code: def test_multitask_gp_mean_abs_error(self):
      likelihood = GaussianLikelihood(
          noise_prior=SmoothedBoxPrior(-6, 6)
      )
      gp_model = HadamardMultitaskGPModel(
          (
              torch.cat([train_x, train_x]),
              torch.cat([y1_inds, y2_inds]),
          ),
          torch.cat([train_y1, train_y2]),
          likelihood,
      )
      mll = gpytorch.mlls.ExactMarginalLogLikelihood(
          likelihood, gp_model
      )
  
      # Optimize the model
      gp_model.train()
      likelihood.eval()
      optimizer = optim.Adam(gp_model.parameters(), lr=0.01)
      for _ in range(100):
          optimizer.zero_grad()
          output = gp_model(
              torch.cat([train_x, train_x]),
              torch.cat([y1_inds, y2_inds]),
          )
          loss = -mll(output, torch.cat([train_y1, train_y2]))
          loss.backward()
          optimizer.step()
  
          for param in gp_model.parameters():
              self.assertTrue(param.grad is not None)
              self.assertGreater(param.grad.norm().item(), 0)
  
      # Test the model
      gp_model.eval()
      likelihood.eval()
      test_preds_task_1 = likelihood(
          gp_model(test_x, y1_inds_test)
      ).mean
      mean_abs_error_task_1 = torch.mean(
          torch.abs(test_y1 - test_preds_task_1)
      )
  
      self.assertLess(mean_abs_error_task_1.item(), 0.1)
  
      test_preds_task_2 = likelihood(
          gp_model(test_x, y2_inds_test)
      ).mean
      mean_abs_error_task_2 = torch.mean(
          torch.abs(test_y2 - test_preds_task_2)
      )
  
      self.assertLess(mean_abs_error_task_2.item(), 0.1)
  
imports: import os
  import random
  import unittest
  from math import exp, pi
  import torch
  from torch import optim
  import gpytorch
  from gpytorch.distributions import MultivariateNormal
  from gpytorch.kernels import IndexKernel, RBFKernel
  from gpytorch.likelihoods import GaussianLikelihood
  from gpytorch.means import ConstantMean
  from gpytorch.priors import LKJCovariancePrior, SmoothedBoxPrior
label_desc: Use image node_id 3 for calling the TestHadamardMultitaskGPRegression obj's underlying member method code with example usage: obj.test_multitask_gp_mean_abs_error() without return types