Trainer batch size auto scaling
# 🚀 Feature request

Since `Trainer` handles both batch_size and gradient_accumulation_steps it seems like it could detect some out-of-memory situations and handle those scenarios automatically.

## Motivation

I've been experimenting with model search (model_type, vocab_size, num_hidden_layers, hidden_size) and it's been somewhat difficult to manage the correct batch size for each variant.   To avoid a process of trial & error and maintaining configuration tables, what I've been doing to overcome this is detecting memory exhaustion and adapting training arguments on the fly.  It's imperfect, but I wonder if there's an official way to achieve this kind of behavior.

## Your contribution

This is just a PoC, I'm sure there are several environments where this might be problematic.  In particular CPU training on Linux is quite likely to trigger the OOM killer where the entire process is simply wiped from memory.  Nevertheless, this strategy seems helpful at least some of the time.

```python
class BatchAutoScaleTrainer(transformers.Trainer):
    ''' Try to detect application crashes due to CUDA/CPU OOMs and
        rescale batch size.  An antiprime batch_size gives best results.
        Inspired by PyTorchLightning/pytorch-lightning#1638
    '''
    def _shrink_bs(self):
        # GAS is used by both .train() and .eval() and we need to find a
        # suitable setting for both
        tbs = self.args.per_device_train_batch_size
        ebs = self.args.per_device_eval_batch_size
        gas = self.args.gradient_accumulation_steps
        for i in range(gas + 1, min(tbs, ebs) + 1):
            if tbs % i or ebs % i:
                continue
            self.args.per_device_train_batch_size = (tbs * gas) // i
            self.args.per_device_eval_batch_size = (ebs * gas) // i
            self.args.gradient_accumulation_steps = i
            return True
        return False
    def _is_oom(self, err):
        # shamelessly stolen from https://github.com/PyTorchLightning/pytorch-lightning/pull/1638/files#diff-5200c11792b86d6a07ea64820e126897aa2e3b7d3d295c92c19b141de6950afeR29-R32
        return len(err.args) == 1 and (
            "CUDA out of memory." in err.args[0]
         or "cuDNN error: CUDNN_STATUS_NOT_SUPPORTED." in err.args[0]
         or "DefaultCPUAllocator: can't allocate memory" in err.args[0]
         or "CUDA error: CUBLAS_STATUS_ALLOC_FAILED " in err.args[0]
        )
    def _auto_scale_batch_size(self, code):
        while True:
            try:
                gc.collect()
                if torch.cuda.is_available():
                    torch.cuda.empty_cache()
                return code()
            except RuntimeError as err:
                if self._is_oom(err) and self._shrink_bs():
                    continue
                raise
            assert(False) # bug in _shrink_bs() most likely
    def train(self, *args, **kwds):
        train = super().train
        return self._auto_scale_batch_size(
            lambda: train(*args, **kwds))
    def evaluate(self, *args, **kwds):
        evaluate = super().evaluate
        return self._auto_scale_batch_size(
            lambda: evaluate(*args, **kwds))
```

Any chance something like this might be integrated with the Trainer?
I am very nervous about adding that kind of feature of auto scaling to the Trainer. Note that the `_is_oom` test for instance will catch way more CUDA errors than the OOM: haivng the wrong number of labels in your model will trigger an error with  `CUBLAS_STATUS_ALLOC_FAILED` on most environments.

In a notebook, the kernel is in an unrecoverable state after the `try`/`except` (and `torch.cuda.empty_cache()` does not help), so this wouldn't work either.

So for now, my sense is that such a feature would be more painful for the user than beneficial and I would leave the tuning of the batch size to the user.
<|||||>Thanks very much for the feedback!<|||||>Perhaps instead of shrinking batch_size, it could work the other direction.  If gradient_accumulation_steps is > 1, the first few steps could monitor the memory footprint and combine steps when the system sees there is enough capacity.  Is that similarly dangerous?

Again, a very rough PoC just to illustrate the behavior:
```python
class BatchAutoScaleTrainer(transformers.Trainer):
    def __init__(self, *args, **kwds):
        self._should_study = True
        super().__init__(*args, **kwds)
        self.mini_bs = self.args.n_gpu
    def _minibatch(self, bs, mbs, batch):
        kl = batch.keys()
        return (dict(zip(kl,
            (_[i:i+mbs] for _ in batch.values()),
        )) for i in range(0, bs, mbs))
    def _ministudy(self, bs, mbs):
        if mbs < bs:
            for i in range(mbs + 1, bs + 1):
                if bs % i == 0:
                    nbs = i
                    break
            d = torch.device
            est = torch.cuda.memory_reserved(d) / mbs * nbs
            if est < torch.cuda.get_device_properties(d).total_memory:
                self.mini_bs = nbs
                return
        transformers.trainer.logger.info(f'{__class__.__name__}: mini_bs={nbs}')
        self._should_study = False
    def training_step(self, model, inputs):
        bs = len(next(iter(inputs.values())))
        mbs = min(bs, self.mini_bs)
        segs = bs // mbs
        ts = super().training_step
        loss = torch.stack(tuple(
            ts(model, batch)
            for batch in self._minibatch(bs, mbs, inputs)
        )).mean()
        if self._should_study:
            self._ministudy(bs, mbs)
        return loss
    def prediction_step(self, model, inputs, prediction_loss_only, ignore_keys):
        bs = len(next(iter(inputs.values())))
        mbs = self.mini_bs
        segs = bs // mbs
        ps = super().prediction_step
        loss, logits, labels = zip(*(
            ps(model, batch, prediction_loss_only, ignore_keys)
            for batch in self._minibatch(bs, mbs, inputs)
        ))
        if prediction_loss_only:
            return (torch.stack(loss).mean(), None, None)
        return (torch.stack(loss).mean(), torch.cat(logits), torch.cat(labels))
```<|||||>This issue has been automatically marked as stale because it has not had recent activity. If you think this still needs to be addressed please comment on this thread.

Please note that issues that do not follow the [contributing guidelines](https://github.com/huggingface/transformers/blob/master/CONTRIBUTING.md) are likely to be ignored.<|||||>Maybe of interest to you @tlby https://github.com/rentruewang/koila<|||||>@LysandreJik Indeed, thanks for the note.  rentruewang/koila#12 is a hopeful sign.