到目前为止，我们主要关注如何更新权重向量的优化算法，而不是更新权重向量的速率。尽管如此，调整学习率通常与实际算法一样重要。有几个方面需要考虑：
-
最明显的是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，训练时间太长，或者我们最终会得到一个次优的结果。我们之前看到问题的条件编号很重要（例如，参见第 12.6 节了解详细信息）。直观地说，它是最不敏感方向的变化量与最敏感方向的变化量之比。
-
其次，衰减率同样重要。如果学习率仍然很大，我们可能最终会在最小值附近跳来跳去，因此无法达到最优。12.5 节 详细讨论了这一点，我们在12.4 节中分析了性能保证。简而言之，我们希望速率下降，但可能比O(t−12)这将是凸问题的不错选择。
-
另一个同样重要的方面是初始化。这既涉及参数的初始设置方式（详见 第 5.4 节），也涉及它们最初的演变方式。这在热身的绰号下进行，即我们最初开始朝着解决方案前进的速度。一开始的大步骤可能没有好处，特别是因为初始参数集是随机的。最初的更新方向也可能毫无意义。
-
最后，还有许多执行循环学习率调整的优化变体。这超出了本章的范围。我们建议读者查看 Izmailov等人的详细信息。( 2018 )，例如，如何通过对整个参数路径进行平均来获得更好的解决方案。
鉴于管理学习率需要很多细节，大多数深度学习框架都有自动处理这个问题的工具。在本章中，我们将回顾不同的调度对准确性的影响，并展示如何通过学习率调度器有效地管理它。
12.11.1。玩具问题
我们从一个玩具问题开始，这个问题足够简单，可以轻松计算，但又足够不平凡，可以说明一些关键方面。为此，我们选择了一个稍微现代化的 LeNet 版本（relu而不是 sigmoid激活，MaxPooling 而不是 AveragePooling）应用于 Fashion-MNIST。此外，我们混合网络以提高性能。由于大部分代码都是标准的，我们只介绍基础知识而不进行进一步的详细讨论。如有需要，请参阅第 7 节进行复习。
%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)
# The code is almost identical to `d2l.train_ch6` defined in the
# lenet section of chapter convolutional neural networks
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__:
# Using PyTorch In-Built scheduler
scheduler.step()
else:
# Using custom defined scheduler
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}')
%matplotlib inline
from mxnet import autograd, gluon, init, lr_scheduler, np, npx
from mxnet.gluon import nn
from d2l import mxnet as d2l
npx.set_np()
net = nn.HybridSequential()
net.add(nn.Conv2D(channels=6, kernel_size=5, padding=2, activation='relu'),
nn.MaxPool2D(pool_size=2, strides=2),
nn.Conv2D(channels=16, kernel_size=5, activation='relu'),
nn.MaxPool2D(pool_size=2, strides=2),
nn.Dense(120, activation='relu'),
nn.Dense(84, activation='relu'),
nn.Dense(10))
net.hybridize()
loss = gluon.loss.SoftmaxCrossEntropyLoss()
device = d2l.try_gpu()
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)
# The code is almost identical to `d2l.train_ch6` defined in the
# lenet section of chapter convolutional neural networks
def train(net, train_iter, test_iter, num_epochs, loss, trainer, device):
net.initialize(force_reinit=True, ctx=device, init=init.Xavier())
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):
X, y = X.as_in_ctx(device), y.as_in_ctx(device)
with autograd.record():
y_hat = net(X)
l = loss(y_hat, y)
l.backward()
trainer.step(X.shape[0])
metric.add(l.sum(), 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))
print(f'train loss {train_loss:.3f}, train acc {train_acc:.3f}, '
f'test acc {test_acc:.3f}')
%matplotlib inline
import math
import tensorflow as tf
from tensorflow.keras.callbacks import LearningRateScheduler
from d2l import tensorflow as d2l
def net():
return tf.keras.models.Sequential([
tf.keras.layers.Conv2D(filters=6, kernel_size=5, activation='relu',
padding='same'),
tf.keras.layers.AvgPool2D(pool_size=2, strides=2),
tf.keras.layers.Conv2D(filters=16, kernel_size=5,
activation='relu'),
tf.keras.layers.AvgPool2D(pool_size=2, strides=2),
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(120, activation='relu'),
tf.keras.layers.Dense(84, activation='sigmoid'),
tf.keras.layers.Dense(10)])
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)
# The code is almost identical to `d2l.train_ch6` defined in the
# lenet section of chapter convolutional neural networks
def train(net_fn, train_iter, test_iter, num_epochs, lr,
device=d2l.try_gpu(), custom_callback = False):
device_name =
