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import torch | |
from torch import Tensor | |
from .optimizer import (Optimizer, _use_grad_for_differentiable, _get_value, _dispatch_sqrt, _stack_if_compiling, | |
_capturable_doc, _differentiable_doc, _foreach_doc, _default_to_fused_or_foreach, _view_as_real) | |
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) | |
state_values = list(self.state.values()) | |
step_is_tensor = (len(state_values) != 0) and torch.is_tensor(state_values[0]['step']) | |
if not step_is_tensor: | |
for s in state_values: | |
s['step'] = torch.tensor(float(s['step']), dtype=torch.float32) | |
mu_product_is_tensor = (len(state_values) != 0) and torch.is_tensor(state_values[0]['mu_product']) | |
if not mu_product_is_tensor: | |
for s in state_values: | |
s['mu_product'] = torch.tensor(s['mu_product'], dtype=torch.float32) | |
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=torch.float32, device=p.device) | |
if group['capturable'] else torch.tensor(0.0, dtype=torch.float32) | |
) | |
state['mu_product'] = ( | |
torch.ones((), dtype=torch.float32, device=p.device) | |
if group['capturable'] else torch.tensor(1.0, dtype=torch.float32) | |
) | |
# 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 | |
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) | |