from collections import defaultdict
import math
from typing import cast, List, Optional, Dict, Tuple
import torch
from torch import Tensor
from .optimizer import Optimizer, _use_grad_for_differentiable
__all__ = ['Adam', 'adam']
# TODO(crcrpar): Move this to soemwhere (e.g. torch/optim/_utils?) else when adding another fused optimizer.
# NOTE(crcrpar): Almost the same as `_MultiDeviceReplicator` defined in
# torch/cuda/amp/grad_scaler.py except for the key being str only for torch script.
class _MultiDeviceReplicator:
main_tensor: Tensor
_per_device_tensors: Dict[str, Tensor]
def __init__(self, main_tensor: Tensor) -> None:
self.main_tensor = main_tensor
self._per_device_tensors = {str(main_tensor.device): main_tensor}
def get(self, device: str):
if device in self._per_device_tensors:
return self._per_device_tensors[device]
tensor = self.main_tensor.to(device=device, non_blocking=True, copy=True)
self._per_device_tensors[device] = tensor
return tensor
# todo(crcrpar): Move this to another place when adding another fused optimizer.
def _get_fp16AMP_params(
*,
optimizer: Optimizer,
grad_scaler: Optional[torch.cuda.amp.GradScaler] = None,
device: torch.device,
) -> Optional[_MultiDeviceReplicator]:
if grad_scaler is None:
return None
found_inf_dict = grad_scaler._check_inf_per_device(optimizer)
# Combines found_inf tensors from all devices. As in GradScaler.update(),
# tensors are combined on the scale's device, which is an arbitrary but
# reasonable choice that avoids new context creation.
found_infs = [f.to(device, non_blocking=True) for f in found_inf_dict.values()]
assert len(found_infs) > 0, "No inf checks were recorded in _check_inf_per_device."
with torch.no_grad():
found_inf_combined = cast(torch.Tensor, sum(found_infs))
return _MultiDeviceReplicator(found_inf_combined)
class Adam(Optimizer):
r"""Implements Adam algorithm.
.. math::
\begin{aligned}
&\rule{110mm}{0.4pt} \\
&\textbf{input} : \gamma \text{ (lr)}, \beta_1, \beta_2
\text{ (betas)},\theta_0 \text{ (params)},f(\theta) \text{ (objective)} \\
&\hspace{13mm} \lambda \text{ (weight decay)}, \: \textit{amsgrad},
\:\textit{maximize} \\
&\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)},
v_0\leftarrow 0 \text{ (second moment)},\: \widehat{v_0}^{max}\leftarrow 0\\[-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}\textbf{if} \: \lambda \neq 0 \\
&\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\
&\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 m_t/\big(1-\beta_1^t \big) \\
&\hspace{5mm}\widehat{v_t} \leftarrow v_t/\big(1-\beta_2^t \big) \\
&\hspace{5mm}\textbf{if} \: amsgrad \\
&\hspace{10mm}\widehat{v_t}^{max} \leftarrow \mathrm{max}(\widehat{v_t}^{max},
\widehat{v_t}) \\
&\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/
\big(\sqrt{\widehat{v_t}^{max}} + \epsilon \big) \\
&\hspace{5mm}\textbf{else} \\
&\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \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 `Adam: A Method for Stochastic Optimization`_.
Args:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): learning rate (default: 1e-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)
amsgrad (bool, optional): whether to use the AMSGrad variant of this
algorithm from the paper `On the Convergence of Adam and Beyond`_
(default: False)
foreach (bool, optional): whether foreach implementation of optimizer
is used (default: None)
maximize (bool, optional): maximize the params based on the objective, instead of
minimizing (default: False)
capturable (bool, optional): whether this instance is safe to capture in a CUDA graph.
Passing True can impair ungraphed performance, so if you don't intend to
graph capture this instance, leave it False (default: False)
fused (bool, optional): whether fused implementation of optimizer is used.
Currently, `torch.float64`, `torch.float32`, `torch.float16`, and `torch.bfloat16`
are supported. (default: False)
.. _Adam\: A Method for Stochastic Optimization:
https://arxiv.org/abs/1412.6980
.. _On the Convergence of Adam and Beyond:
https://openreview.net/forum?id=ryQu7f-RZ
"""
def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
weight_decay=0, amsgrad=False, *, foreach: Optional[bool] = None,
maximize: bool = False, capturable: bool = False,
differentiable: bool = False, fused: bool = False):
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]))
if not 0.0 <= weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults = dict(lr=lr, betas=betas, eps=eps,
weight_decay=weight_decay, amsgrad=amsgrad,
maximize=maximize, foreach=foreach, capturable=capturable,
differentiable=differentiable, fused=fused)
super(Adam, self).__init__(params, defaults)
if fused:
if differentiable:
raise RuntimeError("`fused` cannot be `differentiable`")
self._step_supports_amp_scaling = True
# TODO(crcrpar): [low prec params & their higher prec copy]
# Suppor AMP with FP16/BF16 model params which would need
# higher prec copy of params to do update math in higher prec to
# alleviate the loss of information.
if not all(
p.is_cuda and torch.is_floating_point(p)
for pg in self.param_groups for p in pg['params']
):
raise RuntimeError("FusedAdam requires all the params to be CUDA, floating point")
def __setstate__(self, state):
super().__setstate__(state)
for group in self.param_groups:
group.setdefault('amsgrad', False)
group.setdefault('maximize', False)
group.setdefault('foreach', None)
group.setdefault('capturable', False)
group.setdefault('differentiable', False)
group.setdefault('fused', 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']))
@_use_grad_for_differentiable
def step(self, closure=None, *, grad_scaler=None):
"""Performs a single optimization step.
Args:
closure (Callable, optional): A closure that reevaluates the model
and returns the loss.
grad_scaler (:class:`torch.cuda.amp.GradScaler`, optional): A GradScaler which is
supplied from ``grad_scaler.step(optimizer)``.
"""
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 = []
max_exp_avg_sqs = []
state_steps = []
beta1, beta2 = group['betas']
grad_scale = None
found_inf = None
if group['fused'] and grad_scaler is not None:
grad_scale = grad_scaler._get_scale_async()
device = grad_scale.device
grad_scale = _MultiDeviceReplicator(grad_scale)
found_inf = _get_fp16AMP_params(optimizer=self, grad_scaler=grad_scaler, device=device)
for p in group['params']:
if p.grad is not None:
params_with_grad.append(p)
if p.grad.is_sparse:
raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
grads.append(p.grad)
state = self.state[p]
# Lazy state initialization
if len(state) == 0:
state['step'] = (
torch.zeros((1,), dtype=torch.float, device=p.device)
if self.defaults['capturable'] or self.defaults['fused']
else torch.tensor(0.)
)
# 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)
if group['amsgrad']:
# Maintains max of all exp. moving avg. of sq. grad. values
state['max_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'])
if group['amsgrad']:
max_exp_avg_sqs.append(state['max_exp_avg_sq'])
if group['differentiable'] and state['step'].requires_grad:
raise RuntimeError('`requires_grad` is not supported for `step` in differentiable mode')
state_steps.append(state['step'])
adam(params_with_grad,
grads,
exp_avgs,
exp_avg_sqs,
max_exp_avg_sqs,
state_steps,
amsgrad=group['amsgrad'],
beta1=beta1,
beta2=beta2,
lr=group['lr'],
weight_decay=group['weight_decay'],
eps=group['eps'],
maximize=group['maximize'],
foreach=group['foreach'],
capturable=group['capturable'],
differentiable=group['differentiable'],
fused=group['fused'],
grad_scale=grad_scale,
found_inf=found_inf)
return loss
def adam(params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avg_sqs: List[Tensor],
max_exp_avg_sqs: 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
foreach: Optional[bool] = None,
capturable: bool = False,
differentiable: bool = False,
fused: bool = False,
grad_scale: Optional[_MultiDeviceReplicator] = None,
found_inf: Optional[_MultiDeviceReplicator] = None,
*,
amsgrad: bool,
beta1: float,
beta2: float,
lr: float,
weight_decay: float,
eps: float,
maximize: bool):
r"""Functional API that performs Adam algorithm computation.
See :class:`~torch.optim.Adam` 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 foreach is None:
# Placeholder for more complex foreach logic to be added when value is not set
foreach = 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_adam
elif fused and not torch.jit.is_scripting():
func = _fused_adam
else:
func = _single_tensor_adam
func(params,
grads,
exp_avgs,
exp_avg_sqs,
max_exp_avg_sqs,
state_steps,
amsgrad=amsgrad,
beta1=beta1,
beta2=beta2,
lr=lr,
weight_decay=weight_decay,
eps=eps,
maximize=maximize,
capturable=capturable,
differentiable=differentiable,
grad_scale=grad_scale,
found_inf=found_inf)
def _single_tensor_adam(params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avg_sqs: List[Tensor],
max_exp_avg_sqs: List[Tensor],
state_steps: List[Tensor],
grad_scale: Optional[_MultiDeviceReplicator],
found_inf: Optional[_MultiDeviceReplicator],
*,
amsgrad: bool,
beta1: float,
beta2: float,
lr: float,
weight_decay: float,
eps: float,
maximize: bool,
capturable: bool,
differentiable: bool):
assert grad_scale is None and found_inf is None
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]
step_t = state_steps[i]
if capturable:
assert param.is_cuda and step_t.is_cuda, "If capturable=True, params and state_steps must be CUDA tensors."
# update step
step_t += 1
if weight_decay != 0:
grad = grad.add(param, alpha=weight_decay)
if torch.is_complex(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)
param = torch.view_as_real(param)
# Decay the first and second moment running average coefficient
exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
exp_avg_sq.mul_(beta2).addcmul_(grad, grad.conj(), value=1 - beta2)
if capturable or differentiable:
step = step_t
# 1 - beta1 ** step can't be captured in a CUDA graph, even if step is a CUDA tensor
# (incurs "RuntimeError: CUDA error: operation not permitted when stream is capturing")
bias_correction1 = 1 - torch.pow(beta1, step)
bias_correction2 = 1 - torch.pow(beta2, step)
step_size = lr / bias_correction1
step_size_neg = step_size.neg()
bias_correction2_sqrt = bias_correction2.sqrt()
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
if differentiable:
max_exp_avg_sqs_i = max_exp_avg_sqs[i].clone()
else:
max_exp_avg_sqs_i = max_exp_avg_sqs[i]
max_exp_avg_sqs[i].copy_(torch.maximum(max_exp_avg_sqs_i, exp_avg_sq))
# Uses the max. for normalizing running avg. of gradient
# Folds in (admittedly ugly) 1-elem step_size math here to avoid extra param-set-sized read+write
# (can't fold it into addcdiv_ below because addcdiv_ requires value is a Number, not a Tensor)
denom = (max_exp_avg_sqs[i].sqrt() / (bias_correction2_sqrt * step_size_neg)).add_(eps / step_size_neg)
else:
denom = (exp_avg_sq.sqrt() / (bias_correction2_sqrt * step_size_neg)).add_(eps / step_size_neg)
param.addcdiv_(exp_avg, denom)
else:
step = step_t.item()
bias_correction1 = 1 - beta1 ** step
bias_correction2 = 1 - beta2 ** step
step_size = lr / bias_correction1
bias_correction2_sqrt = math.sqrt(bias_correction2)
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
torch.maximum(max_exp_avg_sqs[i], exp_avg_sq, out=max_exp_avg_sqs[i])
# Use the max. for normalizing running avg. of gradient
denom = (max_exp_avg_sqs[i].sqrt() / bias_correction2_sqrt).add_(eps)
else:
denom = (exp_avg_sq.sqrt() / bias_correction2_sqrt).add_(eps)
param.addcdiv_(exp_avg, denom, value=-step_size)
def _multi_tensor_adam(params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avg_sqs: List[Tensor],
max_exp_avg_sqs: List[Tensor],
state_steps: List[Tensor],
grad_scale: Optional[_MultiDeviceReplicator],
found_inf: Optional[_MultiDeviceReplicator],
*,
amsgrad: bool,
beta1: float,
beta2: float,
lr: float,
weight_decay: float,
eps: float,
maximize: bool,
capturable: bool,
differentiable: bool):
if len(params) == 0:
return
if capturable:
assert all(p.is_cuda and step.is_cuda for p, step in zip(params, state_steps)), \
"If capturable=True, params and state_steps must be CUDA tensors."
assert grad_scale is None and found_inf is None
if maximize:
grads = torch._foreach_neg(tuple(grads)) # type: ignore[assignment]
assert not differentiable, "_foreach ops don't support autograd"
# Handle complex parameters
grads = [torch.view_as_real(x) if torch.is_complex(x) else x for x in grads]
exp_avgs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in exp_avgs]
exp_avg_sqs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in exp_avg_sqs]
params_ = [torch.view_as_real(x) if torch.is_complex(x) else x for x in params]
# update steps
torch._foreach_add_(state_steps, 1)
if weight_decay != 0:
torch._foreach_add_(grads, params, alpha=weight_decay)
# Decay the first and second moment running average coefficient
torch._foreach_mul_(exp_avgs, beta1)
torch._foreach_add_(exp_avgs, grads, alpha=1 - beta1)
torch._foreach_mul_(exp_avg_sqs, beta2)
torch._foreach_addcmul_(exp_avg_sqs, grads, grads, 1 - beta2)
if capturable:
# TODO: use foreach_pow if/when foreach_pow is added
bias_correction1 = [torch.pow(beta1, step) for step in state_steps]
bias_correction2 = [torch.pow(beta2, step) for step in state_steps]
# foreach_sub doesn't allow a scalar as the first arg
torch._foreach_sub_(bias_correction1, 1)
torch._foreach_sub_(bias_correction2, 1)
torch._foreach_neg_(bias_correction1)
torch._foreach_neg_(bias_correction2)
# foreach_div doesn't allow a scalar as the first arg
step_size = torch._foreach_div(bias_correction1, lr)
torch._foreach_reciprocal_(step_size)
torch._foreach_neg_(step_size)
bias_correction2_sqrt = torch._foreach_sqrt(bias_correction2)
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
torch._foreach_maximum_(max_exp_avg_sqs, exp_avg_sqs) # type: ignore[assignment]
# Use the max. for normalizing running avg. of gradient
max_exp_avg_sq_sqrt = torch._foreach_sqrt(max_exp_avg_sqs)
# Folds in (admittedly ugly) 1-elem step_size math here to avoid extra param-set-sized read+write
# (can't fold it into addcdiv_ below because addcdiv_ requires value is a Number, not a Tensor)
torch._foreach_div_(max_exp_avg_sq_sqrt, torch._foreach_mul(bias_correction2_sqrt, step_size))
eps_over_step_size = torch._foreach_div(step_size, eps)
torch._foreach_reciprocal_(eps_over_step_size)
denom = torch._foreach_add(max_exp_avg_sq_sqrt, eps_over_step_size)
else:
exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs)
torch._foreach_div_(exp_avg_sq_sqrt, torch._foreach_mul(bias_correction2_sqrt, step_size))
eps_over_step_size = torch._foreach_div(step_size, eps)
torch._foreach_reciprocal_(eps_over_step_size)
denom = torch._foreach_add(exp_avg_sq_sqrt, eps_over_step_size)
torch._foreach_addcdiv_(params_, exp_avgs, denom)
else:
bias_correction1 = [1 - beta1 ** step.item() for step in state_steps]
bias_correction2 = [1 - beta2 ** step.item() for step in state_steps]
step_size = [(lr / bc) * -1 for bc in bias_correction1]
bias_correction2_sqrt = [math.sqrt(bc) for bc in bias_correction2]
if amsgrad:
# Maintains the maximum of all 2nd moment running avg. till now
torch._foreach_maximum_(max_exp_avg_sqs, exp_avg_sqs)
# Use the max. for normalizing running avg. of gradient
max_exp_avg_sq_sqrt = torch._foreach_sqrt(max_exp_avg_sqs)
torch._foreach_div_(max_exp_avg_sq_sqrt, bias_correction2_sqrt)
denom = torch._foreach_add(max_exp_avg_sq_sqrt, eps)
else:
exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs)
torch._foreach_div_(exp_avg_sq_sqrt, bias_correction2_sqrt)
denom = torch._foreach_add(exp_avg_sq_sqrt, eps)
torch._foreach_addcdiv_(params_, exp_avgs, denom, step_size)
# TODO(crcrpar): Move this to another place when adding another fused optimizer.
# TODO(crcrpar): Make this generic when there's more fused optimizers.
# TODO(crcrpar): Think of rewriting this in C++.
@torch.no_grad()
def _group_params_by_device_and_dtype(
params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avg_sqs: List[Tensor],
max_exp_avg_sqs: List[Tensor],
state_steps: List[Tensor],
) -> Dict[Tuple[str, torch.dtype], List[List[Tensor]]]:
per_device_and_dtype_tensors = defaultdict(lambda: [[] for _ in range(6)])
for i, (p, step) in enumerate(zip(params, state_steps)):
key = (str(p.device), p.dtype)
per_device_and_dtype_tensors[key][0].append(p)
per_device_and_dtype_tensors[key][1].append(grads[i])
per_device_and_dtype_tensors[key][2].append(exp_avgs[i])
per_device_and_dtype_tensors[key][3].append(exp_avg_sqs[i])
if max_exp_avg_sqs:
per_device_and_dtype_tensors[key][4].append(max_exp_avg_sqs[i])
per_device_and_dtype_tensors[key][5].append(step)
return per_device_and_dtype_tensors
def _fused_adam(
params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avg_sqs: List[Tensor],
max_exp_avg_sqs: List[Tensor],
state_steps: List[Tensor],
grad_scale: Optional[_MultiDeviceReplicator],
found_inf: Optional[_MultiDeviceReplicator],
*,
amsgrad: bool,
beta1: float,
beta2: float,
lr: float,
weight_decay: float,
eps: float,
maximize: bool,
capturable: bool, # Needed for consistency.
differentiable: bool,
) -> None:
grouped_tensors = _group_params_by_device_and_dtype(params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps)
for (device, dtype) in grouped_tensors:
(
device_params,
device_grads,
device_exp_avgs,
device_exp_avg_sqs,
device_max_exp_avg_sqs,
device_state_steps,
) = grouped_tensors[(device, dtype)]
if grad_scale is not None and found_inf is not None:
device_grad_scale = grad_scale.get(device)
device_found_inf = found_inf.get(device)
else:
device_grad_scale = None
device_found_inf = None
torch._foreach_add_(device_state_steps, 1)
torch._fused_adam_(
device_params,
device_grads,
device_exp_avgs,
device_exp_avg_sqs,
device_max_exp_avg_sqs,
device_state_steps,
amsgrad=amsgrad,
lr=lr,
beta1=beta1,
beta2=beta2,
weight_decay=weight_decay,
eps=eps,
maximize=maximize,
grad_scale=device_grad_scale,
found_inf=device_found_inf,
)
if device_found_inf is not None:
torch._foreach_sub_(device_state_steps, [device_found_inf] * len(device_state_steps))