I already find the example of paper in keras with code same like you. But I don’t know why my eta just keep increasing.
I give you some parameter per epoch:
epoch 1:
list loss: [ 211.6204, 283.3055,  276.5063] and eta: [5.0511, 5.0714, 5.0698]
epoch 2:
list loss: [210.646, 281.631, 275.2699] and eta: [5.2132, 5.2701, 5.2673]
epoch 3:
list loss: [ 211.3304, 282.8942, 276.3101] and eta: [5.3005, 5.4210, 5.4148]
epoch 4:
list loss: [ 211.3207, 282.6045, 276.2361] and eta: [5.3320, 5.5211, 5.5101]

If I don’t think wrong. the loss_1 =  torch.Tensor(loss) * torch.exp(-self.eta) = [3.3475, 3.4172, 3.4132]
and loss_2 = self.eta =  [5.3320, 5.5211, 5.5101]
loss_2 > loss_1 and if keep increase eta, the loss_2 is still greater more than loss _1. But why me eta still increase.
my code when compute loss:
self.eta = nn.Parameter(torch.Tensor(cf['eta']))
loss_combine = torch.cuda.FloatTensor([loss_1.sum(), loss_2.sum(), loss_3.sum()]) * torch.exp(-self.eta) + self.eta
#                 print("loss combine: ", loss_combine)
                loss_combine = loss_combine.sum()
return loss_combine

And 1 question about the solution: Approx. optimal weights mention in paper table 5. Does it use the sum weighted loss, mean i use grid search to choose the weighted for each loss and summarize like 1/2 * loss_1 + 1/3 * loss_2 + 1/5 * loss_3 ? Is it right?
And 1 question about the reason, why loss don’t in the same scale make the total loss uniform make the 1 task can converge and 2 task not converging. In my case, if i use simple loss sum uniform, loss_1 after 200 epoch approxi 0.5, loss_2 approxi 1.2, and loss 3 greate then 7. I try to search paper or more keyword but not have.
Thank you