Source code for torch.optim.nadam
# mypy: allow-untyped-decorators
# mypy: allow-untyped-defs
r"""Implementation for the NAdam algorithm."""
from typing import cast, List, Optional, Tuple, Union
import torch
from torch import Tensor
from .optimizer import (
_capturable_doc,
_default_to_fused_or_foreach,
_differentiable_doc,
_disable_dynamo_if_unsupported,
_foreach_doc,
_get_capturable_supported_devices,
_get_scalar_dtype,
_get_value,
_maximize_doc,
_stack_if_compiling,
_use_grad_for_differentiable,
_view_as_real,
Optimizer,
ParamsT,
)
__all__ = ["NAdam", "nadam"]
[docs]class NAdam(Optimizer): # noqa: D101
def __init__(
self,
params: ParamsT,
lr: Union[float, Tensor] = 2e-3,
betas: Tuple[float, float] = (0.9, 0.999),
eps: float = 1e-8,
weight_decay: float = 0,
momentum_decay: float = 4e-3,
decoupled_weight_decay: bool = False,
*,
foreach: Optional[bool] = None,
maximize: bool = False,
capturable: bool = False,
differentiable: bool = False,
): # noqa: D107
if isinstance(lr, Tensor) and lr.numel() != 1:
raise ValueError("Tensor lr must be 1-element")
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,
maximize=maximize,
foreach=foreach,
capturable=capturable,
differentiable=differentiable,
)
super().__init__(params, defaults)
def __setstate__(self, state): # noqa: D105
super().__setstate__(state)
for group in self.param_groups:
group.setdefault("maximize", False)
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
[docs] @_use_grad_for_differentiable
def step(self, closure=None):
"""Perform 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: List[Tensor] = []
grads: List[Tensor] = []
exp_avgs: List[Tensor] = []
exp_avg_sqs: List[Tensor] = []
mu_products: List[Tensor] = []
state_steps: List[Tensor] = []
beta1, beta2 = cast(Tuple[float, float], 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"],
maximize=group["maximize"],
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}, \:\textit{maximize} \\
&\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}\textbf{if} \: \textit{maximize}: \\
&\hspace{10mm}g_t \leftarrow -\nabla_{\theta} f_t (\theta_{t-1}) \\
&\hspace{5mm}\textbf{else} \\
&\hspace{10mm}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`_.
"""
+ rf"""
Args:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, Tensor, 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}
{_maximize_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 _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,
maximize: bool,
capturable: bool,
differentiable: bool,
has_complex: bool,
):
for i, param in enumerate(params):
grad = grads[i] if not maximize else -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:
capturable_supported_devices = _get_capturable_supported_devices()
assert (
param.device.type == mu_product.device.type == step_t.device.type
and param.device.type in capturable_supported_devices
), (
f"If capturable=True, params, mu_products and state_steps must be "
f"on supported devices: {capturable_supported_devices}."
)
# 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 - 0.5 * (0.96 ** (step * momentum_decay)))
mu_next = beta1 * (1.0 - 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 * (1.0 - mu) / (1.0 - mu_product))
exp_avg = exp_avg * (-lr * mu_next / (1.0 - 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 * (1.0 - mu) / (1.0 - _get_value(mu_product)))
)
param.addcdiv_(
exp_avg, denom, value=(-lr * mu_next) / (1.0 - 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,
maximize: 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:
capturable_supported_devices = _get_capturable_supported_devices(
supports_xla=False
)
assert all(
p.device.type == mp.device.type == step.device.type
and p.device.type in capturable_supported_devices
for p, mp, step in zip(params, mu_products, state_steps)
), f"If capturable=True, params, mu_products, and state_steps must be on supported devices: {capturable_supported_devices}."
grouped_tensors = Optimizer._group_tensors_by_device_and_dtype(
[params, grads, exp_avgs, exp_avg_sqs, mu_products, state_steps] # type: ignore[list-item]
)
for (
grouped_params_,
grouped_grads_,
grouped_exp_avgs_,
grouped_exp_avg_sqs_,
grouped_mu_products_,
grouped_state_steps_,
), _ in grouped_tensors.values():
grouped_params = cast(List[Tensor], grouped_params_)
grouped_grads = cast(List[Tensor], grouped_grads_)
grouped_exp_avgs = cast(List[Tensor], grouped_exp_avgs_)
grouped_exp_avg_sqs = cast(List[Tensor], grouped_exp_avg_sqs_)
grouped_mu_products = cast(List[Tensor], grouped_mu_products_)
grouped_state_steps = cast(List[Tensor], grouped_state_steps_)
# handle complex
if has_complex:
_view_as_real(
grouped_params, grouped_grads, grouped_exp_avgs, grouped_exp_avg_sqs
)
if maximize:
grouped_grads = torch._foreach_neg(grouped_grads) # type: ignore[assignment]
# 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 not torch._utils.is_compiling() and 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:
# Re-use the intermediate memory (grouped_grads) already allocated for maximize
if maximize:
torch._foreach_add_(
grouped_grads, grouped_params, alpha=weight_decay
)
else:
grouped_grads = torch._foreach_add( # type: ignore[assignment]
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)
bias_correction_sqrt: Union[Tuple[Tensor, ...], List[Tensor]]
mus: Union[Tuple[Tensor, ...], List[Tensor]]
mu_nexts: Union[Tuple[Tensor, ...], List[Tensor]]
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 = [
(1 - beta2 ** _get_value(step)) ** 0.5 for step in grouped_state_steps
]
mus = [
beta1 * (1.0 - 0.5 * (0.96 ** (_get_value(step) * momentum_decay)))
for step in grouped_state_steps
]
mu_nexts = [
beta1
* (1.0 - 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(
[
(_get_value(lr) * (1.0 - mu) / (1.0 - _get_value(mu_product))) * -1
for mu_product, mu in zip(grouped_mu_products, mus)
]
)
step_size_expavg = _stack_if_compiling(
[
(
_get_value(lr)
* mu_next
/ (1.0 - _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 # type: ignore[arg-type]
)
torch._foreach_addcdiv_(
grouped_params, grouped_exp_avgs, exp_avg_sq_sqrt, step_size_expavg # type: ignore[arg-type]
)
@_disable_dynamo_if_unsupported(single_tensor_fn=_single_tensor_nadam)
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,
maximize: 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,
maximize=maximize,
decoupled_weight_decay=decoupled_weight_decay,
eps=eps,
capturable=capturable,
differentiable=differentiable,
has_complex=has_complex,
)
