Strange behavior with Adam optimizer when training for too long

Question

I'm trying to train a single perceptron (1000 input units, 1 output, no hidden layers) on 64 randomly generated data points. I'm using Pytorch using the Adam optimizer:

import torch
from torch.autograd import Variable

torch.manual_seed(545345)
N, D_in, D_out = 64, 1000, 1

x = Variable(torch.randn(N, D_in))
y = Variable(torch.randn(N, D_out))

model = torch.nn.Linear(D_in, D_out)
loss_fn = torch.nn.MSELoss(size_average=False)

optimizer = torch.optim.Adam(model.parameters())
for t in xrange(5000):
  y_pred = model(x)
  loss = loss_fn(y_pred, y)

  print(t, loss.data[0])

  optimizer.zero_grad()
  loss.backward()
  optimizer.step()

Initially, the loss quickly decreases, as expected:

(0, 91.74887084960938)
(1, 76.85824584960938)
(2, 63.434078216552734)
(3, 51.46927261352539)
(4, 40.942893981933594)
(5, 31.819372177124023)

Around 300 iterations, the error reaches near zero:

(300, 2.1734419819452455e-12)
(301, 1.90354676465887e-12)
(302, 2.3347573874232808e-12)

This goes on for a few thousand iterations. However, after training for too long, the error starts to increase again:

(4997, 0.002102422062307596)
(4998, 0.0020302983466535807)
(4999, 0.0017039275262504816)

Why is this happening?