lazy_adam.py

import math
import torch
from torch.optim.optimizer import Optimizer


class LazyAdam(Optimizer):

    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8):
        if not 0.0 < lr:
            raise ValueError("Invalid learning rate: {}".format(lr))
        if not 0.0 < eps:
            raise ValueError("Invalid epsilon value: {}".format(eps))
        if not 0.0 <= betas[0] < 1.0:
            raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
        if not 0.0 <= betas[1] < 1.0:
            raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))

        defaults = dict(lr=lr, betas=betas, eps=eps)
        super(LazyAdam, self).__init__(params, defaults)

    def step(self, closure=None):
        """Performs a single optimization step.

        Arguments:
            closure (callable, optional): A closure that reevaluates the model
                and returns the loss.
        """

        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

                if grad.is_sparse:
                    self.sparse_step(group, p, grad)
                else:
                    self.dense_step(group, p, grad)                

        return loss


    def sparse_step(self, group, param, grad):
        state = self.state[param]

        # State initialization
        if len(state) == 0:
            state['step'] = 0
            # Exponential moving average of gradient values
            state['exp_avg'] = torch.zeros_like(param.data)
            # Exponential moving average of squared gradient values
            state['exp_avg_sq'] = torch.zeros_like(param.data)

        state['step'] += 1

        grad = grad.coalesce()  # the update is non-linear so indices must be unique
        grad_indices = grad._indices()
        grad_values = grad._values()
        size = grad.size()

        def make_sparse(values):
            constructor = grad.new
            if grad_indices.dim() == 0 or values.dim() == 0:
                return constructor().resize_as_(grad)
            return constructor(grad_indices, values, size)

        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
        #      old <- b * old + (1 - b) * new
        # <==> old += (1 - b) * (new - old)
        old_exp_avg_values = exp_avg.sparse_mask(grad)._values()
        exp_avg_update_values = grad_values.sub(old_exp_avg_values).mul_(1 - beta1)
        exp_avg.add_(make_sparse(exp_avg_update_values))
        old_exp_avg_sq_values = exp_avg_sq.sparse_mask(grad)._values()
        exp_avg_sq_update_values = grad_values.pow(2).sub_(old_exp_avg_sq_values).mul_(1 - beta2)
        exp_avg_sq.add_(make_sparse(exp_avg_sq_update_values))

        # Dense addition again is intended, avoiding another sparse_mask
        numer = exp_avg_update_values.add_(old_exp_avg_values)
        exp_avg_sq_update_values.add_(old_exp_avg_sq_values)
        denom = exp_avg_sq_update_values.sqrt_().add_(group['eps'])
        del exp_avg_update_values, exp_avg_sq_update_values

        bias_correction1 = 1 - beta1 ** state['step']
        bias_correction2 = 1 - beta2 ** state['step']
        step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1

        param.data.add_(make_sparse(-step_size * numer.div_(denom)))

    
    def dense_step(self, group, param, grad):
        state = self.state[param]

        # State initialization
        if len(state) == 0:
            state['step'] = 0
            # Exponential moving average of gradient values
            state['exp_avg'] = torch.zeros_like(param.data)
            # Exponential moving average of squared gradient values
            state['exp_avg_sq'] = torch.zeros_like(param.data)

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

        state['step'] += 1
        bias_correction1 = 1 - beta1 ** state['step']
        bias_correction2 = 1 - beta2 ** state['step']

        # Decay the first and second moment running average coefficient
        exp_avg.mul_(beta1).add_(1 - beta1, grad)
        exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
        
        denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])

        step_size = group['lr'] / bias_correction1

        param.data.addcdiv_(-step_size, exp_avg, denom)