Pytorch：如何针对多重损失优化多个变量？

Question

我希望根据不同的变量计算不同的损失的梯度，然后将这些变量全部结合起来。

这是一个演示我想要的东西的简单示例：

import torch as T
x = T.randn(3, requires_grad = True)
y = T.randn(4, requires_grad = True)
z = T.randn(5, requires_grad = True)

x_opt = T.optim.Adadelta([x])
y_opt = T.optim.Adadelta([y])
z_opt = T.optim.Adadelta([z])

for i in range(n_iter):
  x_opt.zero_grad()
  y_opt.zero_grad()
  z_opt.zero_grad()

  shared_computation = foobar(x, y, z)

  x_loss = f(x, y, z, shared_computation)
  y_loss = g(x, y, z, shared_computation)
  z_loss = h(x, y, z, shared_computation)

  x_loss.backward_with_respect_to(x)
  y_loss.backward_with_respect_to(y)
  z_loss.backward_with_respect_to(z)

  x_opt.step()
  y_opt.step()
  z_opt.step()

我的问题是我们如何在 PyTorch 中完成 backward_with_respect_to 部分？我只想要 x 的渐变 w.r.t。 x_loss，等等。然后我希望所有优化器一起执行（基于 x、y 和 z 的当前值）。

Answer 1

我已经编写了一个函数来执行此操作。两个关键组成部分是 (1) 除了对 .backward() 的最终调用之外的所有调用都使用 retain_graph=True 和 (2) 在每次调用 .backward() 后保存梯度，并在 .backward() 之前的最后恢复它们=15=]ing.

def multi_step(losses, optms):
  # optimizers each take a step, with `optms[i]`'s variables being 
  # optimized w.r.t. `losses[i]`.
  grads = [None]*len(losses)
  for i, (loss, optm) in enumerate(zip(losses, optms)):
    retain_graph = i != (len(losses)-1)
    optm.zero_grad()
    loss.backward(retain_graph=retain_graph)
    grads[i] = [ 
          [ 
            p.grad+0 for p in group['params'] 
          ] for group in optm.param_groups
        ]
  for optm, grad in zip(optms, grads):
    for p_group, g_group in zip(optm.param_groups, grad):
      for p, g in zip(p_group['params'], g_group):
        p.grad = g
    optm.step()

在问题中陈述的示例代码中，multi_step 将按如下方式使用：

for i in range(n_iter):
  shared_computation = foobar(x, y, z)

  x_loss = f(x, y, z, shared_computation)
  y_loss = g(x, y, z, shared_computation)
  z_loss = h(x, y, z, shared_computation)

  multi_step([x_loss, y_loss, z_loss], [x_opt, y_opt, z_opt])

Pytorch：如何针对多重损失优化多个变量？

Pytorch: How to optimize multiple variables with respect to multiple losses?

optimization

pytorch

autograd