# PolynomialDecay¶

class paddle.optimizer.lr. PolynomialDecay ( learning_rate, decay_steps, end_lr=0.0001, power=1.0, cycle=False, last_epoch=- 1, verbose=False ) [source]

Applies polynomial decay to the initial learning rate.

The algorithm can be described as following.

If cycle is set to True, then:

\begin{align}\begin{aligned}decay\_steps & = decay\_steps * math.ceil(\frac{epoch}{decay\_steps})\\new\_learning\_rate & = (learning\_rate-end\_lr)*(1-\frac{epoch}{decay\_steps})^{power}+end\_lr\end{aligned}\end{align}

If cycle is set to False, then:

\begin{align}\begin{aligned}epoch & = min(epoch, decay\_steps)\\new\_learning\_rate & = (learning\_rate-end\_lr)*(1-\frac{epoch}{decay\_steps})^{power}+end\_lr\end{aligned}\end{align}
Parameters
• learning_rate (float) – The initial learning rate. It is a python float number.

• decay_steps (int) – The decay step size. It determines the decay cycle. It must be a positive integer.

• end_lr (float, optional) – The minimum final learning rate. Default: 0.0001.

• power (float, optional) – Power of polynomial, should greater than 0.0 to get learning rate decay. Default: 1.0.

• cycle (bool, optional) – Whether the learning rate rises again. If True, then the learning rate will rise when it decrease to end_lr . If False, the learning rate is monotone decreasing. Default: False.

• last_epoch (int, optional) – The index of last epoch. Can be set to restart training. Default: -1, means initial learning rate.

• verbose (bool, optional) – If True, prints a message to stdout for each update. Default: False .

Returns

PolynomialDecay instance to schedule learning rate.

Examples

>>> # Example1: train on default dynamic graph mode
>>> import numpy as np

>>> # train on default dynamic graph mode
>>> scheduler = paddle.optimizer.lr.PolynomialDecay(learning_rate=0.5, decay_steps=20, verbose=True)
>>> for epoch in range(20):
...     for batch_id in range(5):
...         out = linear(x)
...         loss.backward()
...         sgd.step()
...         scheduler.step()    # If you update learning rate each step
...     # scheduler.step()        # If you update learning rate each epoch

>>> # Example2: train on static graph mode
>>> import numpy as np
...     x = paddle.static.data(name='x', shape=[None, 4, 5])
...     y = paddle.static.data(name='y', shape=[None, 4, 5])
...     scheduler = paddle.optimizer.lr.PolynomialDecay(learning_rate=0.5, decay_steps=20, verbose=True)
...     sgd.minimize(loss)
...
>>> exe.run(start_prog)
>>> for epoch in range(20):
...     for batch_id in range(5):
...         out = exe.run(
...             main_prog,
...             feed={
...                 'x': np.random.randn(3, 4, 5).astype('float32'),
...                 'y': np.random.randn(3, 4, 5).astype('float32')
...             },
...             fetch_list=loss.name)
...         scheduler.step()    # If you update learning rate each step
...     # scheduler.step()        # If you update learning rate each epoch

get_lr ( )

For those subclass who overload LRScheduler (Base Class), User should have a custom implementation of get_lr() .

Otherwise, an NotImplementedError exception will be thrown.

set_dict ( state_dict )

set_state_dict ( state_dict )

state_dict ( )

Returns the state of the scheduler as a dict.

It is a subset of self.__dict__ .

state_keys ( )

For those subclass who overload LRScheduler (Base Class). Acquiescently, “last_epoch, last_lr” will be saved by self.keys = ['last_epoch', 'last_lr'] .

last_epoch is the current epoch num, and last_lr is the current learning rate.

If you want to change the default behavior, you should have a custom implementation of _state_keys() to redefine self.keys .

step ( epoch=None )

step should be called after optimizer.step . It will update the learning rate in optimizer according to current epoch . The new learning rate will take effect on next optimizer.step .

Parameters

epoch (int, None) – specify current epoch. Default: None. Auto-increment from last_epoch=-1.

Returns

None

Examples

>>> import paddle
>>> a = paddle.reshape(value, [2, 13])
...                             parameters = linear.parameters())
>>> out = linear(a)
>>> out.backward()

>>> import paddle