
indices = [indices]
weights = [weights]
grads = [grads]
states = [states]
for weight, grad in zip(weights, grads):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
aggregate = (aggregate and
weight.stype == 'default' and
grad.stype == 'default')
self._update_count(indices)
lrs = self._get_lrs(indices)
wds = self._get_wds(indices)
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 aggregate:
if not multi_precision:
if self.momentum > 0:
multi_sgd_mom_update(*_flatten_list(zip(weights, grads, states)), out=weights,
num_weights=len(weights), lrs=lrs, wds=wds, **kwargs)
else:
multi_sgd_update(*_flatten_list(zip(weights, grads)), out=weights,
num_weights=len(weights), lrs=lrs, wds=wds, **kwargs)
else:
if self.momentum > 0:
multi_mp_sgd_mom_update(*_flatten_list(zip(weights, grads, *zip(*states))),
out=weights, num_weights=len(weights),
lrs=lrs, wds=wds, **kwargs)
else:
multi_mp_sgd_update(*_flatten_list(zip(weights, grads,
list(zip(*states))[1])),
out=weights, num_weights=len(weights),
lrs=lrs, wds=wds, **kwargs)
else:
for weight, grad, state, lr, wd in zip(weights, grads, states, lrs, wds):
if not multi_precision:
if state is not None:
sgd_mom_update(weight, grad, state, out=weight,
lazy_update=self.lazy_update, lr=lr, wd=wd, **kwargs)
else:
sgd_update(weight, grad, out=weight, lazy_update=self.lazy_update,
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)
[docs] def update(self, index, weight, grad, state):
self._update_impl(index, weight, grad, state, multi_precision=False)
[docs] def update_multi_precision(self, index, weight, grad, state):
if not isinstance(index, (tuple, list)):
use_multi_precision = self.multi_precision and weight.dtype == numpy.float16
else:
use_multi_precision = self.multi_precision and weight[0].dtype == numpy.float16
self._update_impl(index, weight, grad, state,
multi_precision=use_multi_precision)
[docs]@register
class Signum(Optimizer):
r"""The Signum optimizer that takes the sign of gradient or momentum.
The optimizer updates the weight by::
rescaled_grad = rescale_grad * clip(grad, clip_gradient) + wd * weight
state = momentum * state + (1-momentum)*rescaled_grad
weight = (1 - lr * wd_lh) * weight - lr * sign(state)
References
----------
Jeremy Bernstein, Yu-Xiang Wang, Kamyar Azizzadenesheli & Anima Anandkumar. (2018).
signSGD: Compressed Optimisation for Non-Convex Problems. In ICML'18.
See: https://arxiv.org/abs/1802.04434
For details of the update algorithm see
:class:`~mxnet.ndarray.signsgd_update` and :class:`~mxnet.ndarray.signum_update`.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
momentum : float, optional
The momentum value.
wd_lh : float, optional
The amount of decoupled weight decay regularization, see details in the original paper at:\
https://arxiv.org/abs/1711.05101
"""
def __init__(self, learning_rate=0.01, momentum=0.9, wd_lh=0.0, **kwargs):
super(Signum, self).__init__(learning_rate=learning_rate, **kwargs)
self.momentum = momentum
self.wd_lh = wd_lh
[docs] 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):
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 self.wd_lh:
kwargs['wd_lh'] = self.wd_lh
if state is not None:
signum_update(weight, grad, state, out=weight,
lr=lr, wd=wd, **kwargs)
else:
signsgd_update(weight, grad, out=weight,
lr=lr, wd=wd, **kwargs)
[docs]@register
class FTML(Optimizer):
"""The FTML optimizer.
This class implements the optimizer described in
*FTML - Follow the Moving Leader in Deep Learning*,
available at http://proceedings.mlr.press/v70/zheng17a/zheng17a.pdf.
Denote time step by t. The optimizer updates the weight by::
rescaled_grad = clip(grad * rescale_grad + wd * weight, clip_gradient)
v = beta2 * v + (1 - beta2) * square(rescaled_grad)
d_t = (1 - power(beta1, t)) / lr * square_root(v / (1 - power(beta2, t))) + epsilon)
z = beta1 * z + (1 - beta1) * rescaled_grad - (d_t - beta1 * d_(t-1)) * weight
weight = - z / d_t
For details of the update algorithm, see :class:`~mxnet.ndarray.ftml_update`.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
beta1 : float, optional
0 < beta1 < 1. Generally close to 0.5.
beta2 : float, optional
0 < beta2 < 1. Generally close to 1.
epsilon : float, optional
Small value to avoid division by 0.
"""
def __init__(self, beta1=0.6, beta2=0.999, epsilon=1e-8, **kwargs):
super(FTML, self).__init__(**kwargs)
self.beta1 = beta1
self.beta2 = beta2
self.epsilon = epsilon
[docs] def create_state(self, index, weight):
return (zeros(weight.shape, weight.context, dtype=weight.dtype), # d_0
zeros(weight.shape, weight.context, dtype=weight.dtype), # v_0
zeros(weight.shape, weight.context, dtype=weight.dtype)) # z_0
[docs] 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]
kwargs = {'beta1': self.beta1, 'beta2': self.beta2, 'epsilon': self.epsilon,
'rescale_grad': self.rescale_grad, 't': t}
if self.clip_gradient:
kwargs['clip_grad'] = self.clip_gradient
prev_d, prev_v, prev_z = state
ftml_update(weight, grad, prev_d, prev_v, prev_z, out=weight,
lr=lr, wd=wd, **kwargs)
[docs]@register
class LARS(Optimizer):
"""the LARS optimizer from 'Large Batch Training of Convolution Networks' \
(https://arxiv.org/abs/1708.03888)
Behave mostly like SGD with momentum and weight decay but is scaling \
adaptively the learning for each layer (except bias and batch norm parameters):
w_norm = L2norm(weights)
g_norm = L2norm(gradients)
if w_norm > 0 and g_norm > 0:
lr_layer = lr * lr_mult * eta * w_norm / (g_norm + weight_decay * w_norm + eps)
else:
lr_layer = lr * lr_mult
Parameters
----------
momentum : float, optional
The momentum value.
lazy_update : bool, optional
Default is True. If True, lazy updates are applied \
if the storage types of weight and grad are both ``row_sparse``.
lars_eta : float, optional
LARS coefficient used to scale the learning rate. Default set to 0.001.
lars_epsilon : float, optional
Optional epsilon in case of very small gradients. Default set to 0.
momentum_correction : bool, optional
If True scale momentum w.r.t global learning rate change (with an lr_scheduler) \
as indicated in 'Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour` \
(https://arxiv.org/pdf/1706.02677.pdf)
Default set to True.
"""
def __init__(self, momentum=0.0, lazy_update=True, eta=0.001, eps=0,
momentum_correction=True, **kwargs):
super(LARS, self).__init__(**kwargs)
self.momentum = momentum
self.momentum_correction = momentum_correction
self.lazy_update = lazy_update
self.aggregate_num = int(os.getenv('MXNET_OPTIMIZER_AGGREGATION_SIZE', "4"))
self.eta = eta
self.eps = eps
self.skip = 0
self.last_lr = None
self.cur_lr = None
def _get_lrs(self, indices):
"""Gets the learning rates given the indices of the weights.
Parameters
----------
indices : list of int
Indices corresponding to weights.
Returns
-------
lrs : list of float
Learning rates for those indices.
"""
if self.cur_lr is not None:
self.last_lr = self.cur_lr
if self.lr_scheduler is not None:
lr = self.lr_scheduler(self.num_update)
else:
lr = self.lr
if self.cur_lr is None:
self.last_lr = lr
self.cur_lr = lr
lrs = [lr for _ in indices]
for i, index in enumerate(indices):
if index in self.param_dict:
lrs[i] *= self.param_dict[index].lr_mult
elif index in self.lr_mult:
lrs[i] *= self.lr_mult[index]
elif index in self.idx2name:
lrs[i] *= self.lr_mult.get(self.idx2name[index], 1.0)
return lrs
[docs] def set_wd_mult(self, args_wd_mult):
self.wd_mult = {}
for n in self.idx2name.values():
is_weight = n.endswith('_weight')
if not is_weight:
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)
[docs] 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)
[docs] def create_state(self, index, weight):
momentum = None
if self.momentum != 0.0:
stype = weight.stype if self.lazy_update else 'default'
momentum = zeros(weight.shape, weight.context, dtype=weight.dtype, stype=stype)
return momentum
def _l2norm(self, v, rescale=False):
"""L2 Norm implementation"""
v = v.astype('float32')
if rescale:
v *= self.rescale_grad
norm = NDnorm(v).asnumpy()[0]
return norm
def _get_lars(self, i, weight, g, lr, wd):
"""Returns a scaling factor for the learning rate for this layer"""
name = self.idx2name[i] if i in self.idx2name else str(i)
if name.endswith('gamma') or name.endswith('beta') or name.endswith('bias'):
return lr
w_norm = self._l2norm(weight)
g_norm = self._l2norm(g, rescale=True)
if w_norm > 0.0 and g_norm > 0.0:
lars = self.eta * w_norm/(g_norm + wd * w_norm + self.eps)
else:
lars = 1.0
return lars * lr
def _update_impl(self, indices, weights, grads, states, multi_precision=False):
aggregate = True
if not isinstance(indices, (tuple, list)):
indices = [indices]
weights = [weights]
grads = [grads]
states = [states]
for weight, grad in zip(weights, grads):
assert(isinstance(weight, NDArray))
assert(isinstance(grad, NDArray))
aggregate = (aggregate and
weight.stype == 'default' and
grad.stype == 'default')
self._update_count(indices)
lrs = self._get_lrs(indices)
wds = self._get_wds(indices)
kwargs = {'rescale_grad': self.rescale_grad}
if self.momentum > 0:
kwargs['momentum'] = (self.momentum * (self.cur_lr / self.last_lr)) \
if (self.momentum_correction and self.last_lr != 0) else \
self.momentum
if self.clip_gradient:
kwargs['clip_gradient'] = self.clip_gradient
if aggregate:
nb_params = len(indices)
names = [self.idx2name[i] if i in self.idx2name else str(i) for i in indices]
lars_idx = [i for i in range(nb_params) if
not(names[i].endswith('gamma') or names[i].endswith('beta') or
names[i].endswith('bias'))]
nb_lars = len(lars_idx)
no_lars_idx = [i for i in range(nb_params) if
(names[i].endswith('gamma') or names[i].endswith('beta') or
names[i].endswith('bias'))]
cur_ctx = weights[0].context
full_idx = lars_idx + no_lars_idx
new_lrs = array([lrs[i] for i in full_idx], ctx=cur_ctx, dtype='float32')
new_wds = array([wds[i] for i in full_idx], ctx=cur_ctx, dtype='float32')
new_weights = [weights[i] for i in full_idx]
new_grads = [grads[i] for i in full_idx]
new_states = [states[i] for i in full_idx]
if nb_lars > 0:
w_sum_sq = multi_sum_sq(*new_weights[:nb_lars], num_arrays=nb_lars)
g_sum_sq = multi_sum_sq(*new_grads[:nb_lars], num_arrays=nb_lars)
multi_lars(new_lrs[:nb_lars], w_sum_sq, g_sum_sq, new_wds[:nb_lars],
eta=self.eta, eps=self.eps, rescale_grad=self.rescale_grad,
out=new_lrs[:nb_lars])
# Same than usual using preloaded sgd functions
sidx = 0
while sidx < len(indices):
eidx = sidx + len(new_weights[sidx:sidx+self.aggregate_num])
if not multi_precision:
if self.momentum > 0:
preloaded_multi_sgd_mom_update(
*(_flatten_list(zip(new_weights[sidx:eidx],
new_grads[sidx:eidx],
new_states[sidx:eidx])) +
[new_lrs[sidx:eidx], new_wds[sidx:eidx]]),
out=new_weights[sidx:eidx],
num_weights=len(new_weights[sidx:eidx]),
**kwargs)
else:
preloaded_multi_sgd_update(
*(_flatten_list(zip(new_weights[sidx:eidx],
new_grads[sidx:eidx])) +
[new_lrs[sidx:eidx], new_wds[sidx:eidx]]),
out=new_weights[sidx:eidx],
num_weights=len(new_weights[sidx:eidx]),
**kwargs)
else:
if self.momentum > 0:
preloaded_multi_mp_sgd_mom_update(
*(_flatten_list(zip(new_weights[sidx:eidx],
new_grads[sidx:eidx],
*zip(*new_states[sidx:eidx]))) +
[new_lrs[sidx:eidx], new_wds[sidx:eidx]]),
out=new_weights[sidx:eidx],
num_weights=len(new_weights[sidx:eidx]),
**kwargs)
else:
preloaded_multi_mp_sgd_update(
*(_flatten_list(zip(new_weights[sidx:eidx],
new_grads[sidx:eidx],
list(zip(*new_states[sidx:eidx]))[1])) +
[new_lrs[sidx:eidx], new_wds[sidx:eidx]]),
out=new_weights[sidx:eidx],
num_weights=len(new_weights[sidx:eidx]),
**kwargs)
sidx += self.aggregate_num
else:
lrs = [self._get_lars(i, w, g, lr, wd) for (i, w, g, lr, wd) in
zip(indices, weights, grads, lrs, wds)]
for weight, grad, state, lr, wd in zip(weights, grads, states, lrs, wds):
if not multi_precision:
if state is not None:
sgd_mom_update(weight, grad, state, out=weight,
lazy_update=self.lazy_update, lr=lr, wd=wd, **kwargs)
else:
sgd_update(weight, grad, out=weight, lazy_update=self.lazy_update,
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)
[docs] def update(self, index, weight, grad, state):
self._update_impl(index, weight, grad, state, multi_precision=False)
[docs] def update_multi_precision(self, index, weight, grad, state):
if not isinstance(index, (tuple, list)):
use_multi_precision = self.multi_precision and weight.dtype == numpy.float16
else:
use_multi_precision = self.multi_precision and weight[0].dtype == numpy.float16
self._update_impl(index, weight, grad, state,
multi_precision=use_multi_precision)
#
[docs]@register
class LBSGD(Optimizer):
"""The Large Batch SGD optimizer with momentum and weight decay.
The optimizer updates the weight by::
state = momentum * state + lr * rescale_grad * clip(grad, clip_gradient) + wd * weight
weight = weight - state
For details of the update algorithm see :class:`~mxnet.ndarray.sgd_update`
and :class:`~mxnet.ndarray.sgd_mom_update`.
In addition to the SGD updates the LBSGD optimizer uses the LARS, Layer-wise
Adaptive Rate Scaling, algorithm to have a separate learning rate for each
layer of the network, which leads to better stability over large batch sizes.
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.
warmup_strategy: string ('linear', 'power2', 'sqrt'. , 'lars' default : 'linear')
warmup_epochs: unsigned, default: 5
batch_scale: unsigned, default: 1 (same as batch size * numworkers)
updates_per_epoch: updates_per_epoch (default: 32, Default might not reflect true number batches per epoch. Used for warmup.)
begin_epoch: unsigned, default 0, starting epoch.
"""
def __init__(self, momentum=0.0, multi_precision=False, warmup_strategy='linear',
warmup_epochs=5, batch_scale=1, updates_per_epoch=32, begin_epoch=0, num_epochs=60,
**kwargs):
super(LBSGD, self).__init__(**kwargs)
logging.info('Running Large-Batch SGD Algorithm')
logging.info('(Batch_scale=%f, warmup_epochs=%d, warmup_strategy=%s, updates_per_epoch=%d)',
batch_scale, warmup_epochs, warmup_strategy, updates_per_epoch)
self.momentum = momentum
self.multi_precision = multi_precision
# new user parameters for large batch
self.warmup_strategy = warmup_strategy
self.warmup_epochs = warmup_epochs
self.batch_scale = batch_scale
self.updates_per_epoch = updates_per_epoch
self.init_updates = begin_epoch * updates_per_epoch
self.num_epochs = num_epochs
# addl internal usage parameters and storage
self.lbmult = 1
self.cumgrads = {}
# for adaptive lr
self.adaptive = False
self.admult = 1 # adaptation constant
[docs] def create_state(self, index, weight):
momentum = None
weight_master_copy = None
if self.multi_precision and weight.dtype == numpy.float16:
weight_master_copy = array(weight, ctx=weight.context, dtype=numpy.float32)
if self.momentum != 0.0:
momentum = zeros(weight.shape, weight.context, dtype=numpy.float32,
stype=weight.stype)
return (momentum, 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")
if self.momentum != 0.0:
momentum = zeros(weight.shape, weight.context, dtype=weight.dtype, stype=weight.stype)
return momentum
def _get_lbmult(self, nup):
"""Returns lr scaling factor for large batch according to warmup schedule
(to be implemented)
"""
nwup = self.warmup_epochs * self.updates_per_epoch
strategy = self.warmup_strategy
maxmult = float(self.batch_scale)
if nup >= nwup:
mult = maxmult
elif nwup <= 1:
mult = 1.0
else:
if (strategy == 'linear'):
mult = 1.0 + (maxmult - 1) * nup / nwup
elif (strategy == 'power2'):
mult = 1.0 + (maxmult-1) * (nup*nup)/(nwup*nwup)
elif (strategy == 'sqrt'):
mult = 1.0 + (maxmult - 1) * math.sqrt(float(nup) / nwup)
else:
mult = 1.0
return mult
def _get_lars(self, weight, g, wd):
"""Returns a scaling factor for the learning rate for this layer
default is 1
"""
weight2 = self._l2norm(weight)
grad2 = self._l2norm(g)
lars = math.sqrt(weight2 / (grad2 + wd * weight2 + 1e-18))
if lars < 0.01:
lars = 0.01
elif lars > 100:
lars = 100
return lars
def _l2norm(self, v):
"inner product implementation"
norm = multiply(v, v).asnumpy().sum()
return norm
def _reset_cum_gradient(self, index):
"called every macro-batch to reset cumulated gradients to 0 for a given index"
self.cumgrads[index]['cum_grad'] = 0
def _get_cum_gradient(self, index):
"get the cumulated gradient for index"
if index in self.cumgrads:
return self.cumgrads[index]
else:
return {}
def _put_cum_gradient(self, index, cgrad):
"store cumulated gradient for index"
self.cumgrads[index] = cgrad
def _cumulate_gradient(self, grad, index):
"Cumulate gradients for large-batch emulation. Cumulated by index (layer)"
cgrad = self._get_cum_gradient(index)
if cgrad:
num_cums = cgrad['num_cums']
if num_cums > 0:
cum_grad = cgrad['cum_grad'] + grad
num_cums += 1
else:
cum_grad = grad
num_cums = self.init_updates + 1
else:
cum_grad = grad
num_cums = self.init_updates + 1
cgrad = {'cum_grad': cum_grad, 'num_cums': num_cums}
self._put_cum_gradient(index, cgrad)
return cgrad
[docs] def update(self, index, weight, grad, state):
assert (isinstance(weight, NDArray))
assert (isinstance(grad, NDArray))
lr = self._get_lr(index)
wd = self._get_wd(index)
self._update_count(index)
# new stuff for large batch
cgrad = self._cumulate_gradient(grad, index)
if (cgrad['num_cums'] % self.batch_scale) == 0:
grad = cgrad['cum_grad'] / self.batch_scale
if self.warmup_strategy == 'lars':
lbmult = self._get_lars(weight, grad, wd)
else:
lbmult = self._get_lbmult(cgrad['num_cums'])
lr = lr * lbmult
# do the regular sgd update flow
kwargs = {'rescale_grad': self.rescale_grad}
if self.momentum > 0:
kwargs['momentum'] = self.momentum
if self.clip_gradient:
kwargs['clip_gradient'] = self.clip_gradient
use_multi_precision = isinstance(state, (list, tuple))
if not use_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)
# reset update count and cumulated gradient per large batch
self._reset_cum_gradient(index)
else:
lr = 0.0
kwargs = {}
sgd_update(weight, grad, out=weight, lr=lr, wd=wd, **kwargs)
[docs]@register
class LAMB(Optimizer):
"""LAMB Optimizer.
"""
def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-6,
lower_bound=None, upper_bound=None, bias_correction=True, **kwargs):
super(LAMB, self).__init__(learning_rate=learning_rate, **kwargs)
self.beta1 = beta1
self.beta2 = beta2
self.epsilon = epsilon
self.lower_bound = lower_bound
self.upper_bound = upper_bound
self.bias_correction = bias_correction
[docs] def create_state(self, index, weight):
stype = weight.stype
return (zeros(weight.shape, weight.context, dtype=numpy.float32, stype=stype),
zeros(weight.shape, weight.context, dtype=numpy.float32, stype=stype))
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)
t = self._index_update_count[index]
kwargs = {'beta1': self.beta1, 'beta2': self.beta2, 'epsilon': self.epsilon,
'bias_correction': self.bias_correction, 't': t,
'rescale_grad': self.rescale_grad}
if self.clip_gradient:
kwargs['clip_gradient'] = self.clip_gradient
if multi_precision:
mean, var = state[1]
weight32 = state[0]
g = mp_lamb_update_phase1(weight, grad, mean, var, weight32, wd=wd, **kwargs)
kwargs = {}
if self.lower_bound:
kwargs['lower_bound'] = self.lower_bound
if self.upper_bound:
kwargs['upper_bound'] = self.upper_bound
r_1 = weight32.norm()
r_2 = g.norm()
mp_lamb_update_phase2(weight, g, r_1, r_2, weight32, lr=lr, out=weight, **kwargs)
else:
mean, var = state
g = lamb_update_phase1(weight, grad, mean, var, wd=wd, **kwargs)
kwargs = {}
if self.lower_bound:
kwargs['lower_bound'] = self.lower_bound
if self.upper_bound:
kwargs['upper_bound'] = self.upper_bound
r_1 = weight.norm()
r_2 = g.norm()
lamb_update_phase2(weight, g, r_1, r_2, lr=lr, out=weight, **kwargs)
[docs] def update(self, index, weight, grad, state):
self._update_impl(index, weight, grad, state, multi_precision=False)
[docs] def update_multi_precision(self, index, weight, grad, state):
if not isinstance(index, (tuple, list)):
use_multi_precision = self.multi_precision and weight.dtype == numpy.float16
else:
use_multi_precision = self.multi_precision and weight[0].dtype == numpy.float16
self._update_impl(index, weight, grad, state,
multi_precision=use_multi_precision)
# pylint: enable=line-too-long
[docs]@register
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
[docs] 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
[docs] 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
[docs]@register
class NAG(Optimizer):
"""Nesterov accelerated gradient.
This optimizer updates each weight by::
state = momentum * state + grad + wd * weight
weight = weight - (lr * (grad + momentum * state))
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(NAG, self).__init__(**kwargs)
self.momentum = momentum
[docs] 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 "
"NAG optimizer")
return self.create_state(index, weight)
[docs] def create_state(self, index, weight):
momentum = None
if self.momentum != 0.0:
momentum = zeros(weight.shape, weight.context, dtype=weight.dtype)
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:
nag_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_nag_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)
[docs] def update(self, index, weight, grad, state):
self._update_impl(index, weight, grad, state, multi_precision=False)
[docs] def update_multi_precision(self, index, weight, grad, state):
use_multi_precision = self.multi_precision and weight.dtype == numpy.float16 \
and isinstance(state, (tuple, list))
self._update_impl(index, weight, grad, state,
multi_precision=use_multi_precision)
[docs]@register
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)
[docs] 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)
weight[:] += normal(0, math.sqrt(lr), shape=weight.shape,
dtype=weight.dtype, ctx=weight.context)
[docs]@register # pylint: disable=invalid-name
class ccSGD(SGD):
"""[DEPRECATED] Same as `SGD`. Left here for backward compatibility."""
def __init__(self, *args, **kwargs):
super(ccSGD, self).__init__(*args, **kwargs)
[docs]@register
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.
If the storage types of grad is ``row_sparse``, and ``lazy_update`` is True, \
**lazy updates** at step t 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)
lr = learning_rate * sqrt(1 - beta1**t) / (1 - beta2**t)
w[row] = w[row] - lr * m[row] / (sqrt(v[row]) + epsilon)
The lazy 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.
Otherwise, **standard updates** at step t are applied 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)
lr = learning_rate * sqrt(1 - beta1**t) / (1 - beta2**t)
w = w - lr * m / (sqrt(v) + epsilon)
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.
lazy_update : bool, optional
Default is True. If True, lazy updates are applied \
if the storage types of weight and grad are both ``row_sparse``.
"""
def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-8,
lazy_update=True, **kwargs):
super(Adam, self).__init__(learning_rate=learning_rate, **kwargs)
self.beta1 = beta1
self.beta2 = beta2
self.epsilon = epsilon
self.lazy_update = lazy_update
[docs] def create_state(self, index, weight):
stype = weight.stype if self.lazy_update else 'default'
return (zeros(weight.shape, weight.context, dtype=weight.dtype,
stype=stype), # mean
zeros(weight.shape, weight.context, dtype=weight.dtype,
stype=stype)) # variance
[docs] 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,
lazy_update=self.lazy_update, lr=lr, wd=wd, **kwargs)
[docs]@register
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 updates each weight by::
grad = clip(grad * rescale_grad, clip_gradient)
history += square(grad)
div = grad / sqrt(history + float_stable_eps)
weight += (div + weight * wd) * -lr
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
See Also
----------
:meth:`mxnet.ndarray.sparse.adagrad_update`.
Parameters
----------
eps: float, optional
Initial value of the history accumulator. Avoids division by 0.
"""
def __init__(self, eps=1e-7, **kwargs):
super(AdaGrad, self).__init__(**kwargs)
self.float_stable_eps = eps
[docs] def create_state(self, index, weight):
return zeros(weight.shape, weight.context, stype=weight.stype) # history
[docs] 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 = grad.stype == 'row_sparse'
history = state
if is_sparse:
kwargs = {'epsilon': self.float_stable_eps,
'rescale_grad': self.rescale_grad}
if self.clip_gradient:
kwargs['clip_gradient'] = self.clip_gradient
sparse.adagrad_update(weight, grad, history, out=weight, lr=lr, wd=wd, **kwargs)
else:
grad = grad * self.rescale_grad
if self.clip_gradient is not None:
grad = clip(grad, -self.clip_gradient, self.clip_gradient)
history[:] += square(grad)
div = grad / sqrt(history + self.float_stable_eps)
weight[:] += (div + weight * wd) * -lr
[docs]@register
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
[docs] 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
[docs] 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)
[docs]@register
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 updates each weight by::
grad = clip(grad * rescale_grad + wd * weight, clip_gradient)
acc_grad = rho * acc_grad + (1. - rho) * grad * grad
delta = sqrt(acc_delta + epsilon) / sqrt(acc_grad + epsilon) * grad
acc_delta = rho * acc_delta + (1. - rho) * delta * delta
weight -= (delta + wd * weight)
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
[docs] def create_state(self, index, weight):
return (zeros(weight.shape, weight.context), # accumulated g
zeros(weight.shape, weight.context)) # accumulated delta
[docs] 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
[docs]@register
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
[docs] 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
[docs] 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
[docs]@register
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.
The optimizer updates the weight by::
grad = clip(grad * rescale_grad + wd * weight, clip_gradient)
m = beta1 * m_t + (1 - beta1) * grad
u = maximum(beta2 * u, abs(grad))
weight -= lr / (1 - beta1**t) * m / u
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
[docs] 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
[docs] 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
[docs]@register
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.
[docs] 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
[docs] 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)
[docs]@register
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
def _as_classic(a, allow_np):
# TODO(junwu): This is a temp solution for allowing converting
# np.ndarray to mx.nd.NDArray to be fed into the optimizer since
# users may have custom optimizers implemented using mx.nd.NDArray ops.
from ..numpy import ndarray as np_ndarray
if isinstance(a, (tuple, list)):
if any(isinstance(x, np_ndarray) for x in a):
if allow_np:
return [x.as_nd_ndarray() for x in a]
else:
raise ValueError('Converting np.ndarray to mx.nd.NDArray is not allowed')
else:
if isinstance(a, np_ndarray):
if allow_np:
return a.as_nd_ndarray()
else:
raise ValueError('Converting np.ndarray to mx.nd.NDArray is not allowed')
return a
[docs]class Updater(object):
"""Updater for kvstore."""
def __init__(self, optimizer):
self.optimizer = optimizer
self.states = {}
self.states_synced = {}
self.aggregate_updates = optimizer.aggregate_num > 0
def __call__(self, index, grad, weight):
"""Updates weight given gradient and index."""
allow_np = self.optimizer.allow_np_array if hasattr(self.optimizer, "allow_np_array") else is_np_array()
if not isinstance(index, (list, tuple)):
indices = [index]
grads = [_as_classic(grad, allow_np)]
weights = [_as_classic(weight, allow_np)]
else:
indices = index
grads = _as_classic(grad, allow_np)
weights = _as_classic(weight, allow_np)
if weights:
self.optimizer._set_current_context(weights[0].context.device_id)
for i, idx in enumerate(indices):
# convert ctypes.char_p.value back to python str if needed
if isinstance(idx, bytes):
indices[i] = py_str(idx)
idx = indices[i]
if idx not in self.states:
self.states[idx] = self.optimizer.create_state_multi_precision(idx, weights[i])
self.states_synced[idx] = True
elif not self.states_synced[idx]:
self.states[idx] = \
self.sync_state_context(self.states[idx], weights[i].context)
self.states_synced[idx] = True
if self.aggregate_updates:
# segregate values based on type
type_map = {}
for i, w, g in zip(indices, weights, grads):
if w.dtype in type_map:
type_map[w.dtype].append((i, w, g))
else:
type_map[w.dtype] = [(i, w, g)]
for idx in type_map:
current_index = 0
indices, weights, grads = zip(*type_map[idx])
while current_index < len(indices):
states = []
step = min(self.optimizer.aggregate_num, len(indices) - current_index)
for j in range(step):
states.append(self.states[indices[current_index + j]])
self.optimizer.update_multi_precision(
indices[current_index:current_index + self.optimizer.aggregate_num],
weights[current_index:current_index + self.optimizer.aggregate_num],
grads[current_index:current_index + self.optimizer.aggregate_num],
states)
current_index += self.optimizer.aggregate_num
else:
for i, w, g in zip(indices, weights, grads):
self.optimizer.update_multi_precision(i, w, g, self.states[i])
[docs] def sync_state_context(self, state, context):
"""sync 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)