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PyTorch 学习 -8- 优化器
Yiwei Zhang · 2023-07-21 · via 又见苍岚

优化器是神经网络根据网络反向传播的梯度信息来更新网络的参数,以起到降低loss函数计算值,使得模型输出更加接近真实标签。

参考 深入浅出PyTorch ,系统补齐基础知识。

本节目录

  • 了解PyTorch的优化器
  • 学会使用PyTorch提供的优化器进行优化
  • 优化器的属性和构造
  • 优化器的对比

简介

深度学习的目标是通过不断改变网络参数,使得参数能够对输入做各种非线性变换拟合输出,本质上就是一个函数去寻找最优解,只不过这个最优解是一个矩阵,而如何快速求得这个最优解是深度学习研究的一个重点,以经典的resnet-50为例,它大约有2000万个系数需要进行计算,那么我们如何计算出这么多系数,有以下两种方法:

  1. 第一种是直接暴力穷举一遍参数,这种方法从理论上行得通,但是实施上可能性基本为0,因为参数量过于庞大。
  2. 为了使求解参数过程更快,人们提出了第二种办法,即BP+优化器逼近求解。

Pytorch 提供的优化器

Pytorch很人性化的给我们提供了一个优化器的库torch.optim,在这里面提供了十种优化器。

  • torch.optim.ASGD
  • torch.optim.Adadelta
  • torch.optim.Adagrad
  • torch.optim.Adam
  • torch.optim.AdamW
  • torch.optim.Adamax
  • torch.optim.LBFGS
  • torch.optim.RMSprop
  • torch.optim.Rprop
  • torch.optim.SGD
  • torch.optim.SparseAdam

而以上这些优化算法均继承于Optimizer,下面我们先来看下所有优化器的基类Optimizer。定义如下:

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class Optimizer(object):
def __init__(self, params, defaults):
self.defaults = defaults
self.state = defaultdict(dict)
self.param_groups = []

Optimizer有三个属性:

  • defaults:存储的是优化器的超参数,例子如下:
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{'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False}
  • state:参数的缓存,例子如下:
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defaultdict(<class 'dict'>, {tensor([[ 0.3864, -0.0131],
[-0.1911, -0.4511]], requires_grad=True): {'momentum_buffer': tensor([[0.0052, 0.0052],
[0.0052, 0.0052]])}})
  • param_groups:管理的参数组,是一个list,其中每个元素是一个字典,顺序是params,lr,momentum,dampening,weight_decay,nesterov,例子如下:
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[{'params': [tensor([[-0.1022, -1.6890],[-1.5116, -1.7846]], requires_grad=True)], 'lr': 1, 'momentum': 0, 'dampening': 0, 'weight_decay': 0, 'nesterov': False}]

Optimizer还有以下的方法:

  • zero_grad():清空所管理参数的梯度,PyTorch的特性是张量的梯度不自动清零,因此每次反向传播后都需要清空梯度。
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def zero_grad(self, set_to_none: bool = False):
for group in self.param_groups:
for p in group['params']:
if p.grad is not None: #梯度不为空
if set_to_none:
p.grad = None
else:
if p.grad.grad_fn is not None:
p.grad.detach_()
else:
p.grad.requires_grad_(False)
p.grad.zero_()# 梯度设置为0
  • step():执行一步梯度更新,参数更新
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def step(self, closure): 
raise NotImplementedError
  • add_param_group():添加参数组
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def add_param_group(self, param_group):
assert isinstance(param_group, dict), "param group must be a dict"
# 检查类型是否为tensor
params = param_group['params']
if isinstance(params, torch.Tensor):
param_group['params'] = [params]
elif isinstance(params, set):
raise TypeError('optimizer parameters need to be organized in ordered collections, but '
'the ordering of tensors in sets will change between runs. Please use a list instead.')
else:
param_group['params'] = list(params)
for param in param_group['params']:
if not isinstance(param, torch.Tensor):
raise TypeError("optimizer can only optimize Tensors, "
"but one of the params is " + torch.typename(param))
if not param.is_leaf:
raise ValueError("can't optimize a non-leaf Tensor")

for name, default in self.defaults.items():
if default is required and name not in param_group:
raise ValueError("parameter group didn't specify a value of required optimization parameter " +
name)
else:
param_group.setdefault(name, default)

params = param_group['params']
if len(params) != len(set(params)):
warnings.warn("optimizer contains a parameter group with duplicate parameters; "
"in future, this will cause an error; "
"see github.com/pytorch/pytorch/issues/40967 for more information", stacklevel=3)
# 上面好像都在进行一些类的检测,报Warning和Error
param_set = set()
for group in self.param_groups:
param_set.update(set(group['params']))

if not param_set.isdisjoint(set(param_group['params'])):
raise ValueError("some parameters appear in more than one parameter group")
# 添加参数
self.param_groups.append(param_group)

  • load_state_dict() :加载状态参数字典,可以用来进行模型的断点续训练,继续上次的参数进行训练
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def load_state_dict(self, state_dict):
r"""Loads the optimizer state.

Arguments:
state_dict (dict): optimizer state. Should be an object returned
from a call to :meth:`state_dict`.
"""
# deepcopy, to be consistent with module API
state_dict = deepcopy(state_dict)
# Validate the state_dict
groups = self.param_groups
saved_groups = state_dict['param_groups']

if len(groups) != len(saved_groups):
raise ValueError("loaded state dict has a different number of "
"parameter groups")
param_lens = (len(g['params']) for g in groups)
saved_lens = (len(g['params']) for g in saved_groups)
if any(p_len != s_len for p_len, s_len in zip(param_lens, saved_lens)):
raise ValueError("loaded state dict contains a parameter group "
"that doesn't match the size of optimizer's group")

# Update the state
id_map = {old_id: p for old_id, p in
zip(chain.from_iterable((g['params'] for g in saved_groups)),
chain.from_iterable((g['params'] for g in groups)))}

def cast(param, value):
r"""Make a deep copy of value, casting all tensors to device of param."""
.....

# Copy state assigned to params (and cast tensors to appropriate types).
# State that is not assigned to params is copied as is (needed for
# backward compatibility).
state = defaultdict(dict)
for k, v in state_dict['state'].items():
if k in id_map:
param = id_map[k]
state[param] = cast(param, v)
else:
state[k] = v

# Update parameter groups, setting their 'params' value
def update_group(group, new_group):
...
param_groups = [
update_group(g, ng) for g, ng in zip(groups, saved_groups)]
self.__setstate__({'state': state, 'param_groups': param_groups})

  • state_dict():获取优化器当前状态信息字典
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def state_dict(self):
r"""Returns the state of the optimizer as a :class:`dict`.

It contains two entries:

* state - a dict holding current optimization state. Its content
differs between optimizer classes.
* param_groups - a dict containing all parameter groups
"""
# Save order indices instead of Tensors
param_mappings = {}
start_index = 0

def pack_group(group):
......
param_groups = [pack_group(g) for g in self.param_groups]
# Remap state to use order indices as keys
packed_state = {(param_mappings[id(k)] if isinstance(k, torch.Tensor) else k): v
for k, v in self.state.items()}
return {
'state': packed_state,
'param_groups': param_groups,

实际操作

构造参数更新环境变量

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import os
import torch

# 设置权重,服从正态分布 --> 2 x 2
weight = torch.randn((2, 2), requires_grad=True)

# 设置梯度为全1矩阵 --> 2 x 2
weight.grad = torch.ones((2, 2))

# 输出现有的weight和data
print("The data of weight before step:\n{}".format(weight.data))
print("The grad of weight before step:\n{}".format(weight.grad))

-->
The data of weight before step:
tensor([[-0.2796, 0.1785],
[-2.0026, -0.6214]])
The grad of weight before step:
tensor([[1., 1.],
[1., 1.]])

梯度更新

为了使得 Loss 变小,梯度更新会沿着梯度的反方向以 lr 为步长更新

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# 实例化优化器
optimizer = torch.optim.SGD([weight], lr=0.1, momentum=0.9)

# 进行一步操作
optimizer.step()

# 查看进行一步后的值,梯度
print("The data of weight after step:\n{}".format(weight.data))
print("The grad of weight after step:\n{}".format(weight.grad))

-->
The data of weight after step:
tensor([[-0.3796, 0.0785],
[-2.1026, -0.7214]])
The grad of weight after step:
tensor([[1., 1.],
[1., 1.]])

梯度默认不清零,为了不影响后续操作,需要手动置零

从输出看,已经清空了

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# 权重清零
optimizer.zero_grad()

# 检验权重是否为0
print("The grad of weight after optimizer.zero_grad():\n{}".format(weight.grad))

-->
None

优化器参数

optimizer 中的 params 保存了模型参数的引用(同一个对象),因此可以获得梯度信息

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# 输出参数
print("optimizer.params_group is \n{}".format(optimizer.param_groups))
# 查看参数位置,optimizer和weight的位置一样,我觉得这里可以参考Python是基于值管理
print("weight in optimizer:{}\nweight in weight:{}\n".format(id(optimizer.param_groups[0]['params'][0]), id(weight)))

-->
optimizer.params_group is
[{'params': [tensor([[-0.3796, 0.0785],
[-2.1026, -0.7214]], requires_grad=True)], 'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False, 'maximize': False, 'foreach': None, 'differentiable': False}]
weight in optimizer:2505870057776
weight in weight:2505870057776

向优化器添加参数

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# 添加参数:weight2
weight2 = torch.randn((3, 3), requires_grad=True)
optimizer.add_param_group({"params": weight2, 'lr': 0.0001, 'nesterov': True})

# 查看现有的参数
print("optimizer.param_groups is\n{}".format(optimizer.param_groups))

-->
optimizer.param_groups is
[{'params': [tensor([[-0.3796, 0.0785],
[-2.1026, -0.7214]], requires_grad=True)], 'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False, 'maximize': False, 'foreach': None, 'differentiable': False}, {'params': [tensor([[-0.4390, -0.0237, 1.4610],
[ 1.3862, 0.3362, -0.3615],
[ 0.0876, -0.8942, 0.2905]], requires_grad=True)], 'lr': 0.0001, 'nesterov': True, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'maximize': False, 'foreach': None, 'differentiable': False}]

查看优化器 state_dict 参数

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# 查看当前状态信息
opt_state_dict = optimizer.state_dict()
print("state_dict before step:\n", opt_state_dict)

-->
state_dict before step:
{'state': {0: {'momentum_buffer': tensor([[1., 1.],
[1., 1.]])}}, 'param_groups': [{'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False, 'maximize': False, 'foreach': None, 'differentiable': False, 'params': [0]}, {'lr': 0.0001, 'nesterov': True, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'maximize': False, 'foreach': None, 'differentiable': False, 'params': [1]}]}

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# 进行50次step操作
for _ in range(50):
optimizer.step()

# 输出现有状态信息
print("state_dict after step:\n", optimizer.state_dict())

-->
state_dict after step:
{'state': {0: {'momentum_buffer': tensor([[1., 1.],
[1., 1.]])}}, 'param_groups': [{'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False, 'maximize': False, 'foreach': None, 'differentiable': False, 'params': [0]}, {'lr': 0.0001, 'nesterov': True, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'maximize': False, 'foreach': None, 'differentiable': False, 'params': [1]}]}

保存、加载优化器参数

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# 保存参数信息
torch.save(optimizer.state_dict(),os.path.join(r"D:\test", "optimizer_state_dict.pkl"))
print("----------done-----------")

# 加载参数信息
state_dict = torch.load(r"D:\test\optimizer_state_dict.pkl")

# 需要修改为你自己的路径
optimizer.load_state_dict(state_dict)
print("load state_dict successfully\n{}".format(state_dict))

# 输出最后属性信息
print("\n{}".format(optimizer.defaults))
print("\n{}".format(optimizer.state))
print("\n{}".format(optimizer.param_groups))

-->
[{'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False, 'maximize': False, 'foreach': None, 'differentiable': False, 'params': [tensor([[-0.9254, -0.2677],
[-0.6678, 0.1051]], requires_grad=True)]}, {'lr': 0.0001, 'nesterov': True, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'maximize': False, 'foreach': None, 'differentiable': False, 'params': [tensor([[-0.4079, -1.7280, -0.7602],
[-0.0784, -1.1958, -0.0492],
[ 1.3130, 0.0540, 0.6167]], requires_grad=True)]}]

注意

  1. 每个优化器都是一个类,我们一定要进行实例化才能使用,比如下方实现:
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class Net(nn.Moddule):
···
net = Net()
optim = torch.optim.SGD(net.parameters(),lr=lr)
optim.step()
  1. optimizer在一个神经网络的epoch中需要实现下面两个步骤:
    1. 梯度置零
    2. 梯度更新
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optimizer = torch.optim.SGD(net.parameters(), lr=1e-5)
for epoch in range(EPOCH):
...
optimizer.zero_grad() #梯度置零
loss = ... #计算loss
loss.backward() #BP反向传播
optimizer.step() #梯度更新
  1. 给网络不同的层赋予不同的优化器参数。
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from torch import optim
from torchvision.models import resnet18

net = resnet18()

optimizer = optim.SGD([
{'params':net.fc.parameters()},#fc的lr使用默认的1e-5
{'params':net.layer4[0].conv1.parameters(),'lr':1e-2}],lr=1e-5)

# 可以使用param_groups查看属性

实验

为了更好的帮大家了解优化器,我们对PyTorch中的优化器进行了一个小测试

数据生成

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a = torch.linspace(-1, 1, 1000)
# 升维操作
x = torch.unsqueeze(a, dim=1)
y = x.pow(2) + 0.1 * torch.normal(torch.zeros(x.size()))

数据分布曲线

网络结构

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class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.hidden = nn.Linear(1, 20)
self.predict = nn.Linear(20, 1)

def forward(self, x):
x = self.hidden(x)
x = F.relu(x)
x = self.predict(x)
return x

测试代码

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import os
import mtutils as mt
import torch
from torch import nn
import torch.nn.functional as F
from torch.utils.data import Dataset
from torch.utils.data import DataLoader
from copy import deepcopy

a = torch.linspace(-1, 1, 1000)
# 升维操作
x = torch.unsqueeze(a, dim=1)
y = x.pow(2) + 0.1 * torch.normal(torch.zeros(x.size()))
gt = x.pow(2).tolist()

class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.hidden = nn.Linear(1, 20)
self.predict = nn.Linear(20, 1)

nn.init.kaiming_normal_(self.hidden.weight)
nn.init.constant_(self.hidden.bias, 0)

nn.init.kaiming_normal_(self.predict.weight)
nn.init.constant_(self.predict.bias, 0)

def forward(self, x):
x = self.hidden(x)
x = F.relu(x)
x = self.predict(x)
return x

class dataset(Dataset):
def __init__(self, x, y):
assert len(x) == len(y)

self.x = x
self.y = y
pass

def __len__(self):
return len(self.x)

def __getitem__(self, index):
return self.x[index], self.y[index]

if __name__ == '__main__':

training_data_set = dataset(x, y)
training_data_loader = DataLoader(training_data_set, 16, shuffle=True, drop_last=True)

model = Net()
model.train()

loss = nn.MSELoss()

lr = 0.1

optimizer_dict = dict()
optimizer_dict['SGD'] = torch.optim.SGD
optimizer_dict['ASGD'] = torch.optim.ASGD
optimizer_dict['Adadelta'] = torch.optim.Adadelta
optimizer_dict['Adagrad'] = torch.optim.Adagrad
optimizer_dict['Adam'] = torch.optim.Adam
optimizer_dict['AdamW'] = torch.optim.AdamW
optimizer_dict['Adamax'] = torch.optim.Adamax
optimizer_dict['RMSprop'] = torch.optim.RMSprop
optimizer_dict['Rprop'] = torch.optim.Rprop

loss_dict = dict()
res_dict = dict()
for name, optimizer in optimizer_dict.items():
temp_model = deepcopy(model)
temp_model.train()
loss_list = list()
temp_optimizer = optimizer(temp_model.parameters(), lr)
for epoch in mt.tqdm(range(4)):
for index, data in enumerate(training_data_loader):
temp_optimizer.zero_grad()
input_data, target_data = data
output = temp_model(data[0])

loss_res = loss(output, target_data)

loss_list.append(loss_res.detach().numpy())

loss_res.backward()
temp_optimizer.step()

loss_dict[name] = loss_list
temp_model.eval()
with torch.no_grad():
res = temp_model(torch.tensor(x))
res = res.detach().numpy().squeeze().tolist()
res_dict[name] = res

res_dict['gt'] = gt

fig = mt.plt.figure(figsize=(10, 10), dpi=100)
mt.plt.subplot(1,2,1)
for key, values in loss_dict.items():
mt.plt.plot(list(range(len(values))), values, label=key)
pass
mt.plt.ylim(0, 1)
mt.plt.legend()
mt.plt.title("loss")

mt.plt.subplot(1,2,2)
for key, values in res_dict.items():
mt.plt.plot(list(range(len(values))), values, label=key)
pass
mt.plt.legend()
mt.plt.title("results")

mt.plt.show()

  • 结果示意:

在上面的图片上,曲线下降的趋势和对应的steps代表了在这轮数据,模型下的收敛速度

注意: 优化器的选择是需要根据模型进行改变的,不存在绝对的好坏之分,我们需要多进行一些测试。

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import os
import mtutils as mt
import torch
from torch import nn
import torch.nn.functional as F
from torch.utils.data import Dataset
from torch.utils.data import DataLoader
from copy import deepcopy

a = torch.linspace(-1, 1, 1000)
# 升维操作
x = torch.unsqueeze(a, dim=1)
y = x.pow(2) + 0.1 * torch.normal(torch.zeros(x.size()))

class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.hidden = nn.Linear(1, 20)
self.predict = nn.Linear(20, 1)

nn.init.kaiming_normal_(self.hidden.weight)
nn.init.constant_(self.hidden.bias, 0)

nn.init.kaiming_normal_(self.predict.weight)
nn.init.constant_(self.predict.bias, 0)

def forward(self, x):
x = self.hidden(x)
x = F.relu(x)
x = self.predict(x)
return x

class dataset(Dataset):
def __init__(self, x, y):
assert len(x) == len(y)

self.x = x
self.y = y
pass

def __len__(self):
return len(self.x)

def __getitem__(self, index):
return self.x[index], self.y[index]

if __name__ == '__main__':

training_data_set = dataset(x, y)
training_data_loader = DataLoader(training_data_set, 16, shuffle=True, drop_last=True)

model = Net()
model.train()

loss = nn.MSELoss()

lr = 0.1

optimizer_dict = dict()
optimizer_dict['SGD'] = torch.optim.SGD
optimizer_dict['ASGD'] = torch.optim.ASGD
optimizer_dict['Adadelta'] = torch.optim.Adadelta
optimizer_dict['Adagrad'] = torch.optim.Adagrad
optimizer_dict['Adam'] = torch.optim.Adam
optimizer_dict['AdamW'] = torch.optim.AdamW
optimizer_dict['Adamax'] = torch.optim.Adamax
# optimizer_dict['LBFGS'] = torch.optim.LBFGS
optimizer_dict['RMSprop'] = torch.optim.RMSprop
optimizer_dict['Rprop'] = torch.optim.Rprop
# optimizer_dict['SparseAdam'] = torch.optim.SparseAdam

loss_dict = dict()
for name, optimizer in optimizer_dict.items():
temp_model = deepcopy(model)
loss_list = list()
temp_optimizer = optimizer(temp_model.parameters(), lr)
for epoch in mt.tqdm(range(7)):
for index, data in enumerate(training_data_loader):
temp_optimizer.zero_grad()
input_data, target_data = data
output = temp_model(data[0])

loss_res = loss(output, target_data)

loss_list.append(loss_res.detach().numpy())

loss_res.backward()
temp_optimizer.step()

loss_dict[name] = loss_list

pass

参考资料

文章链接:
https://www.zywvvd.com/notes/study/deep-learning/pytorch/torch-learning/torch-learning-8/