.. _sec_scheduler:
学习率调度器
============
到目前为止，我们主要关注如何更新权重向量的优化算法，而不是它们的更新速率。
然而，调整学习率通常与实际算法同样重要，有如下几方面需要考虑：
- 首先，学习率的大小很重要。如果它太大，优化就会发散；如果它太小，训练就会需要过长时间，或者我们最终只能得到次优的结果。我们之前看到问题的条件数很重要（有关详细信息，请参见
:numref:`sec_momentum`\ ）。直观地说，这是最不敏感与最敏感方向的变化量的比率。
- 其次，衰减速率同样很重要。如果学习率持续过高，我们可能最终会在最小值附近弹跳，从而无法达到最优解。
:numref:`sec_minibatch_sgd`\ 比较详细地讨论了这一点，在
:numref:`sec_sgd`\ 中我们则分析了性能保证。简而言之，我们希望速率衰减，但要比\ :math:`\mathcal{O}(t^{-\frac{1}{2}})`\ 慢，这样能成为解决凸问题的不错选择。
- 另一个同样重要的方面是初始化。这既涉及参数最初的设置方式（详情请参阅
:numref:`sec_numerical_stability`\ ），又关系到它们最初的演变方式。这被戏称为\ *预热*\ （warmup），即我们最初开始向着解决方案迈进的速度有多快。一开始的大步可能没有好处，特别是因为最初的参数集是随机的。最初的更新方向可能也是毫无意义的。
- 最后，还有许多优化变体可以执行周期性学习率调整。这超出了本章的范围，我们建议读者阅读
:cite:`Izmailov.Podoprikhin.Garipov.ea.2018`\ 来了解个中细节。例如，如何通过对整个路径参数求平均值来获得更好的解。
鉴于管理学习率需要很多细节，因此大多数深度学习框架都有自动应对这个问题的工具。
在本章中，我们将梳理不同的调度策略对准确性的影响，并展示如何通过\ *学习率调度器*\ （learning
rate scheduler）来有效管理。
一个简单的问题
--------------
我们从一个简单的问题开始，这个问题可以轻松计算，但足以说明要义。
为此，我们选择了一个稍微现代化的LeNet版本（激活函数使用\ ``relu``\ 而不是\ ``sigmoid``\ ，汇聚层使用最大汇聚层而不是平均汇聚层），并应用于Fashion-MNIST数据集。
此外，我们混合网络以提高性能。
由于大多数代码都是标准的，我们只介绍基础知识，而不做进一步的详细讨论。如果需要，请参阅
:numref:`chap_cnn`\ 进行复习。
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\diilbookstyleinputcell
.. code:: python
%matplotlib inline
import math
import mindspore
from mindspore import nn, ops, value_and_grad
from d2l import mindspore as d2l
def net_fn():
model = nn.SequentialCell(
nn.Conv2d(1, 6, kernel_size=5, padding=2, pad_mode='pad'), nn.ReLU(),
nn.MaxPool2d(kernel_size=2, stride=2),
nn.Conv2d(6, 16, kernel_size=5, pad_mode='valid'), nn.ReLU(),
nn.MaxPool2d(kernel_size=2, stride=2),
nn.Flatten(),
nn.Dense(16 * 5 * 5, 120), nn.ReLU(),
nn.Dense(120, 84), nn.ReLU(),
nn.Dense(84, 10))
return model
loss = nn.CrossEntropyLoss()
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)
steps_per_epoch = train_iter.get_dataset_size()
# 代码几乎与d2l.train_ch6定义在卷积神经网络一章LeNet一节中的相同
def train(net, train_iter, test_iter, num_epochs, loss, trainer, device=None):
# 定义前向传播函数
def forward_fn(x, y):
y_hat = net(x)
l = loss(y_hat, y)
return l, y_hat
grad_fn = value_and_grad(forward_fn, None, weights=net.trainable_params(), has_aux=True)
# 定义模型单步训练
def train_step(X, y):
(l, y_hat), grads = grad_fn(X, y)
trainer(grads) # optim
return l, y_hat
animator = d2l.Animator(xlabel='epoch', xlim=[0, num_epochs], ylim=[0, 2.3],
legend=['train loss', 'train acc', 'test acc'])
for epoch in range(num_epochs):
metric = d2l.Accumulator(3) # train_loss,train_acc,num_examples
for i, (X, y) in enumerate(train_iter):
l, y_hat = train_step(X, y)
metric.add(l.asnumpy() * X.shape[0], d2l.accuracy(y_hat, y), X.shape[0])
train_loss = metric[0] / metric[2]
train_acc = metric[1] / metric[2]
if (i + 1) % 50 == 0:
animator.add(epoch + i / train_iter.get_dataset_size(),
(train_loss, train_acc, None))
test_acc = d2l.evaluate_accuracy_gpu(net, test_iter)
animator.add(epoch+1, (None, None, test_acc))
print(f'train loss {train_loss:.3f}, train acc {train_acc:.3f}, '
f'test acc {test_acc:.3f}')
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\diilbookstyleinputcell
.. code:: python
%matplotlib inline
import math
import torch
from torch import nn
from torch.optim import lr_scheduler
from d2l import torch as d2l
def net_fn():
model = nn.Sequential(
nn.Conv2d(1, 6, kernel_size=5, padding=2), nn.ReLU(),
nn.MaxPool2d(kernel_size=2, stride=2),
nn.Conv2d(6, 16, kernel_size=5), nn.ReLU(),
nn.MaxPool2d(kernel_size=2, stride=2),
nn.Flatten(),
nn.Linear(16 * 5 * 5, 120), nn.ReLU(),
nn.Linear(120, 84), nn.ReLU(),
nn.Linear(84, 10))
return model
loss = nn.CrossEntropyLoss()
device = d2l.try_gpu()
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)
# 代码几乎与d2l.train_ch6定义在卷积神经网络一章LeNet一节中的相同
def train(net, train_iter, test_iter, num_epochs, loss, trainer, device,
scheduler=None):
net.to(device)
animator = d2l.Animator(xlabel='epoch', xlim=[0, num_epochs],
legend=['train loss', 'train acc', 'test acc'])
for epoch in range(num_epochs):
metric = d2l.Accumulator(3) # train_loss,train_acc,num_examples
for i, (X, y) in enumerate(train_iter):
net.train()
trainer.zero_grad()
X, y = X.to(device), y.to(device)
y_hat = net(X)
l = loss(y_hat, y)
l.backward()
trainer.step()
with torch.no_grad():
metric.add(l * X.shape[0], d2l.accuracy(y_hat, y), X.shape[0])
train_loss = metric[0] / metric[2]
train_acc = metric[1] / metric[2]
if (i + 1) % 50 == 0:
animator.add(epoch + i / len(train_iter),
(train_loss, train_acc, None))
test_acc = d2l.evaluate_accuracy_gpu(net, test_iter)
animator.add(epoch+1, (None, None, test_acc))
if scheduler:
if scheduler.__module__ == lr_scheduler.__name__:
# UsingPyTorchIn-Builtscheduler
scheduler.step()
else:
# Usingcustomdefinedscheduler
for param_group in trainer.param_groups:
param_group['lr'] = scheduler(epoch)
print(f'train loss {train_loss:.3f}, train acc {train_acc:.3f}, '
f'test acc {test_acc:.3f}')
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\diilbookstyleinputcell
.. code:: python
lr, num_epochs = 0.3, 30
net = net_fn()
trainer = nn.SGD(net.trainable_params(), lr)
train(net, train_iter, test_iter, num_epochs, loss, trainer)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.137, train acc 0.948, test acc 0.884
.. figure:: output_lr-scheduler_1dfeb6_12_1.svg
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\diilbookstyleinputcell
.. code:: python
lr, num_epochs = 0.3, 30
net = net_fn()
trainer = torch.optim.SGD(net.parameters(), lr=lr)
train(net, train_iter, test_iter, num_epochs, loss, trainer, device)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.135, train acc 0.949, test acc 0.894
.. figure:: output_lr-scheduler_1dfeb6_15_1.svg
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\diilbookstyleinputcell
.. code:: python
lr = 0.1
mindspore.ops.assign(trainer.learning_rate, lr)
print(f'learning rate is now {trainer.learning_rate.data.asnumpy():.2f}')
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
learning rate is now 0.10
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\diilbookstyleinputcell
.. code:: python
lr = 0.1
trainer.param_groups[0]["lr"] = lr
print(f'learning rate is now {trainer.param_groups[0]["lr"]:.2f}')
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
learning rate is now 0.10
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\diilbookstyleinputcell
.. code:: python
scheduler = SquareRootScheduler(lr=0.1)
d2l.plot(ops.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_1dfeb6_32_0.svg
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\diilbookstyleinputcell
.. code:: python
scheduler = SquareRootScheduler(lr=0.1)
d2l.plot(torch.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_1dfeb6_35_0.svg
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\diilbookstyleinputcell
.. code:: python
net = net_fn()
lr_list = mindspore.Tensor([scheduler(t) for t in range(num_epochs) for i in range(steps_per_epoch)])
trainer = nn.SGD(net.trainable_params(), lr_list)
train(net, train_iter, test_iter, num_epochs, loss, trainer)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.297, train acc 0.892, test acc 0.874
.. figure:: output_lr-scheduler_1dfeb6_41_1.svg
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.. raw:: latex
\diilbookstyleinputcell
.. code:: python
net = net_fn()
trainer = torch.optim.SGD(net.parameters(), lr)
train(net, train_iter, test_iter, num_epochs, loss, trainer, device,
scheduler)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.278, train acc 0.899, test acc 0.881
.. figure:: output_lr-scheduler_1dfeb6_44_1.svg
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\diilbookstyleinputcell
.. code:: python
class FactorScheduler:
def __init__(self, factor=1, stop_factor_lr=1e-7, base_lr=0.1):
self.factor = factor
self.stop_factor_lr = stop_factor_lr
self.base_lr = base_lr
def __call__(self, num_update):
self.base_lr = max(self.stop_factor_lr, self.base_lr * self.factor)
return self.base_lr
scheduler = FactorScheduler(factor=0.9, stop_factor_lr=1e-2, base_lr=2.0)
d2l.plot(ops.arange(50), [scheduler(t) for t in range(50)])
.. figure:: output_lr-scheduler_1dfeb6_50_0.svg
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\diilbookstyleinputcell
.. code:: python
class FactorScheduler:
def __init__(self, factor=1, stop_factor_lr=1e-7, base_lr=0.1):
self.factor = factor
self.stop_factor_lr = stop_factor_lr
self.base_lr = base_lr
def __call__(self, num_update):
self.base_lr = max(self.stop_factor_lr, self.base_lr * self.factor)
return self.base_lr
scheduler = FactorScheduler(factor=0.9, stop_factor_lr=1e-2, base_lr=2.0)
d2l.plot(torch.arange(50), [scheduler(t) for t in range(50)])
.. figure:: output_lr-scheduler_1dfeb6_53_0.svg
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\diilbookstyleinputcell
.. code:: python
class MultiFactorScheduler:
def __init__(self, step, factor, base_lr):
self.step = step
self.factor = factor
self.base_lr = base_lr
self.applied = set()
def __call__(self, epoch):
if epoch in self.step and epoch not in self.applied:
self.base_lr = self.base_lr * self.factor
self.applied.add(epoch)
return self.base_lr
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\diilbookstyleinputcell
.. code:: python
net = net_fn()
trainer = torch.optim.SGD(net.parameters(), lr=0.5)
scheduler = lr_scheduler.MultiStepLR(trainer, milestones=[15, 30], gamma=0.5)
def get_lr(trainer, scheduler):
lr = scheduler.get_last_lr()[0]
trainer.step()
scheduler.step()
return lr
d2l.plot(torch.arange(num_epochs), [get_lr(trainer, scheduler)
for t in range(num_epochs)])
.. figure:: output_lr-scheduler_1dfeb6_62_0.svg
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\diilbookstyleinputcell
.. code:: python
net = net_fn()
lr_list = mindspore.Tensor([scheduler(t) for t in range(num_epochs) for i in range(steps_per_epoch)])
trainer = nn.SGD(net.trainable_params(), lr_list)
train(net, train_iter, test_iter, num_epochs, loss, trainer)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.448, train acc 0.839, test acc 0.838
.. figure:: output_lr-scheduler_1dfeb6_68_1.svg
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\diilbookstyleinputcell
.. code:: python
net = net_fn()
trainer = torch.optim.SGD(net.parameters(), lr=0.5)
scheduler = lr_scheduler.MultiStepLR(trainer, milestones=[15, 30], gamma=0.5)
train(net, train_iter, test_iter, num_epochs, loss, trainer, device,
scheduler)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.145, train acc 0.945, test acc 0.879
.. figure:: output_lr-scheduler_1dfeb6_71_1.svg
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\diilbookstyleinputcell
.. code:: python
class CosineScheduler:
def __init__(self, max_update, base_lr=0.01, final_lr=0,
warmup_steps=0, warmup_begin_lr=0):
self.base_lr_orig = base_lr
self.max_update = max_update
self.final_lr = final_lr
self.warmup_steps = warmup_steps
self.warmup_begin_lr = warmup_begin_lr
self.max_steps = self.max_update - self.warmup_steps
def get_warmup_lr(self, epoch):
increase = (self.base_lr_orig - self.warmup_begin_lr) \
* float(epoch) / float(self.warmup_steps)
return self.warmup_begin_lr + increase
def __call__(self, epoch):
if epoch < self.warmup_steps:
return self.get_warmup_lr(epoch)
if epoch <= self.max_update:
self.base_lr = self.final_lr + (
self.base_lr_orig - self.final_lr) * (1 + math.cos(
math.pi * (epoch - self.warmup_steps) / self.max_steps)) / 2
return self.base_lr
scheduler = CosineScheduler(max_update=20, base_lr=0.3, final_lr=0.01)
d2l.plot(ops.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_1dfeb6_77_0.svg
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\diilbookstyleinputcell
.. code:: python
class CosineScheduler:
def __init__(self, max_update, base_lr=0.01, final_lr=0,
warmup_steps=0, warmup_begin_lr=0):
self.base_lr_orig = base_lr
self.max_update = max_update
self.final_lr = final_lr
self.warmup_steps = warmup_steps
self.warmup_begin_lr = warmup_begin_lr
self.max_steps = self.max_update - self.warmup_steps
def get_warmup_lr(self, epoch):
increase = (self.base_lr_orig - self.warmup_begin_lr) \
* float(epoch) / float(self.warmup_steps)
return self.warmup_begin_lr + increase
def __call__(self, epoch):
if epoch < self.warmup_steps:
return self.get_warmup_lr(epoch)
if epoch <= self.max_update:
self.base_lr = self.final_lr + (
self.base_lr_orig - self.final_lr) * (1 + math.cos(
math.pi * (epoch - self.warmup_steps) / self.max_steps)) / 2
return self.base_lr
scheduler = CosineScheduler(max_update=20, base_lr=0.3, final_lr=0.01)
d2l.plot(torch.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_1dfeb6_80_0.svg
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\diilbookstyleinputcell
.. code:: python
net = net_fn()
lr_list = mindspore.Tensor([scheduler(t) for t in range(num_epochs) for i in range(steps_per_epoch)])
trainer = nn.SGD(net.trainable_params(), lr_list)
train(net, train_iter, test_iter, num_epochs, loss, trainer)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.209, train acc 0.923, test acc 0.893
.. figure:: output_lr-scheduler_1dfeb6_86_1.svg
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\diilbookstyleinputcell
.. code:: python
net = net_fn()
trainer = torch.optim.SGD(net.parameters(), lr=0.3)
train(net, train_iter, test_iter, num_epochs, loss, trainer, device,
scheduler)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.220, train acc 0.918, test acc 0.894
.. figure:: output_lr-scheduler_1dfeb6_89_1.svg
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\diilbookstyleinputcell
.. code:: python
scheduler = CosineScheduler(20, warmup_steps=5, base_lr=0.3, final_lr=0.01)
d2l.plot(ops.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_1dfeb6_95_0.svg
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\diilbookstyleinputcell
.. code:: python
scheduler = CosineScheduler(20, warmup_steps=5, base_lr=0.3, final_lr=0.01)
d2l.plot(torch.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_1dfeb6_98_0.svg
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\diilbookstyleinputcell
.. code:: python
net = net_fn()
lr_list = mindspore.Tensor([scheduler(t) for t in range(num_epochs) for i in range(steps_per_epoch)])
trainer = nn.SGD(net.trainable_params(), lr_list)
train(net, train_iter, test_iter, num_epochs, loss, trainer)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.201, train acc 0.926, test acc 0.898
.. figure:: output_lr-scheduler_1dfeb6_104_1.svg
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\diilbookstyleinputcell
.. code:: python
net = net_fn()
trainer = torch.optim.SGD(net.parameters(), lr=0.3)
train(net, train_iter, test_iter, num_epochs, loss, trainer, device,
scheduler)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.181, train acc 0.933, test acc 0.900
.. figure:: output_lr-scheduler_1dfeb6_107_1.svg
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`讨论 `__
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`讨论 `__
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