Fixed normalizing factor

[nthhiep]

Hi, Congratulation for your great work. I've a question. In the case that the local epoch is fixed for each user, vector ai and it's norm ||ai|| is unchanged across rounds?

For example, consider SGDMomentum-Nova, vector ai is as following: [1+m+m2+m3+...m^(ti-1), ..., 1+m, 1] where ti is the number of round's steps. When ti is fixed, ai is always equal to [1+m+m2+m3+...m^(ti-1), ..., 1+m, 1]

So, the value ||ai|| is known in advance as a certain function f(number of steps). It can be calculated once and reused for every round?

Thank you in advance for your feedback.