pytorch/torch/optim/nadam.py

import torch
from torch import Tensor
from .optimizer import (Optimizer, _use_grad_for_differentiable, _get_value, _dispatch_sqrt,
                        _stack_if_compiling, _get_scalar_dtype, _default_to_fused_or_foreach,
                        _view_as_real, _capturable_doc, _differentiable_doc, _foreach_doc,)
from typing import List, Optional

__all__ = ['NAdam', 'nadam']

class NAdam(Optimizer):
    def __init__(self, params, lr=2e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0, momentum_decay=4e-3, decoupled_weight_decay: bool = False,
                 *, foreach: Optional[bool] = None, capturable: bool = False,
                 differentiable: bool = False):
        if not 0.0 <= lr:
            raise ValueError(f"Invalid learning rate: {lr}")
        if not 0.0 <= eps:
            raise ValueError(f"Invalid epsilon value: {eps}")
        if not 0.0 <= betas[0] < 1.0:
            raise ValueError(f"Invalid beta parameter at index 0: {betas[0]}")
        if not 0.0 <= betas[1] < 1.0:
            raise ValueError(f"Invalid beta parameter at index 1: {betas[1]}")
        if not 0.0 <= weight_decay:
            raise ValueError(f"Invalid weight_decay value: {weight_decay}")
        if not 0.0 <= momentum_decay:
            raise ValueError(f"Invalid momentum_decay value: {momentum_decay}")
        defaults = dict(lr=lr, betas=betas, eps=eps,
                        weight_decay=weight_decay, momentum_decay=momentum_decay,
                        decoupled_weight_decay=decoupled_weight_decay,
                        foreach=foreach, capturable=capturable, differentiable=differentiable)
        super().__init__(params, defaults)

    def __setstate__(self, state):
        super().__setstate__(state)
        for group in self.param_groups:
            group.setdefault('foreach', None)
            group.setdefault('capturable', False)
            group.setdefault('differentiable', False)
            group.setdefault('decoupled_weight_decay', False)
            for p in group["params"]:
                p_state = self.state.get(p, [])
                if len(p_state) != 0:
                    if not torch.is_tensor(p_state['step']):
                        step_val = float(p_state["step"])
                        p_state["step"] = (torch.tensor(step_val, dtype=_get_scalar_dtype(), device=p.device)
                                           if group['capturable'] else torch.tensor(step_val, dtype=_get_scalar_dtype()))
                    if not torch.is_tensor(p_state['mu_product']):
                        mu_prod_val = p_state["mu_product"]
                        p_state["mu_product"] = (torch.tensor(mu_prod_val, dtype=_get_scalar_dtype(), device=p.device)
                                                 if group['capturable'] else torch.tensor(mu_prod_val, dtype=_get_scalar_dtype()))


    def _init_group(self, group, params_with_grad, grads, exp_avgs, exp_avg_sqs, mu_products, state_steps):
        has_complex = False
        for p in group['params']:
            if p.grad is not None:
                has_complex |= torch.is_complex(p)
                params_with_grad.append(p)
                if p.grad.is_sparse:
                    raise RuntimeError('NAdam does not support sparse gradients')
                grads.append(p.grad)

                state = self.state[p]
                # Lazy state initialization
                if len(state) == 0:
                    # note(crcrpar): [special device hosting for step]
                    # Deliberately host `step` and `mu_product` on CPU if capturable is False.
                    # This is because kernel launches are costly on CUDA and XLA.
                    state['step'] = (
                        torch.zeros((), dtype=_get_scalar_dtype(), device=p.device)
                        if group['capturable'] else torch.tensor(0.0, dtype=_get_scalar_dtype())
                    )
                    state['mu_product'] = (
                        torch.ones((), dtype=_get_scalar_dtype(), device=p.device)
                        if group['capturable'] else torch.tensor(1.0, dtype=_get_scalar_dtype())
                    )
                    # Exponential moving average of gradient values
                    state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)

                exp_avgs.append(state['exp_avg'])
                exp_avg_sqs.append(state['exp_avg_sq'])
                mu_products.append(state['mu_product'])
                state_steps.append(state['step'])
        return has_complex

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

        Args:
            closure (Callable, optional): A closure that reevaluates the model
                and returns the loss.
        """
        self._cuda_graph_capture_health_check()

        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            params_with_grad = []
            grads = []
            exp_avgs = []
            exp_avg_sqs = []
            mu_products = []
            state_steps = []
            beta1, beta2 = group['betas']

            has_complex = self._init_group(group, params_with_grad, grads, exp_avgs, exp_avg_sqs, mu_products, state_steps)

            nadam(params_with_grad,
                  grads,
                  exp_avgs,
                  exp_avg_sqs,
                  mu_products,
                  state_steps,
                  beta1=beta1,
                  beta2=beta2,
                  lr=group['lr'],
                  weight_decay=group['weight_decay'],
                  momentum_decay=group['momentum_decay'],
                  eps=group['eps'],
                  decoupled_weight_decay=group['decoupled_weight_decay'],
                  foreach=group['foreach'],
                  capturable=group['capturable'],
                  differentiable=group['differentiable'],
                  has_complex=has_complex)

        return loss

NAdam.__doc__ = r"""Implements NAdam algorithm.

    .. math::
       \begin{aligned}
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{input}      : \gamma_t \text{ (lr)}, \: \beta_1,\beta_2 \text{ (betas)},
                \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)}                   \\
            &\hspace{13mm} \: \lambda \text{ (weight decay)}, \:\psi \text{ (momentum decay)}    \\
            &\hspace{13mm} \: \textit{decoupled\_weight\_decay}                                  \\
            &\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
                v_0 \leftarrow 0 \text{ ( second moment)}                                 \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                                 \\
            &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do}                         \\
            &\hspace{5mm}g_t           \leftarrow   \nabla_{\theta} f_t (\theta_{t-1})           \\
            &\hspace{5mm} \theta_t \leftarrow \theta_{t-1}                                       \\
            &\hspace{5mm} \textbf{if} \: \lambda \neq 0                                          \\
            &\hspace{10mm}\textbf{if} \: \textit{decoupled\_weight\_decay}                       \\
            &\hspace{15mm} \theta_t \leftarrow \theta_{t-1} - \gamma \lambda \theta_{t-1}                    \\
            &\hspace{10mm}\textbf{else}                                                          \\
            &\hspace{15mm} g_t \leftarrow g_t + \lambda \theta_{t-1}                             \\
            &\hspace{5mm} \mu_t \leftarrow \beta_1 \big(1 - \frac{1}{2}  0.96^{t \psi} \big)     \\
            &\hspace{5mm} \mu_{t+1} \leftarrow \beta_1 \big(1 - \frac{1}{2} 0.96^{(t+1)\psi}\big)\\
            &\hspace{5mm}m_t           \leftarrow   \beta_1 m_{t-1} + (1 - \beta_1) g_t          \\
            &\hspace{5mm}v_t           \leftarrow   \beta_2 v_{t-1} + (1-\beta_2) g^2_t          \\
            &\hspace{5mm}\widehat{m_t} \leftarrow \mu_{t+1} m_t/(1-\prod_{i=1}^{t+1}\mu_i)\\[-1.ex]
            & \hspace{11mm} + (1-\mu_t) g_t /(1-\prod_{i=1}^{t} \mu_{i})                         \\
            &\hspace{5mm}\widehat{v_t} \leftarrow   v_t/\big(1-\beta_2^t \big)                   \\
            &\hspace{5mm}\theta_t \leftarrow \theta_t - \gamma \widehat{m_t}/
                \big(\sqrt{\widehat{v_t}} + \epsilon \big)                                       \\
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
            &\bf{return} \:  \theta_t                                                     \\[-1.ex]
            &\rule{110mm}{0.4pt}                                                          \\[-1.ex]
       \end{aligned}

    For further details regarding the algorithm we refer to `Incorporating Nesterov Momentum into Adam`_.
    """ + fr"""
    Args:
        params (iterable): iterable of parameters to optimize or dicts defining
            parameter groups
        lr (float, optional): learning rate (default: 2e-3)
        betas (Tuple[float, float], optional): coefficients used for computing
            running averages of gradient and its square (default: (0.9, 0.999))
        eps (float, optional): term added to the denominator to improve
            numerical stability (default: 1e-8)
        weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
        momentum_decay (float, optional): momentum momentum_decay (default: 4e-3)
        decoupled_weight_decay (bool, optional): whether to use decoupled weight
            decay as in AdamW to obtain NAdamW (default: False)
        {_foreach_doc}
        {_capturable_doc}
        {_differentiable_doc}

    .. _Incorporating Nesterov Momentum into Adam:
        https://openreview.net/forum?id=OM0jvwB8jIp57ZJjtNEZ
    .. _Decoupled Weight Decay Regularization:
        https://arxiv.org/abs/1711.05101

    """


def nadam(params: List[Tensor],
          grads: List[Tensor],
          exp_avgs: List[Tensor],
          exp_avg_sqs: List[Tensor],
          mu_products: List[Tensor],
          state_steps: List[Tensor],
          # kwonly args with defaults are not supported by functions compiled with torchscript issue #70627
          # setting this as kwarg for now as functional API is compiled by torch/distributed/optim
          decoupled_weight_decay: bool = False,
          foreach: Optional[bool] = None,
          capturable: bool = False,
          differentiable: bool = False,
          has_complex: bool = False,
          *,
          beta1: float,
          beta2: float,
          lr: float,
          weight_decay: float,
          momentum_decay: float,
          eps: float):
    r"""Functional API that performs NAdam algorithm computation.

    See :class:`~torch.optim.NAdam` for details.
    """


    if not all(isinstance(t, torch.Tensor) for t in state_steps):
        raise RuntimeError("API has changed, `state_steps` argument must contain a list of singleton tensors")

    if not all(isinstance(t, torch.Tensor) for t in mu_products):
        raise RuntimeError("API has changed, `mu_products` argument must contain a list of singleton tensors")

    if foreach is None:
        _, foreach = _default_to_fused_or_foreach(params, differentiable, use_fused=False)

    if foreach and torch.jit.is_scripting():
        raise RuntimeError('torch.jit.script not supported with foreach optimizers')

    if foreach and not torch.jit.is_scripting():
        func = _multi_tensor_nadam
    else:
        func = _single_tensor_nadam

    func(params,
         grads,
         exp_avgs,
         exp_avg_sqs,
         mu_products,
         state_steps,
         beta1=beta1,
         beta2=beta2,
         lr=lr,
         weight_decay=weight_decay,
         momentum_decay=momentum_decay,
         decoupled_weight_decay=decoupled_weight_decay,
         eps=eps,
         capturable=capturable,
         differentiable=differentiable,
         has_complex=has_complex)


def _single_tensor_nadam(params: List[Tensor],
                         grads: List[Tensor],
                         exp_avgs: List[Tensor],
                         exp_avg_sqs: List[Tensor],
                         mu_products: List[Tensor],
                         state_steps: List[Tensor],
                         *,
                         beta1: float,
                         beta2: float,
                         lr: float,
                         weight_decay: float,
                         momentum_decay: float,
                         eps: float,
                         decoupled_weight_decay: bool,
                         capturable: bool,
                         differentiable: bool,
                         has_complex: bool):

    for i, param in enumerate(params):
        grad = grads[i]
        exp_avg = exp_avgs[i]
        exp_avg_sq = exp_avg_sqs[i]
        mu_product = mu_products[i]
        step_t = state_steps[i]

        if torch.is_complex(param):
            param = torch.view_as_real(param)
            grad = torch.view_as_real(grad)
            exp_avg = torch.view_as_real(exp_avg)
            exp_avg_sq = torch.view_as_real(exp_avg_sq)

        # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
        if not torch._utils.is_compiling() and capturable:
            assert (
                (param.is_cuda and mu_product.is_cuda and step_t.is_cuda) or (param.is_xla and mu_product.is_xla and step_t.is_xla)
            ), "If capturable=True, params, mu_products, and state_steps must be CUDA or XLA tensors."

        # update step
        step_t += 1

        if capturable:
            step = step_t
        else:
            step = _get_value(step_t)

        bias_correction2 = 1 - beta2 ** step

        if weight_decay != 0:
            if decoupled_weight_decay:
                # Perform stepweight decay
                param.mul_(1 - lr * weight_decay)
            else:
                grad = grad.add(param, alpha=weight_decay)

        # calculate the momentum cache \mu^{t} and \mu^{t+1}
        mu = beta1 * (1. - 0.5 * (0.96 ** (step * momentum_decay)))
        mu_next = beta1 * (1. - 0.5 * (0.96 ** ((step + 1) * momentum_decay)))

        # update mu_product
        mu_product *= mu

        # decay the first and second moment running average coefficient
        exp_avg.lerp_(grad, 1 - beta1)
        exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
        denom = exp_avg_sq.div(bias_correction2).sqrt()

        if differentiable or capturable:
            denom = denom.add(eps)
            # Make autograd track the operations
            # by updating the grad and exp_avg directly and not using the
            # scalar "value" argument of addcdiv.
            mu_product_next = mu_product * mu_next
            grad = grad * (-lr * (1. - mu) / (1. - mu_product))
            exp_avg = exp_avg * (-lr * mu_next / (1. - mu_product_next))
            param.addcdiv_(grad, denom)
            param.addcdiv_(exp_avg, denom)
        else:
            mu_product_next = _get_value(mu_product) * mu_next
            denom.add_(eps)
            param.addcdiv_(grad, denom, value=(-lr * (1. - mu) / (1. - _get_value(mu_product))))
            param.addcdiv_(exp_avg, denom, value=(-lr * mu_next) / (1. - mu_product_next))


def _multi_tensor_nadam(params: List[Tensor],
                        grads: List[Tensor],
                        exp_avgs: List[Tensor],
                        exp_avg_sqs: List[Tensor],
                        mu_products: List[Tensor],
                        state_steps: List[Tensor],
                        *,
                        beta1: float,
                        beta2: float,
                        lr: float,
                        weight_decay: float,
                        momentum_decay: float,
                        eps: float,
                        decoupled_weight_decay: bool,
                        capturable: bool,
                        differentiable: bool,
                        has_complex: bool):

    if len(params) == 0:
        return

    assert not differentiable, "_foreach ops don't support autograd"

    # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable]
    if not torch._utils.is_compiling() and capturable:
        assert all(p.is_cuda and mp.is_cuda and step.is_cuda
                   for p, mp, step in zip(params, mu_products, state_steps)), \
            "If capturable=True, params, mu_products, and state_steps must be CUDA tensors."


    grouped_tensors = Optimizer._group_tensors_by_device_and_dtype([params, grads, exp_avgs, exp_avg_sqs, mu_products, state_steps])
    for ((grouped_params, grouped_grads, grouped_exp_avgs,
         grouped_exp_avg_sqs, grouped_mu_products, grouped_state_steps), _) in grouped_tensors.values():

        # handle complex
        if has_complex:
            _view_as_real(grouped_params, grouped_grads, grouped_exp_avgs, grouped_exp_avg_sqs)

        # Update steps
        # If steps are on CPU, foreach will fall back to the slow path, which is a for-loop calling t.add(1) over
        # and over. 1 will then be wrapped into a Tensor over and over again, which is slower than if we just
        # wrapped it once now. The alpha is required to assure we go to the right overload.
        if grouped_state_steps[0].is_cpu:
            torch._foreach_add_(grouped_state_steps, torch.tensor(1.0, device='cpu'), alpha=1.0)
        else:
            torch._foreach_add_(grouped_state_steps, 1)

        if weight_decay != 0:
            if decoupled_weight_decay:
                # Perform stepweight decay
                torch._foreach_mul_(grouped_params, 1 - lr * weight_decay)
            else:
                grouped_grads = torch._foreach_add(grouped_grads, grouped_params, alpha=weight_decay)

        # Decay the first and second moment running average coefficient
        torch._foreach_lerp_(grouped_exp_avgs, grouped_grads, 1 - beta1)

        torch._foreach_mul_(grouped_exp_avg_sqs, beta2)
        torch._foreach_addcmul_(grouped_exp_avg_sqs, grouped_grads, grouped_grads, 1 - beta2)

        exp_avg_sq_sqrt = torch._foreach_sqrt(grouped_exp_avg_sqs)

        if capturable:
            # mus will be beta1 * (1 - 0.5 * 0.96 ** (step * momentum_decay))
            exponent = torch._foreach_mul(grouped_state_steps, momentum_decay)
            mus = torch._foreach_pow(0.96, exponent)
            torch._foreach_mul_(mus, -0.5)
            torch._foreach_add_(mus, 1.0)
            torch._foreach_mul_(mus, beta1)

            # mu_nexts will be beta1 * (1 - 0.5 * 0.96 ** ((step + 1) * momentum_decay))
            torch._foreach_add_(exponent, momentum_decay)
            mu_nexts = torch._foreach_pow(0.96, exponent)
            torch._foreach_mul_(mu_nexts, -0.5)
            torch._foreach_add_(mu_nexts, 1.0)
            torch._foreach_mul_(mu_nexts, beta1)

            # save peak memory as we don't need exponent anymore
            del exponent

            bias_correction_sqrt = torch._foreach_pow(beta2, grouped_state_steps)
            # foreach_sub doesn't allow a scalar as the first arg
            torch._foreach_sub_(bias_correction_sqrt, 1.0)
            torch._foreach_neg_(bias_correction_sqrt)
            torch._foreach_sqrt_(bias_correction_sqrt)
        else:
            bias_correction_sqrt = [_dispatch_sqrt(1 - beta2 ** _get_value(step)) for step in grouped_state_steps]
            mus = [beta1 * (1. - 0.5 * (0.96 ** (_get_value(step) * momentum_decay))) for step in grouped_state_steps]
            mu_nexts = [beta1 * (1. - 0.5 * (0.96 ** ((_get_value(step) + 1) * momentum_decay)))
                        for step in grouped_state_steps]

        # update mu_products
        torch._foreach_mul_(grouped_mu_products, mus)

        torch._foreach_div_(exp_avg_sq_sqrt, bias_correction_sqrt)
        torch._foreach_add_(exp_avg_sq_sqrt, eps)

        # explicitly delete bias_correction refs to save memory
        del bias_correction_sqrt

        if capturable:
            # Build up the step_size multiplier for grad, reusing mus' memory
            torch._foreach_sub_(mus, 1.0)
            torch._foreach_mul_(mus, lr)
            # foreach_sub doesn't allow a scalar as the first arg
            denom = torch._foreach_sub(grouped_mu_products, 1.0)
            torch._foreach_neg_(denom)
            torch._foreach_div_(mus, denom)
            # - lr * (1 - mu) / (1 - mu_product)
            step_size_grads = mus
            # explicitly delete denom to save memory
            del denom

            # Build up the step_size multiplier for exp_avg, reusing mu_nexts' memory
            denom = torch._foreach_mul(grouped_mu_products, mu_nexts)
            torch._foreach_mul_(mu_nexts, lr)
            # foreach_sub doesn't allow a scalar as the first arg, but it's okay because
            # we need a negative here anyway
            torch._foreach_sub_(denom, 1.0)
            torch._foreach_div_(mu_nexts, denom)
            # - lr * mu_next / (1 - mu_product * mu_next)
            step_size_expavg = mu_nexts
            # explicitly delete denom to save memory
            del denom

            # we cannot inplace into step_size_grads cuz it is a list of ScalarTensors
            # and mul'ing with grouped_grads will result in a list of bigger Tensors
            numerator = torch._foreach_mul(step_size_grads, grouped_grads)
            torch._foreach_addcmul_(numerator, step_size_expavg, grouped_exp_avgs)

            # finally, update params
            torch._foreach_addcdiv_(grouped_params, numerator, exp_avg_sq_sqrt)
        else:
            step_size_grads = _stack_if_compiling([(lr * (1. - mu) / (1. - _get_value(mu_product))) * -1
                                                   for mu_product, mu in zip(grouped_mu_products, mus)])
            step_size_expavg = _stack_if_compiling([(lr * mu_next / (1. - _get_value(mu_product) * mu_next)) * -1
                                                    for mu_product, mu_next in zip(grouped_mu_products, mu_nexts)])

            torch._foreach_addcdiv_(grouped_params, grouped_grads, exp_avg_sq_sqrt, step_size_grads)
            torch._foreach_addcdiv_(grouped_params, grouped_exp_avgs, exp_avg_sq_sqrt, step_size_expavg)