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- cover them in terms of code path only
- numerically, AdaScale is different on SDP/FSDP than DDP, mainly
  due to partial view of the gradients.
- this doesn't mean it is definitely not useful but it is yet to
  be validated.
- not going to spend too much time until we have a real use case.

* adding a parity unit test
* code review, better testing, use torch defaults and check for the loss, log world size

* [doc]: AdaScale example and notes

* formatted notes correctly as suggested by Benjamin

* added feature and unit test to make sure lr_scheduler works

* update the example with lr_scheduler

* fixed doc with "make html"

* addressed Mike's suggestions

Workaround PyTorch bug that casts state (pytorch/pytorch#43706).

Copied from https://github.com/pytorch/fairseq/blob/v0.9.0/fairseq/optim/fp16_optimizer.py#L251-L268