[R] loss weighting - theoretical guarantees?

For a model training on a loss function consisting of weighted losses:

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I want to know what can be said about a model that converges based on this ℒ loss in terms of the losses ℒ\_i, or perhaps the models that converge on the ℒ\_i losses seperately.For instance, if I have some guarantees / properties for models m\_i that converge to losses ℒ\_i, if some of those guarantees properties transition over to the model m that converges on …

converge function instance loss losses machinelearning terms training