How do I use loss instead of accuracy in the formula?

Question

The below function is applied as a filtering procedure for a set of clients that are represented by accuracy values.

where accuracy is used to measure the model’s performance.

So, my question is: If I use loss instead of accuracy in the above formula, should I keep the same formula or something should change since:

Accuracy can be seen as the count of mistakes/misclassifications you made on the data. The larger the accuracy, the fewer misclassifications you made on the data.

Loss can be seen as a distance between the true values of the problem and the values predicted by the model. The larger the loss, the larger the errors you made on the data.

reference resource

Answer 1

The link you provided to the paper links to a paywalled article and is therefore not accessible for everyone. But the paper mentions the following:

The filtering mechanism verifies whether the performance of the client ∈ 𝐶 is lower or equal the mean performance, given by the following equation

So the formula simply checks if the performance is better than the mean performance, where they use accuracy as a performance measure. You can most likely swap accuracy for any other performance measure and only select the clients that perform better than average.