.. _sec_scheduler:
学習率スケジューリング
======================
これまで主に、重みベクトルをどのように更新するかという最適化の\ *アルゴリズム*\ に注目してきたが、更新される\ *速度*\ についてはあまり扱ってこなかった。とはいえ、学習率の調整は実際のアルゴリズムと同じくらい重要であることがよくある。考慮すべき点はいくつかある。
- まず明らかなのは、学習率の\ *大きさ*\ が重要だということである。大きすぎれば最適化は発散し、小さすぎれば学習に時間がかかりすぎるか、あるいは準最適な結果に終わってしまう。以前、問題の条件数が重要であることを見た（詳細は例えば
:numref:`sec_momentum`
を参照）。直感的には、最も感度の低い方向における変化量と、最も感度の高い方向における変化量の比である。
- 第二に、減衰の速さも同様に重要である。学習率が大きいままだと、単に最小値の周りを行ったり来たりするだけで、最適性に到達できないかもしれない。
:numref:`sec_minibatch_sgd` でこれを詳しく議論し、
:numref:`sec_sgd`
では性能保証を解析した。要するに、学習率は減衰してほしいのだが、凸問題に対しては良い選択となる
:math:`\mathcal{O}(t^{-\frac{1}{2}})`
よりはおそらくゆっくり減衰するほうがよいだろう。
- もう一つ同じくらい重要なのが\ *初期化*\ である。これは、パラメータを最初にどう設定するか（詳細は
:numref:`sec_numerical_stability`
を参照）だけでなく、初期段階でそれらがどう変化するかにも関係する。これは\ *ウォームアップ*\ という名目で扱われ、つまり最初に解へ向かってどれだけ速く動き始めるかということである。特に、初期のパラメータ設定はランダムなので、最初の大きなステップは有益でないかもしれない。初期の更新方向も、かなり無意味である可能性がある。
- 最後に、周期的に学習率を調整する最適化の変種もいくつかある。これは本章の範囲を超える。読者には
:cite:t:`Izmailov.Podoprikhin.Garipov.ea.2018`
の詳細、たとえばパラメータの全\ *経路*\ にわたって平均を取ることでより良い解を得る方法などを参照することを勧める。
学習率の管理には多くの詳細が必要であるため、ほとんどの深層学習フレームワークにはこれを自動的に扱うためのツールがある。本章では、異なるスケジュールが精度に与える影響を確認し、さらにこれを\ *学習率スケジューラ*\ によって効率的に管理する方法を示す。
おもちゃ問題
------------
まず、計算コストが低く簡単に扱える一方で、いくつかの重要な点を示すのに十分に非自明なおもちゃ問題から始める。そのために、Fashion-MNIST
に適用した LeNet の少し現代的な版（活性化関数は ``sigmoid`` ではなく
``relu``\ 、AveragePooling ではなく
MaxPooling）を用いる。さらに、性能向上のためにネットワークをハイブリダイズする。コードの大部分は標準的なので、ここでは基本だけを紹介し、詳細な議論はしない。必要に応じて
:numref:`chap_cnn` を復習されたい。
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
%matplotlib inline
from d2l import torch as d2l
import math
import torch
from torch import nn
from torch.optim import lr_scheduler
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}')
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
%matplotlib inline
from d2l import mxnet as d2l
from mxnet import autograd, gluon, init, lr_scheduler, np, npx
from mxnet.gluon import nn
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}')
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
[07:52:47] ../src/storage/storage.cc:196: Using Pooled (Naive) StorageManager for CPU
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
class SquareRootScheduler:
def __init__(self, lr=0.1):
self.lr = lr
def __call__(self, num_update):
return self.lr * pow(num_update + 1.0, -0.5)
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
%matplotlib inline
from d2l import tensorflow as d2l
import tensorflow as tf
import math
from tensorflow.keras.callbacks import LearningRateScheduler
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 = device._device_name
strategy = tf.distribute.OneDeviceStrategy(device_name)
with strategy.scope():
optimizer = tf.keras.optimizers.SGD(learning_rate=lr)
loss = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
net = net_fn()
net.compile(optimizer=optimizer, loss=loss, metrics=['accuracy'])
callback = d2l.TrainCallback(net, train_iter, test_iter, num_epochs,
device_name)
if custom_callback is False:
net.fit(train_iter, epochs=num_epochs, verbose=0,
callbacks=[callback])
else:
net.fit(train_iter, epochs=num_epochs, verbose=0,
callbacks=[callback, custom_callback])
return net
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\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 0.145, train acc 0.943, test acc 0.873
.. figure:: output_lr-scheduler_df469a_18_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
lr, num_epochs = 0.3, 30
net.initialize(force_reinit=True, ctx=device, init=init.Xavier())
trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': lr})
train(net, train_iter, test_iter, num_epochs, loss, trainer, device)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 2.303, train acc 0.099, test acc 0.100
.. figure:: output_lr-scheduler_df469a_21_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
scheduler = SquareRootScheduler(lr=0.1)
d2l.plot(d2l.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
lr, num_epochs = 0.3, 30
train(net, train_iter, test_iter, num_epochs, lr)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.216, train acc 0.919, test acc 0.891
51230.9 examples/sec on /GPU:0
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
.. figure:: output_lr-scheduler_df469a_27_2.svg
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
lr = 0.1
trainer.param_groups[0]["lr"] = lr
print(f'learning rate is now {trainer.param_groups[0]["lr"]:.2f}')
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
learning rate is now 0.10
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
trainer.set_learning_rate(0.1)
print(f'learning rate is now {trainer.learning_rate:.2f}')
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
learning rate is now 0.10
.. raw:: html
.. raw:: html
.. raw:: latex
\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(d2l.arange(50), [scheduler(t) for t in range(50)])
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
lr = 0.1
dummy_model = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
dummy_model.compile(tf.keras.optimizers.SGD(learning_rate=lr), loss='mse')
print(f'learning rate is now ,', dummy_model.optimizer.lr.numpy())
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
learning rate is now , 0.1
.. raw:: html
.. raw:: html
.. raw:: html
.. 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 0.279, train acc 0.899, test acc 0.884
.. figure:: output_lr-scheduler_df469a_52_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
trainer = gluon.Trainer(net.collect_params(), 'sgd',
{'lr_scheduler': scheduler})
train(net, train_iter, test_iter, num_epochs, loss, trainer, device)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.522, train acc 0.812, test acc 0.811
.. figure:: output_lr-scheduler_df469a_55_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
train(net, train_iter, test_iter, num_epochs, lr,
custom_callback=LearningRateScheduler(scheduler))
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.369, train acc 0.865, test acc 0.850
49886.9 examples/sec on /GPU:0
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
.. figure:: output_lr-scheduler_df469a_58_2.svg
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\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(d2l.arange(num_epochs), [get_lr(trainer, scheduler)
for t in range(num_epochs)])
.. figure:: output_lr-scheduler_df469a_66_0.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
scheduler = lr_scheduler.MultiFactorScheduler(step=[15, 30], factor=0.5,
base_lr=0.5)
d2l.plot(d2l.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_df469a_69_0.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
class MultiFactorScheduler:
def __init__(self, step, factor, base_lr):
self.step = step
self.factor = factor
self.base_lr = base_lr
def __call__(self, epoch):
if epoch in self.step:
self.base_lr = self.base_lr * self.factor
return self.base_lr
else:
return self.base_lr
scheduler = MultiFactorScheduler(step=[15, 30], factor=0.5, base_lr=0.5)
d2l.plot(d2l.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_df469a_72_0.svg
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
train(net, train_iter, test_iter, num_epochs, loss, trainer, device,
scheduler)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.186, train acc 0.929, test acc 0.887
.. figure:: output_lr-scheduler_df469a_78_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
trainer = gluon.Trainer(net.collect_params(), 'sgd',
{'lr_scheduler': scheduler})
train(net, train_iter, test_iter, num_epochs, loss, trainer, device)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.213, train acc 0.920, test acc 0.896
.. figure:: output_lr-scheduler_df469a_81_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
train(net, train_iter, test_iter, num_epochs, lr,
custom_callback=LearningRateScheduler(scheduler))
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.224, train acc 0.917, test acc 0.887
50810.6 examples/sec on /GPU:0
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
.. figure:: output_lr-scheduler_df469a_84_2.svg
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\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(d2l.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_df469a_90_0.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
scheduler = lr_scheduler.CosineScheduler(max_update=20, base_lr=0.3,
final_lr=0.01)
d2l.plot(d2l.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_df469a_93_0.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\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(d2l.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_df469a_96_0.svg
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\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)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.187, train acc 0.931, test acc 0.902
.. figure:: output_lr-scheduler_df469a_102_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
trainer = gluon.Trainer(net.collect_params(), 'sgd',
{'lr_scheduler': scheduler})
train(net, train_iter, test_iter, num_epochs, loss, trainer, device)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.345, train acc 0.877, test acc 0.868
.. figure:: output_lr-scheduler_df469a_105_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
train(net, train_iter, test_iter, num_epochs, lr,
custom_callback=LearningRateScheduler(scheduler))
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.261, train acc 0.905, test acc 0.882
50105.5 examples/sec on /GPU:0
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
.. figure:: output_lr-scheduler_df469a_108_2.svg
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
scheduler = CosineScheduler(20, warmup_steps=5, base_lr=0.3, final_lr=0.01)
d2l.plot(d2l.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_df469a_114_0.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
scheduler = lr_scheduler.CosineScheduler(20, warmup_steps=5, base_lr=0.3,
final_lr=0.01)
d2l.plot(np.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_df469a_117_0.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
scheduler = CosineScheduler(20, warmup_steps=5, base_lr=0.3, final_lr=0.01)
d2l.plot(d2l.arange(num_epochs), [scheduler(t) for t in range(num_epochs)])
.. figure:: output_lr-scheduler_df469a_120_0.svg
.. raw:: html
.. raw:: html
.. raw:: html
.. raw:: latex
\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)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.181, train acc 0.933, test acc 0.901
.. figure:: output_lr-scheduler_df469a_126_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
trainer = gluon.Trainer(net.collect_params(), 'sgd',
{'lr_scheduler': scheduler})
train(net, train_iter, test_iter, num_epochs, loss, trainer, device)
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
train loss 0.352, train acc 0.873, test acc 0.865
.. figure:: output_lr-scheduler_df469a_129_1.svg
.. raw:: html
.. raw:: html
.. raw:: latex
\diilbookstyleinputcell
.. code:: python
train(net, train_iter, test_iter, num_epochs, lr,
custom_callback=LearningRateScheduler(scheduler))
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.269, train acc 0.903, test acc 0.881
51441.5 examples/sec on /GPU:0
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
.. figure:: output_lr-scheduler_df469a_132_2.svg
.. raw:: html
.. raw:: html