# How to balance different loss term?

For example,
The network has two outputs, ouput1 is from an intermedia layer and output2 is from the last layer.
And my total loss:
loss_total = loss_1 + loss_2
where loss_1 is calculated using output1 and loss_2 is calculated using output2.
Now the problem is the loss_total seems to be dominated by loss_1 , and loss_2 doesn’t play a role。
I try to put some weights on loss_1, loss_2, like:
loss_total = loss_1 * 0.001 + loss_2 *0.01
However, this is not likely to work.
Does any one has some ideals on the similar problems?

I have no idea which specific losses you are using. Anyway, the following may help solving your problem.

loss_total = alpha*loss_1 + (1-alpha)*loss_2

and finetune the hyperparameter alpha in the interval (0,1).

If you say that loss_1 dominates the total_loss, then you’ll have o choose an alpha that is closer to 0 than to 1. Maybe you can start with alpha = 0.4 and, if it still does not work, decrease it by a fixed step of 0.05 or so, until you get reasonable results.

However, before doing this cross-validation, you may wish to try training with alpha = 0, just to make sure that you can in fact minimize loss_2. There could be a bug in the definition of loss_2 and this procedure allows you to check that.

Hi @dpernes. I have met the same problem as above and appreciate your solution. And I hope the network can learn the alpha itself just like other hyperparameters of the network. But the parameters in the network are optimized by the optimizer like SGD. So how can I do to optimize the alpha automaticly ?

Hi @Pongroc.

In principle, alpha is a hyperparameter, so it is not learned by gradient-based optimization, but rather by cross-validation. (You know what cross-validation is, right?)

You may ask why is that so - and that’s precisely what I am going to try to explain. Suppose that loss_1 is typically much larger than loss_2. Then, if you try to learn alpha and the remaining parameters jointly, in such a way that the loss_total is minimized, most likely you will get a value for alpha that is very close to 0, i.e. the optimization simply removes the contribution of loss_1 to your loss_total. This does not mean, however, that loss_1 will be low - on the contrary, it will probably be high. If both loss_1 and loss_2 are measurements of how well your model behaves (in two different senses), then probably you want both to be relatively low instead of having one that is very low and the other one that is very high. The role of the hyperparameter alpha is, therefore, to weight these two losses in some way that optimizes the performance of your model, not necessarily minimizing loss_total.

If it makes it easier for you to understand, you may also think of it in the context of regularization. You usually do not learn your regularization hyperparameter together with the model parameters, do you?
Note that the usual regularized loss has a form that is very similar to the loss I proposed:

,

where is some regularization function (e.g. L-2 norm).
Dividing the RHS by a constant (independent of theta) does not change the minimizer of the function, so I may equivalently redefine the loss as:

,

which, by setting

,

has exactly the same form as the loss_total that I proposed in my first reply to this topic.
Now, note that if we set alpha to a value that is very close to 0 (or, equivalently, if we set lambda to a very large value), our loss_total will be totally dominated by the regularization term, and so we’ll get a model with a very poor performance (high bias), because it basically learns nothing related with the specific problem we are trying to solve. On the other hand, if we set alpha to a value that is very close to 1 (or, equivalently, if we set lambda to a very small value), our loss_total will be almost unregularized, and so we are likely to have a model that does not generalize well (high variance).