摘要：?作者丨知乎科技猛兽极市平台编辑本文思想来自下面这篇大佬的文章：Juliuszh：一个框架看懂优化算法之异同SGD/AdaGrad/主要是对深度学习各种优化器(从SGD到AdamW)使用统一的框架做一次整理，本文相比于链接从源代码的角度理解这些优化器的思路。代码
统一框架：
共性的方法有：
(param_group)：把参数放进优化器中，这在 Fine-tune 预训练网络时很有用，因为可以使冻结层可训练并随着训练的进行添加到优化器中。 (state_dict)：把优化器的状态加载进去。 ()：返回优化器的状态，以dict的形式返回。 (closure=None)：优化一步参数。 (set_to_none=False)：把所有的梯度值设为0。
使用方法：
for input, target in dataset:
def closure():
optimizer.zero_grad()
output=model(input)
loss=loss_fn(output, target)
loss.backward()
return loss
optimizer.step(closure)
定义优化器：
CLASS torch.optim.SGD(params, lr=<required parameter>, momentum=0, dampening=0, weight_decay=0, nesterov=False)
参数：
params (iterable) – 优化器作用的模型参数。 lr (float) – learning rate，相当于是统一框架中的 。 momentum (float, optional) – 动量参数。(默认值：0) weight_decay (float, optional) – 权重衰减系数 weight decay (L2 penalty) (默认值：0) dampening (float, optional) – dampening for momentum (默认值：0) nesterov (bool, optional) – 允许 Nesterov momentum (默认值：False)
源码解读：
import torch
from .optimizer import Optimizer, required
[docs]class SGD(Optimizer):
r"""Implements stochastic gradient descent (optionally with momentum).
Nesterov momentum is based on the formula from
`On the importance of initialization and momentum in deep learning`__.
Args:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float): learning rate
momentum (float, optional): momentum factor (default: 0)
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
dampening (float, optional): dampening for momentum (default: 0)
nesterov (bool, optional): enables Nesterov momentum (default: False)
Example:
>>> optimizer=torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
>>> optimizer.zero_grad()
>>> loss_fn(model(input), target).backward()
>>> optimizer.step()
__ http://www.cs.toronto.edu/%7Ehinton/absps/momentum.pdf
.. note::
The implementation of SGD with Momentum/Nesterov subtly differs from
Sutskever et. al. and implementations in some other frameworks.
Considering the specific case of Momentum, the update can be written as
.. math::
\begin{aligned}
v_{t+1} &=\mu * v_{t} + g_{t+1}, \\
p_{t+1} &=p_{t} - ext{lr} * v_{t+1},
\end{aligned}
where :math:`p`, :math:`g`, :math:`v` and :math:`\mu` denote the
parameters, gradient, velocity, and momentum respectively.
This is in contrast to Sutskever et. al. and
other frameworks which employ an update of the form
.. math::
\begin{aligned}
v_{t+1} &=\mu * v_{t} + ext{lr} * g_{t+1}, \\
p_{t+1} &=p_{t} - v_{t+1}.
\end{aligned}
The Nesterov version is analogously modified.
"""
def __init__(self, params, lr=required, momentum=0, dampening=0,
weight_decay=0, nesterov=False):
if lr is not required and lr < 0.0:
raise ValueError("Invalid learning rate: {}".format(lr))
if momentum < 0.0:
raise ValueError("Invalid momentum value: {}".format(momentum))
if weight_decay < 0.0:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults=dict(lr=lr, momentum=momentum, dampening=dampening,
weight_decay=weight_decay, nesterov=nesterov)
if nesterov and (momentum <=0 or dampening !=0):
raise ValueError("Nesterov momentum requires a momentum and zero dampening")
super(SGD, self).__init__(params, defaults)
def __setstate__(self, state):
super(SGD, self).__setstate__(state)
for group in self.param_groups:
group.setdefault('nesterov', False)
[docs] @torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss=None
if closure is not None:
with torch.enable_grad():
loss=closure()
for group in self.param_groups:
weight_decay=group['weight_decay']
momentum=group['momentum']
dampening=group['dampening']
nesterov=group['nesterov']
for p in group['params']:
if p.grad is None:
continue
d_p=p.grad
if weight_decay !=0:
d_p=d_p.add(p, alpha=weight_decay)
if momentum !=0:
param_state=self.state[p]
if 'momentum_buffer' not in param_state:
buf=param_state['momentum_buffer']=torch.clone(d_p).detach()
else:
buf=param_state['momentum_buffer']
buf.mul_(momentum).add_(d_p, alpha=1 - dampening)
if nesterov:
d_p=d_p.add(buf, alpha=momentum)
else:
d_p=buf
p.add_(d_p, alpha=-group['lr'])
return loss
这里通过 d_p=p.grad 得到每个参数的梯度，也就是1式的 。 如果使用 weight_decay 的话，那么相当于目标函数加上 ，所以相当于是梯度相当于要再加上 ，所以使用了 d_p=d_p.add(p, alpha=weight_decay)。 通过 buf.mul_(momentum).add_(d_p, alpha=1 - dampening) 来计算动量，momentum参数 一般取0.9，就相当于是之前的动量buf乘以 ，再加上此次的梯度d_p乘以 。 如果不通过nesterov方式更新参数，那么3式中的 就相当于是上一步计算出的动量 了。如果通过nesterov方式更新参数，那么3式中的 就相当于 ，和不用nesterov方式相比，相差了 。 最后通过 p.add_(d_p, alpha=-group['lr']) 更新梯度，相当于是上面的 3 式。
定义优化器：
CLASS torch.optim.Adagrad(params,lr=0.01,lr_decay=0,weight_decay=0,initial_accumulator_value=0,eps=1e-10)
参数：
params (iterable) – 优化器作用的模型参数。 lr (float) – learning rate – 相当于是统一框架中的 。 lr_decay(float,optional) – 学习率衰减 (默认值：0) weight_decay (float, optional) – 权重衰减系数 weight decay (L2 penalty) (默认值：0) eps(float,optional)：防止分母为0的一个小数 (默认值：1e-10)
源码解读：
[docs]class Adagrad(Optimizer):
"""Implements Adagrad algorithm.
It has been proposed in `Adaptive Subgradient Methods for Online Learning
and Stochastic Optimization`_.
Arguments:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): learning rate (default: 1e-2)
lr_decay (float, optional): learning rate decay (default: 0)
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
eps (float, optional): term added to the denominator to improve
numerical stability (default: 1e-10)
.. _Adaptive Subgradient Methods for Online Learning and Stochastic
Optimization: http://jmlr.org/papers/v12/duchi11a.html
"""
def __init__(self, params, lr=1e-2, lr_decay=0, weight_decay=0, initial_accumulator_value=0, eps=1e-10):
if not 0.0 <=lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <=lr_decay:
raise ValueError("Invalid lr_decay value: {}".format(lr_decay))
if not 0.0 <=weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
if not 0.0 <=initial_accumulator_value:
raise ValueError("Invalid initial_accumulator_value value: {}".format(initial_accumulator_value))
if not 0.0 <=eps:
raise ValueError("Invalid epsilon value: {}".format(eps))
defaults=dict(lr=lr, lr_decay=lr_decay, eps=eps, weight_decay=weight_decay,
initial_accumulator_value=initial_accumulator_value)
super(Adagrad, self).__init__(params, defaults)
for group in self.param_groups:
for p in group['params']:
state=self.state[p]
state['step']=0
state['sum']=torch.full_like(p, initial_accumulator_value, memory_format=torch.preserve_format)
def share_memory(self):
for group in self.param_groups:
for p in group['params']:
state=self.state[p]
state['sum'].share_memory_()
[docs] @torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss=None
if closure is not None:
with torch.enable_grad():
loss=closure()
for group in self.param_groups:
params_with_grad=[]
grads=[]
state_sums=[]
state_steps=[]
for p in group['params']:
if p.grad is not None:
params_with_grad.append(p)
grads.append(p.grad)
state=self.state[p]
state_sums.append(state['sum'])
# update the steps for each param group update
state['step'] +=1
# record the step after step update
state_steps.append(state['step'])
F.adagrad(params_with_grad,
grads,
state_sums,
state_steps,
group['lr'],
group['weight_decay'],
group['lr_decay'],
group['eps'])
return loss
定义优化器：
CLASS torch.optim.RMSprop(params, lr=0.01, alpha=0.99, eps=1e-08, weight_decay=0, momentum=0, centered=False)
参数：
params (iterable) – 优化器作用的模型参数。 lr (float) – learning rate – 相当于是统一框架中的 。 momentum (float, optional) – 动量参数。(默认值：0)。 alpha(float,optional) – 平滑常数 (默认值：0.99)。 centered(bool,optional) – if, compute the centered RMSProp, the gradient is normalized by an estimation of its variance，就是这一项是 True 的话就把方差使用梯度作归一化。 weight_decay (float, optional) – 权重衰减系数 weight decay (L2 penalty) (默认值：0) eps(float,optional)：防止分母为0的一个小数 (默认值：1e-10)
源码解读：
import torch
from .optimizer import Optimizer
[docs]class RMSprop(Optimizer):
r"""Implements RMSprop algorithm.
Proposed by G. Hinton in his
`course <https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf>`_.
The centered version first appears in `Generating Sequences
With Recurrent Neural Networks <https://arxiv.org/pdf/1308.0850v5.pdf>`_.
The implementation here takes the square root of the gradient average before
adding epsilon (note that TensorFlow interchanges these two operations). The effective
learning rate is thus :math:`\alpha/(\sqrt{v} + \epsilon)` where :math:`\alpha`
is the scheduled learning rate and :math:`v` is the weighted moving average
of the squared gradient.
Arguments:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): learning rate (default: 1e-2)
momentum (float, optional): momentum factor (default: 0)
alpha (float, optional): smoothing constant (default: 0.99)
eps (float, optional): term added to the denominator to improve
numerical stability (default: 1e-8)
centered (bool, optional) : if ``True``, compute the centered RMSProp,
the gradient is normalized by an estimation of its variance
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
"""
def __init__(self, params, lr=1e-2, alpha=0.99, eps=1e-8, weight_decay=0, momentum=0, centered=False):
if not 0.0 <=lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <=eps:
raise ValueError("Invalid epsilon value: {}".format(eps))
if not 0.0 <=momentum:
raise ValueError("Invalid momentum value: {}".format(momentum))
if not 0.0 <=weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
if not 0.0 <=alpha:
raise ValueError("Invalid alpha value: {}".format(alpha))
defaults=dict(lr=lr, momentum=momentum, alpha=alpha, eps=eps, centered=centered, weight_decay=weight_decay)
super(RMSprop, self).__init__(params, defaults)
def __setstate__(self, state):
super(RMSprop, self).__setstate__(state)
for group in self.param_groups:
group.setdefault('momentum', 0)
group.setdefault('centered', False)
[docs] @torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss=None
if closure is not None:
with torch.enable_grad():
loss=closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
grad=p.grad
if grad.is_sparse:
raise RuntimeError('RMSprop does not support sparse gradients')
state=self.state[p]
# State initialization
if len(state)==0:
state['step']=0
state['square_avg']=torch.zeros_like(p, memory_format=torch.preserve_format)
if group['momentum'] > 0:
state['momentum_buffer']=torch.zeros_like(p, memory_format=torch.preserve_format)
if group['centered']:
state['grad_avg']=torch.zeros_like(p, memory_format=torch.preserve_format)
square_avg=state['square_avg']
alpha=group['alpha']
state['step'] +=1
if group['weight_decay'] !=0:
grad=grad.add(p, alpha=group['weight_decay'])
square_avg.mul_(alpha).addcmul_(grad, grad, value=1 - alpha)
if group['centered']:
grad_avg=state['grad_avg']
grad_avg.mul_(alpha).add_(grad, alpha=1 - alpha)
avg=square_avg.addcmul(grad_avg, grad_avg, value=-1).sqrt_().add_(group['eps'])
else:
avg=square_avg.sqrt().add_(group['eps'])
if group['momentum'] > 0:
buf=state['momentum_buffer']
buf.mul_(group['momentum']).addcdiv_(grad, avg)
p.add_(buf, alpha=-group['lr'])
else:
p.addcdiv_(grad, avg, value=-group['lr'])
return loss
这里通过 grad=p.grad 得到每个参数的梯度，也就是1式的 。 如果使用 weight_decay 的话，那么相当于目标函数加上 ，所以相当于是梯度相当于要再加上 ，故使用了 grad=grad.add(p, alpha=group['weight_decay'])。 square_avg.mul_(alpha).addcmul_(grad, grad, value=1 - alpha) 对应10式，计算当前步的 。 centered 这一项是 False 的话直接 square_avg.sqrt().add_(group['eps']) 对 开根号。
centered 这一项是 True 的话就把方差使用梯度作归一化。最后通过 p.addcdiv_(grad, avg, value=-group['lr']) 更新梯度，相当于是上面的 3 式。
RMSprop算是Adagrad的一种发展，和Adadelta的变体，效果趋于二者之间
定义优化器：
CLASS torch.optim.Adadelta(params, lr=1.0, rho=0.9, eps=1e-06, weight_decay=0)
参数：
params (iterable) – 优化器作用的模型参数。 lr (float) – learning rate – 相当于是统一框架中的 。 rho(float,optional) – 计算梯度平方的滑动平均超参数 (默认值：0.9) weight_decay (float, optional) – 权重衰减系数 weight decay (L2 penalty) (默认值：0) eps(float,optional)：防止分母为0的一个小数 (默认值：1e-10)
源码解读：
import torch
from .optimizer import Optimizer
[docs]class Adadelta(Optimizer):
"""Implements Adadelta algorithm.
It has been proposed in `ADADELTA: An Adaptive Learning Rate Method`__.
Arguments:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
rho (float, optional): coefficient used for computing a running average
of squared gradients (default: 0.9)
eps (float, optional): term added to the denominator to improve
numerical stability (default: 1e-6)
lr (float, optional): coefficient that scale delta before it is applied
to the parameters (default: 1.0)
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
__ https://arxiv.org/abs/1212.5701
"""
def __init__(self, params, lr=1.0, rho=0.9, eps=1e-6, weight_decay=0):
if not 0.0 <=lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <=rho <=1.0:
raise ValueError("Invalid rho value: {}".format(rho))
if not 0.0 <=eps:
raise ValueError("Invalid epsilon value: {}".format(eps))
if not 0.0 <=weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults=dict(lr=lr, rho=rho, eps=eps, weight_decay=weight_decay)
super(Adadelta, self).__init__(params, defaults)
[docs] @torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss=None
if closure is not None:
with torch.enable_grad():
loss=closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
grad=p.grad
if grad.is_sparse:
raise RuntimeError('Adadelta does not support sparse gradients')
state=self.state[p]
# State initialization
if len(state)==0:
state['step']=0
state['square_avg']=torch.zeros_like(p, memory_format=torch.preserve_format)
state['acc_delta']=torch.zeros_like(p, memory_format=torch.preserve_format)
square_avg, acc_delta=state['square_avg'], state['acc_delta']
rho, eps=group['rho'], group['eps']
state['step'] +=1
if group['weight_decay'] !=0:
grad=grad.add(p, alpha=group['weight_decay'])
square_avg.mul_(rho).addcmul_(grad, grad, value=1 - rho)
std=square_avg.add(eps).sqrt_()
delta=acc_delta.add(eps).sqrt_().div_(std).mul_(grad)
p.add_(delta, alpha=-group['lr'])
acc_delta.mul_(rho).addcmul_(delta, delta, value=1 - rho)
return loss
这里通过 grad=p.grad 得到每个参数的梯度，也就是1式的 。 如果使用 weight_decay 的话，那么相当于目标函数加上 ，所以相当于是梯度相当于要再加上 ，故使用了 grad=grad.add(p, alpha=group['weight_decay'])。 square_avg.mul_(rho).addcmul_(grad, grad, value=1 - rho) 对应10式，计算当前步的 。std=square_avg.add(eps).sqrt_() 对 开根号。 最后通过 p.add_(delta, alpha=-group['lr']) 更新梯度，相当于是上面的 3 式。
delta 的分子项是 ，分母项是 开根号。acc_delta 是对 delta 的滑动平均。
定义优化器：
CLASS torch.optim.Adam(params, lr=0.001, betas=(0.9, 0.999), eps=1e-08, weight_decay=0, amsgrad=False)
参数：
params (iterable) – 优化器作用的模型参数。 lr (float) – learning rate – 相当于是统一框架中的 。 betas(Tuple[float,float],optional) – coefficients used for computing running averages of gradient and its square ((默认值：(0.9, 0.999)) weight_decay (float, optional) – 权重衰减系数 weight decay (L2 penalty) (默认值：0) eps(float,optional)：防止分母为0的一个小数 (默认值：1e-10)
源码解读：
import math
import torch
from .optimizer import Optimizer
[docs]class Adam(Optimizer):
r"""Implements Adam algorithm.
It has been proposed in `Adam: A Method for Stochastic Optimization`_.
Arguments:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): learning rate (default: 1e-3)
betas (Tuple[float, float], optional): coefficients used for computing
running averages of gradient and its square (default: (0.9, 0.999))
eps (float, optional): term added to the denominator to improve
numerical stability (default: 1e-8)
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
amsgrad (boolean, optional): whether to use the AMSGrad variant of this
algorithm from the paper `On the Convergence of Adam and Beyond`_
(default: False)
.. _Adam\: A Method for Stochastic Optimization:
https://arxiv.org/abs/1412.6980
.. _On the Convergence of Adam and Beyond:
https://openreview.net/forum?id=ryQu7f-RZ
"""
def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
weight_decay=0, amsgrad=False):
if not 0.0 <=lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <=eps:
raise ValueError("Invalid epsilon value: {}".format(eps))
if not 0.0 <=betas[0] < 1.0:
raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
if not 0.0 <=betas[1] < 1.0:
raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
if not 0.0 <=weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults=dict(lr=lr, betas=betas, eps=eps,
weight_decay=weight_decay, amsgrad=amsgrad)
super(Adam, self).__init__(params, defaults)
def __setstate__(self, state):
super(Adam, self).__setstate__(state)
for group in self.param_groups:
group.setdefault('amsgrad', False)
[docs] @torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss=None
if closure is not None:
with torch.enable_grad():
loss=closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
grad=p.grad
if grad.is_sparse:
raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
amsgrad=group['amsgrad']
state=self.state[p]
# State initialization
if len(state)==0:
state['step']=0
# Exponential moving average of gradient values
state['exp_avg']=torch.zeros_like(p, memory_format=torch.preserve_format)
# Exponential moving average of squared gradient values
state['exp_avg_sq']=torch.zeros_like(p, memory_format=torch.preserve_format)
if amsgrad:
# Maintains max of all exp. moving avg. of sq. grad. values
state['max_exp_avg_sq']=torch.zeros_like(p, memory_format=torch.preserve_format)
exp_avg, exp_avg_sq=state['exp_avg'], state['exp_avg_sq']
if amsgrad:
max_exp_avg_sq=state['max_exp_avg_sq']
beta1, beta2=group['betas']
state['step'] +=1
bias_correction1=1 - beta1 ** state['step']
bias_correction2=1 - beta2 ** state['step']
if group['weight_decay'] !=0:
grad=grad.add(p, alpha=group['weight_decay'])
# Decay the first and second moment running average coefficient
exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
# Use the max. for normalizing running avg. of gradient
denom=(max_exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
else:
denom=(exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
step_size=group['lr'] / bias_correction1
p.addcdiv_(exp_avg, denom, value=-step_size)
return loss
这里通过 grad=p.grad 得到每个参数的梯度，也就是1式的 。 如果使用 weight_decay 的话，那么相当于目标函数加上 ，所以相当于是梯度相当于要再加上 ，故使用了 grad=grad.add(p, alpha=group['weight_decay'])。 exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1) 计算12式。
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2) 计算13式。
因为15式的缘故，要给分母除以 math**.**sqrt(bias_correction2)。
因为14式的缘故，要给分子除以 bias_correction1。
最后通过 p.addcdiv_(exp_avg, denom, value=-step_size) 更新梯度，相当于是上面的 3 式。
Just adding the square of the weights to the loss function is *not* the correct way of using L2 regularization/weight decay with Adam, since that will interact with the m and v parameters in strange ways. Instead we want to decay the weights in a manner that doesn't interact with the m/v parameters. This is equivalent to adding the square of the weights to the loss with plain (non-momentum) SGD. Add weight decay at the end (fixed version).
定义优化器：
CLASS torch.optim.AdamW(params, lr=0.001, betas=(0.9, 0.999), eps=1e-08, weight_decay=0.01, amsgrad=False)
参数：
params (iterable) – 优化器作用的模型参数。 lr (float) – learning rate – 相当于是统一框架中的 。 betas(Tuple[float,float],optional) – coefficients used for computing running averages of gradient and its square ((默认值：(0.9, 0.999)) weight_decay (float, optional) – 权重衰减系数 weight decay (L2 penalty) (默认值：0) eps(float,optional)：防止分母为0的一个小数 (默认值：1e-10)
源码解读：
import math
import torch
from .optimizer import Optimizer
[docs]class AdamW(Optimizer):
r"""Implements AdamW algorithm.
The original Adam algorithm was proposed in `Adam: A Method for Stochastic Optimization`_.
The AdamW variant was proposed in `Decoupled Weight Decay Regularization`_.
Arguments:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): learning rate (default: 1e-3)
betas (Tuple[float, float], optional): coefficients used for computing
running averages of gradient and its square (default: (0.9, 0.999))
eps (float, optional): term added to the denominator to improve
numerical stability (default: 1e-8)
weight_decay (float, optional): weight decay coefficient (default: 1e-2)
amsgrad (boolean, optional): whether to use the AMSGrad variant of this
algorithm from the paper `On the Convergence of Adam and Beyond`_
(default: False)
.. _Adam\: A Method for Stochastic Optimization:
https://arxiv.org/abs/1412.6980
.. _Decoupled Weight Decay Regularization:
https://arxiv.org/abs/1711.05101
.. _On the Convergence of Adam and Beyond:
https://openreview.net/forum?id=ryQu7f-RZ
"""
def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
weight_decay=1e-2, amsgrad=False):
if not 0.0 <=lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <=eps:
raise ValueError("Invalid epsilon value: {}".format(eps))
if not 0.0 <=betas[0] < 1.0:
raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
if not 0.0 <=betas[1] < 1.0:
raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
if not 0.0 <=weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults=dict(lr=lr, betas=betas, eps=eps,
weight_decay=weight_decay, amsgrad=amsgrad)
super(AdamW, self).__init__(params, defaults)
def __setstate__(self, state):
super(AdamW, self).__setstate__(state)
for group in self.param_groups:
group.setdefault('amsgrad', False)
[docs] @torch.no_grad()
def step(self, closure=None):
"""Performs a single optimization step.
Arguments:
closure (callable, optional): A closure that reevaluates the model
and returns the loss.
"""
loss=None
if closure is not None:
with torch.enable_grad():
loss=closure()
for group in self.param_groups:
for p in group['params']:
if p.grad is None:
continue
# Perform stepweight decay
p.mul_(1 - group['lr'] * group['weight_decay'])
# Perform optimization step
grad=p.grad
if grad.is_sparse:
raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
amsgrad=group['amsgrad']
state=self.state[p]
# State initialization
if len(state)==0:
state['step']=0
# Exponential moving average of gradient values
state['exp_avg']=torch.zeros_like(p, memory_format=torch.preserve_format)
# Exponential moving average of squared gradient values
state['exp_avg_sq']=torch.zeros_like(p, memory_format=torch.preserve_format)
if amsgrad:
# Maintains max of all exp. moving avg. of sq. grad. values
state['max_exp_avg_sq']=torch.zeros_like(p, memory_format=torch.preserve_format)
exp_avg, exp_avg_sq=state['exp_avg'], state['exp_avg_sq']
if amsgrad:
max_exp_avg_sq=state['max_exp_avg_sq']
beta1, beta2=group['betas']
state['step'] +=1
bias_correction1=1 - beta1 ** state['step']
bias_correction2=1 - beta2 ** state['step']
# Decay the first and second moment running average coefficient
exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
# Use the max. for normalizing running avg. of gradient
denom=(max_exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
else:
denom=(exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
step_size=group['lr'] / bias_correction1
p.addcdiv_(exp_avg, denom, value=-step_size)
return loss
与 Adam 不一样的地方是：
Adam 如果使用 weight_decay 的话，那么相当于目标函数加上 ，所以相当于是梯度相当于要再加上 ，故使用了 grad=grad.add(p, alpha=group['weight_decay'])。而 AdamW 是 p.mul_(1 - group['lr'] * group['weight_decay']) 直接让参数：
这样才能和绿色框一致。
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