How do you optimize when dealing with two loss functions that have different ranges?

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When dealing with two loss functions that have different ranges, one potential approach to optimization is to normalize each loss function into a common range. This can involve scaling the values of each loss function so that they have the same maximum and minimum values, or transforming them into a standardized form (such as z-scores or percentiles).

Once the loss functions have been normalized, they can be combined into a weighted sum or some other composite function. The weights assigned to each loss function should reflect their relative importance, and can be adjusted based on expert knowledge or empirical evidence.

Finally, the composite function can be optimized using standard techniques such as gradient descent or stochastic gradient descent. During the optimization process, it may be necessary to experiment with different weightings and normalization methods in order to find the most effective approach.