Ralamb optimizer (RAdam + LARS trick)

ralamb.py

class Ralamb(Optimizer):

    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, weight_decay=0):
        defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay)
        self.buffer = [[None, None, None] for ind in range(10)]
        super(Ralamb, self).__init__(params, defaults)

    def __setstate__(self, state):
        super(Ralamb, self).__setstate__(state)

    def step(self, closure=None):

        loss = None
        if closure is not None:
            loss = closure()

        for group in self.param_groups:

            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad.data.float()
                if grad.is_sparse:
                    raise RuntimeError('Ralamb does not support sparse gradients')

                p_data_fp32 = p.data.float()

                state = self.state[p]

                if len(state) == 0:
                    state['step'] = 0
                    state['exp_avg'] = torch.zeros_like(p_data_fp32)
                    state['exp_avg_sq'] = torch.zeros_like(p_data_fp32)
                else:
                    state['exp_avg'] = state['exp_avg'].type_as(p_data_fp32)
                    state['exp_avg_sq'] = state['exp_avg_sq'].type_as(p_data_fp32)

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                beta1, beta2 = group['betas']

                # Decay the first and second moment running average coefficient
                # m_t
                exp_avg.mul_(beta1).add_(1 - beta1, grad)
                # v_t
                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)

                state['step'] += 1
                buffered = self.buffer[int(state['step'] % 10)]

                if state['step'] == buffered[0]:
                    N_sma, radam_step_size = buffered[1], buffered[2]
                else:
                    buffered[0] = state['step']
                    beta2_t = beta2 ** state['step']
                    N_sma_max = 2 / (1 - beta2) - 1
                    N_sma = N_sma_max - 2 * state['step'] * beta2_t / (1 - beta2_t)
                    buffered[1] = N_sma

                    # more conservative since it's an approximated value
                    if N_sma >= 5:
                        radam_step_size = group['lr'] * math.sqrt((1 - beta2_t) * (N_sma - 4) / (N_sma_max - 4) * (N_sma - 2) / N_sma * N_sma_max / (N_sma_max - 2)) / (1 - beta1 ** state['step'])
                    else:
                        radam_step_size = group['lr'] / (1 - beta1 ** state['step'])
                    buffered[2] = radam_step_size

                if group['weight_decay'] != 0:
                    p_data_fp32.add_(-group['weight_decay'] * group['lr'], p_data_fp32)

                # more conservative since it's an approximated value
                radam_step = p_data_fp32.clone()
                if N_sma >= 5:
                    denom = exp_avg_sq.sqrt().add_(group['eps'])
                    radam_step.addcdiv_(-radam_step_size, exp_avg, denom)
                else:
                    radam_step.add_(-radam_step_size, exp_avg)

                radam_norm = radam_step.pow(2).sum().sqrt()
                weight_norm = p.data.pow(2).sum().sqrt().clamp(0, 10)
                if weight_norm == 0 or radam_norm == 0:
                    trust_ratio = 1
                else:
                    trust_ratio = weight_norm / radam_norm

                state['weight_norm'] = weight_norm
                state['adam_norm'] = radam_norm
                state['trust_ratio'] = trust_ratio

                if N_sma >= 5:
                    p_data_fp32.addcdiv_(-radam_step_size * trust_ratio, exp_avg, denom)
                else:
                    p_data_fp32.add_(-radam_step_size * trust_ratio, exp_avg)

                p.data.copy_(p_data_fp32)

        return loss

And you remove LARS from the actual base optimizer?

Yes, you take out LARS from the base optimizer.

If I get your idea correctly, you want to rescale the interpolation/update of slow weights in Lookahead based on a distance metric between the gradients of intermediate fast steps? (and suggesting the distance metric should be cosine similarity)

Yes, I suggested cosine similarity because you can picture it in your head in 2 dimensions. As you mentioned when the 'curve' is an actual curve, the similarity of the vectors is bad, therefore you have to use the normal schedule...

In 2D this is what I have in mind.

I didn't consider overshooting, but selecting alpha automatically based on the variance of the fast updates:

I did a LARS style version of Lookahead which uses the 'trust_ratio' between the norm of the fast and slow weights... and at 5 epochs you don't see such a noticeable change... but havent have the time to run it further OR with Annealing schedule. Which looks like is making a lot of difference based on the results just published by @mgrankin. Quick question, those numbers already include the change to use Mish activation?

EDIT: Quick caveat... when I am saying you can overshoot, what I mean is that you update the fast weights to overshooting and the slow weights are modified in such a way that you do not move into overshooting range.

Quick question, those numbers already include the change to use Mish activation?

No, I haven't looked into Mish yet.

@redknightlois. Hi, Thanks for the implementation. I have a question, how to save the Ralamb optimizer state_dict. There is no function for that. There is no load_state_dict function as well. Thanks

No, this was a prototype that I knocked up in a few hours time. Feel free to add those and I will update it.