Pytorch打卡第9天：10种优化器、学习率、动量

任务

• 掌握常用优化器SGD，了解10种优化器

---

知识点

基本知识

• pytorch的优化器: 管理并更新模型中可学习参数的值，使得模型输出更接近真实标签
• 导数:函数在指定坐标轴上的变化率
• 方向导数:指定方向上的变化率
• 梯度:一个向量，方向为方向导数 取得最大值的方向

基本属性

• defaults:优化器超参数
• state:参数的缓存，如momentum的缓存
• params_groups:管理的参数组
• _step_count:记录更新次数，学习率调整中使用

基本方法

import os
import torch
import torch.nn as nn
import torch.optim as optim
from tools.common_tools2 import set_seed
BASE_DIR = os.path.dirname(os.path.abspath(__file__))

set_seed(1)
weight = torch.randn((2, 2), requires_grad=True)
weight.grad = torch.ones((2, 2))
optimizer = optim.SGD([weight], lr=0.1)

• zero_grad():清空所管理参数的梯度
pytorch特性:张量梯度不自动清零

# ----------------------------------- zero_grad
# flag = 0
flag = 1
if flag:
    print("weight befor step:{}".format(weight.data))
    optimizer.step()
    print("weight after strp:{}".format(weight.data))

    print("weight in optimizer:{}\nweight in weight:{}\n".format(id(optimizer.param_groups[0]['params'][0]), id(weight)))

    print("weight.grad is {}\n".format(weight.grad))
    optimizer.zero_grad()
    print("after optimizer.zerograd(), weight.grad is\n {}".format(weight.grad))
    

输出：

weight befor step:tensor([[0.6614, 0.2669],
        [0.0617, 0.6213]])
weight after strp:tensor([[ 0.5614,  0.1669],
        [-0.0383,  0.5213]])
weight in optimizer:4384748480
weight in weight:4384748480

weight.grad is tensor([[1., 1.],
        [1., 1.]])

after optimizer.zerograd(), weight.grad is
 tensor([[0., 0.],
        [0., 0.]])

• step():执行一步更新

# ----------------------------------- step
# flag = 0
flag = 1
if flag:
    print("weight before step:{}".format(weight.data))
    optimizer.step()
    print("weight after step:{}".format(weight.data))

输出：

weight before step:tensor([[0.6614, 0.2669],
        [0.0617, 0.6213]])
weight after step:tensor([[ 0.5614,  0.1669],
        [-0.0383,  0.5213]])

• add_param_group():添加参数组

# ----------------------------------- add_param_group
# flag = 0
flag = 1
if flag:
    print("optimizer.param_groups is\n{}".format(optimizer.param_groups))
    w2 = torch.randn((3, 3), requires_grad=True)

    optimizer.add_param_group({"params": w2, 'lr': 0.0001})
    
    print("optimizer.param_groups is\n{}".format(optimizer.param_groups))
    

输出：

optimizer.param_groups is
[{'params': [tensor([[0.6614, 0.2669],
        [0.0617, 0.6213]], requires_grad=True)], 'lr': 0.1, 'momentum': 0, 'dampening': 0, 'weight_decay': 0, 'nesterov': False}]
optimizer.param_groups is
[{'params': [tensor([[0.6614, 0.2669],
        [0.0617, 0.6213]], requires_grad=True)], 'lr': 0.1, 'momentum': 0, 'dampening': 0, 'weight_decay': 0, 'nesterov': False}, {'params': [tensor([[-0.4519, -0.1661, -1.5228],
        [ 0.3817, -1.0276, -0.5631],
        [-0.8923, -0.0583, -0.1955]], requires_grad=True)], 'lr': 0.0001, 'momentum': 0, 'dampening': 0, 'weight_decay': 0, 'nesterov': False}]

• state_dict():获取优化器当前状态信息字典

# ----------------------------------- state_dict
# flag = 0
flag = 1
if flag:
    optimizer = optim.SGD([weight], lr=0.1, momentum=0.9)
    opt_state_dict = optimizer.state_dict()

    print("state_dict before step:\n", opt_state_dict)

    for i in range(10):
        optimizer.step()

    print("state_dict after step:\n", optimizer.state_dict())
    torch.save(optimizer.state_dict(), os.path.join(BASE_DIR, "optimizer_state_dict.pkl"))

输出：

state_dict before step:
 {'state': {}, 'param_groups': [{'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False, 'params': [4384027344]}]}
state_dict after step:
 {'state': {4384027344: {'momentum_buffer': tensor([[6.5132, 6.5132],
        [6.5132, 6.5132]])}}, 'param_groups': [{'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False, 'params': [4384027344]}]}

• load_state_dict() :加载状态信息字典

# -----------------------------------load state_dict
flag = 0
flag = 1
if flag:
    optimizer = optim.SGD([weight], lr=0.1, momentum=0.9)
    state_dict = torch.load(os.path.join(BASE_DIR, "optimizer_state_dict.pkl"))

    print('state_dict before load state:\n', optimizer.state_dict())
    optimizer.load_state_dict(state_dict)
    print('state_dict after load state:\n', optimizer.state_dict())
    

输出：

state_dict before load state:
 {'state': {}, 'param_groups': [{'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False, 'params': [4508197744]}]}
state_dict after load state:
 {'state': {4508197744: {'momentum_buffer': tensor([[6.5132, 6.5132],
        [6.5132, 6.5132]])}}, 'param_groups': [{'lr': 0.1, 'momentum': 0.9, 'dampening': 0, 'weight_decay': 0, 'nesterov': False, 'params': [4508197744]}]}

---

学习率

• 学习率(learning rate)控制更新的步伐
• 梯度下降: + = − ()
• + = − LR * ()

import torch
import numpy as np
import matplotlib.pyplot as plt

torch.manual_seed(1)

def func(x_t):
    return torch.pow(2 * x_t, 2)

# init
x = torch.tensor([2.], requires_grad=True)

# ------------------------------ plot data
flag = 0
# flag = 1
if flag:
    x_t = torch.linspace(-3, 3, 100)
    y = func(x_t)

    plt.plot(x_t.numpy(), y.numpy(), label='y=4*x^2')
    plt.grid()
    plt.xlabel('x')
    plt.ylabel('y')
    plt.legend()
    plt.show()

# ------------------------------ gradient descent
flag = 0
# flag = 1
if flag:
    iter_rec, loss_rec, x_rec = list(), list(), list()
    lr = 0.01
    max_iteration = 20

    for i in range(max_iteration):
        y = func(x)
        y.backward()
        print("Iter:{}, X:{:8}, X.grad:{:8}, loss:{:10}".format(
            i, x.detach().numpy()[0], x.grad.detach().numpy()[0], y.item()))

        x_rec.append(x.item())
        x.data.sub_(lr * x.grad)  # x -= x.grad  数学表达式意义:  x = x - x.grad    # 0.5 0.2 0.1 0.125
        x.grad.zero_()

        iter_rec.append(i)
        loss_rec.append(y)

    plt.subplot(121).plot(iter_rec, loss_rec, '-ro')
    plt.xlabel("Iteration")
    plt.ylabel("Loss value")

    x_t = torch.linspace(-3, 3, 100)
    y = func(x_t)
    plt.subplot(122).plot(x_t.numpy(), y.numpy(), label="y = 4*x^2")
    plt.grid()
    y_rec = [func(torch.tensor(i)).item() for i in x_rec]
    plt.subplot(122).plot(x_rec, y_rec, '-ro')
    plt.legend()
    plt.show()

# ------------------------------ multi learning rate 

# flag = 0
flag = 1
if flag:
    iteration = 100
    num_lr = 10
    lr_min, lr_max = 0.01, 0.2  # .5 .3 .2

    lr_list = np.linspace(lr_min, lr_max, num=num_lr).tolist()
    loss_rec = [[] for l in range(len(lr_list))]
    iter_rec = list()

    for i, lr in enumerate(lr_list):
        x = torch.tensor([2.], requires_grad=True)
        for iter in range(iteration):
            y = func(x)
            y.backward()
            x.data.sub_(lr * x.grad)  # x.data -= x.grad
            x.grad.zero_()

            loss_rec[i].append(y.item())

    for i, loss_r in enumerate(loss_rec):
        plt.plot(range(len(loss_r)), loss_r, label="LR: {}".format(lr_list[i]))
    plt.legend()
    plt.xlabel('Iterations')
    plt.ylabel('Loss value')
    plt.show()

---

动量 momentum

Momentum(动量，冲量)
指数加权平均: v =∗− + − ∗

# -*- coding:utf-8 -*-
"""
@brief      : 梯度下降的动量 momentum
"""
import torch
import numpy as np
import torch.optim as optim
import matplotlib.pyplot as plt
torch.manual_seed(1)


def exp_w_func(beta, time_list):
    return [(1 - beta) * np.power(beta, exp) for exp in time_list]


beta = 0.9
num_point = 100
time_list = np.arange(num_point).tolist()

# ------------------------------ exponential weight
flag = 0
# flag = 1
if flag:
    weights = exp_w_func(beta, time_list)

    plt.plot(time_list, weights, '-ro', label="Beta: {}\ny = B^t * (1-B)".format(beta))
    plt.xlabel("time")
    plt.ylabel("weight")
    plt.legend()
    plt.title("exponentially weighted average")
    plt.show()

    print(np.sum(weights))


# ------------------------------ multi weights
flag = 0
# flag = 1
if flag:
    beta_list = [0.98, 0.95, 0.9, 0.8]
    w_list = [exp_w_func(beta, time_list) for beta in beta_list]
    for i, w in enumerate(w_list):
        plt.plot(time_list, w, label="Beta: {}".format(beta_list[i]))
        plt.xlabel("time")
        plt.ylabel("weight")
    plt.legend()
    plt.show()


# ------------------------------ SGD momentum
# flag = 0
flag = 1
if flag:
    def func(x):
        return torch.pow(2*x, 2)    # y = (2x)^2 = 4*x^2        dy/dx = 8x

    iteration = 100
    m = 0.9     # .9 .63

    lr_list = [0.01, 0.03]

    momentum_list = list()
    loss_rec = [[] for l in range(len(lr_list))]
    iter_rec = list()

    for i, lr in enumerate(lr_list):
        x = torch.tensor([2.], requires_grad=True)

        momentum = 0. if lr == 0.03 else m
        momentum_list.append(momentum)

        optimizer = optim.SGD([x], lr=lr, momentum=momentum)

        for iter in range(iteration):

            y = func(x)
            y.backward()

            optimizer.step()
            optimizer.zero_grad()

            loss_rec[i].append(y.item())

    for i, loss_r in enumerate(loss_rec):
        plt.plot(range(len(loss_r)), loss_r, label="LR: {} M:{}".format(lr_list[i], momentum_list[i]))
    plt.legend()
    plt.xlabel('Iterations')
    plt.ylabel('Loss value')
    plt.show()

---

torch.optim.SGD

• 主要参数:
  • params:管理的参数组
  • lr:初始学习率
  • momentum:动量系数，贝塔
  • weight_decay:L2正则化系数
  • nesterov:是否采用NAG

pytorch的十种优化器

1. optim.SGD:随机梯度下降法
2. optim.Adagrad:自适应学习率梯度下降法 3. optim.RMSprop: Adagrad的改进
3. optim.Adadelta: Adagrad的改进
4. optim.Adam:RMSprop结合Momentum 6. optim.Adamax:Adam增加学习率上限
5. optim.SparseAdam:稀疏版的Adam
6. optim.ASGD:随机平均梯度下降
7. optim.Rprop:弹性反向传播
8. optim.LBFGS:BFGS的改进

---