!pip install d2l==0.17.6


%matplotlib inline
import torch
from d2l import torch as d2l

eta = 0.4
def f_2d(x1, x2):
    return 0.1 * x1 ** 2 + 2 * x2 ** 2
def gd_2d(x1, x2, s1, s2):
    return (x1 - eta * 0.2 * x1, x2 - eta * 4 * x2, 0, 0)

d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))

eta = 0.6
d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))

def momentum_2d(x1, x2, v1, v2):
    v1 = beta * v1 + 0.2 * x1
    v2 = beta * v2 + 4 * x2
    return x1 - eta * v1, x2 - eta * v2, v1, v2

eta, beta = 0.6, 0.5
d2l.show_trace_2d(f_2d, d2l.train_2d(momentum_2d))

eta, beta = 0.6, 0.25
d2l.show_trace_2d(f_2d, d2l.train_2d(momentum_2d))

d2l.set_figsize()
betas = [0.95, 0.9, 0.6, 0]
for beta in betas:
    x = torch.arange(40).detach().numpy()
    d2l.plt.plot(x, beta ** x, label=f'beta = {beta:.2f}')
d2l.plt.xlabel('time')
d2l.plt.legend();

def init_momentum_states(feature_dim):
    v_w = torch.zeros((feature_dim, 1))
    v_b = torch.zeros(1)
    return (v_w, v_b)

def sgd_momentum(params, states, hyperparams):
    for p, v in zip(params, states):
        with torch.no_grad():
            v[:] = hyperparams['momentum'] * v + p.grad
            p[:] -= hyperparams['lr'] * v
        p.grad.data.zero_()

def train_momentum(lr, momentum, num_epochs=2):
    d2l.train_ch11(sgd_momentum, init_momentum_states(feature_dim),
                   {'lr': lr, 'momentum': momentum}, data_iter,
                   feature_dim, num_epochs)

data_iter, feature_dim = d2l.get_data_ch11(batch_size=10)
train_momentum(0.02, 0.5)

train_momentum(0.01, 0.9)

train_momentum(0.005, 0.9)

trainer = torch.optim.SGD
d2l.train_concise_ch11(trainer, {'lr': 0.005, 'momentum': 0.9}, data_iter)

lambdas = [0.1, 1, 10, 19]
eta = 0.1
d2l.set_figsize((6, 4))
for lam in lambdas:
    t = torch.arange(20).detach().numpy()
    d2l.plt.plot(t, (1 - eta * lam) ** t, label=f'lambda = {lam:.2f}')
d2l.plt.xlabel('time')
d2l.plt.legend();