Source code for torch.optim.radam
import math
import torch
from torch import Tensor
from .optimizer import (Optimizer, _use_grad_for_differentiable, _get_value, _dispatch_sqrt, _stack_if_compiling,
_default_to_fused_or_foreach, _differentiable_doc, _foreach_doc)
from typing import List, Optional
__all__ = ["RAdam", "radam"]
[docs]class RAdam(Optimizer):
def __init__(
self,
params,
lr=1e-3,
betas=(0.9, 0.999),
eps=1e-8,
weight_decay=0,
*,
foreach: Optional[bool] = None,
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}")
defaults = dict(
lr=lr,
betas=betas,
eps=eps,
weight_decay=weight_decay,
foreach=foreach,
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("differentiable", 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"]))
def _init_group(self, group, params_with_grad, grads, exp_avgs, exp_avg_sqs, state_steps):
for p in group["params"]:
if p.grad is not None:
params_with_grad.append(p)
if p.grad.is_sparse:
raise RuntimeError("RAdam does not support sparse gradients")
grads.append(p.grad)
state = self.state[p]
# Lazy state initialization
if len(state) == 0:
state["step"] = torch.tensor(0.0)
# 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
)
exp_avgs.append(state["exp_avg"])
exp_avg_sqs.append(state["exp_avg_sq"])
state_steps.append(state["step"])
[docs] @_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.
"""
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 = []
state_steps = []
beta1, beta2 = group["betas"]
self._init_group(group, params_with_grad, grads, exp_avgs, exp_avg_sqs, state_steps)
radam(
params_with_grad,
grads,
exp_avgs,
exp_avg_sqs,
state_steps,
beta1=beta1,
beta2=beta2,
lr=group["lr"],
weight_decay=group["weight_decay"],
eps=group["eps"],
foreach=group["foreach"],
differentiable=group["differentiable"],
)
return loss
RAdam.__doc__ = r"""Implements RAdam 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)}, \:
\lambda \text{ (weightdecay)}, \\
&\hspace{13mm} \epsilon \text{ (epsilon)} \\
&\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)},
v_0 \leftarrow 0 \text{ ( second moment)}, \\
&\hspace{18mm} \rho_{\infty} \leftarrow 2/(1-\beta_2) -1 \\[-1.ex]
&\rule{110mm}{0.4pt} \\
&\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\
&\hspace{6mm}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{6mm}m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\
&\hspace{6mm}v_t \leftarrow \beta_2 v_{t-1} + (1-\beta_2) g^2_t \\
&\hspace{6mm}\widehat{m_t} \leftarrow m_t/\big(1-\beta_1^t \big) \\
&\hspace{6mm}\rho_t \leftarrow \rho_{\infty} -
2 t \beta^t_2 /\big(1-\beta_2^t \big) \\[0.1.ex]
&\hspace{6mm}\textbf{if} \: \rho_t > 5 \\
&\hspace{12mm} l_t \leftarrow \frac{\sqrt{ (1-\beta^t_2) }}{ \sqrt{v_t} +\epsilon } \\
&\hspace{12mm} r_t \leftarrow
\sqrt{\frac{(\rho_t-4)(\rho_t-2)\rho_{\infty}}{(\rho_{\infty}-4)(\rho_{\infty}-2) \rho_t}} \\
&\hspace{12mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t} r_t l_t \\
&\hspace{6mm}\textbf{else} \\
&\hspace{12mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t} \\
&\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 `On the variance of the adaptive learning rate and beyond`_.
This implementation uses the same weight_decay implementation as Adam (were the weight_decay is applied
to the gradient) and not the one from AdamW (were weight_decay is applied to the update). This
is different from the `author's implementation`_.
""" + fr"""
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)
{_foreach_doc}
{_differentiable_doc}
.. _On the variance of the adaptive learning rate and beyond:
https://arxiv.org/abs/1908.03265
.. _author's implementation:
https://github.com/LiyuanLucasLiu/RAdam
"""
def radam(
params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
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,
differentiable: bool = False,
*,
beta1: float,
beta2: float,
lr: float,
weight_decay: float,
eps: float,
):
r"""Functional API that performs RAdam algorithm computation.
See :class:`~torch.optim.RAdam` 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:
_, 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_radam
else:
func = _single_tensor_radam
func(
params,
grads,
exp_avgs,
exp_avg_sqs,
state_steps,
beta1=beta1,
beta2=beta2,
lr=lr,
weight_decay=weight_decay,
eps=eps,
differentiable=differentiable,
)
def _single_tensor_radam(
params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avg_sqs: List[Tensor],
state_steps: List[Tensor],
*,
beta1: float,
beta2: float,
lr: float,
weight_decay: float,
eps: float,
differentiable: bool,
):
for i, param in enumerate(params):
grad = grads[i]
exp_avg = exp_avgs[i]
exp_avg_sq = exp_avg_sqs[i]
step_t = state_steps[i]
# update step
step_t += 1
step = _get_value(step_t)
bias_correction1 = 1 - beta1 ** step
bias_correction2 = 1 - beta2 ** step
if weight_decay != 0:
grad = grad.add(param, alpha=weight_decay)
# 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)
# correcting bias for the first moving moment
bias_corrected_exp_avg = exp_avg / bias_correction1
# maximum length of the approximated SMA
rho_inf = 2 / (1 - beta2) - 1
# compute the length of the approximated SMA
rho_t = rho_inf - 2 * step * (beta2 ** step) / bias_correction2
if rho_t > 5.0:
# Compute the variance rectification term and update parameters accordingly
rect = math.sqrt(
(rho_t - 4)
* (rho_t - 2)
* rho_inf
/ ((rho_inf - 4) * (rho_inf - 2) * rho_t)
)
exp_avg_sq_sqrt = exp_avg_sq.sqrt()
if differentiable:
exp_avg_sq_sqrt = exp_avg_sq_sqrt.add(eps)
else:
exp_avg_sq_sqrt = exp_avg_sq_sqrt.add_(eps)
adaptive_lr = math.sqrt(bias_correction2) / exp_avg_sq_sqrt
param.add_(bias_corrected_exp_avg * lr * adaptive_lr * rect, alpha=-1.0)
else:
param.add_(bias_corrected_exp_avg * lr, alpha=-1.0)
def _multi_tensor_radam(
params: List[Tensor],
grads: List[Tensor],
exp_avgs: List[Tensor],
exp_avg_sqs: List[Tensor],
state_steps: List[Tensor],
*,
beta1: float,
beta2: float,
lr: float,
weight_decay: float,
eps: float,
differentiable: bool,
):
if len(params) == 0:
return
assert not differentiable, "_foreach ops don't support autograd"
grouped_tensors = Optimizer._group_tensors_by_device_and_dtype([params, grads, exp_avgs, exp_avg_sqs, state_steps])
for ((
grouped_params,
grouped_grads,
grouped_exp_avgs,
grouped_exp_avg_sqs,
grouped_state_steps,
), _) in grouped_tensors.values():
# Update steps
torch._foreach_add_(grouped_state_steps, 1)
# maximum length of the approximated SMA
rho_inf = 2 / (1 - beta2) - 1
# compute the length of the approximated SMA
rho_t_list = [rho_inf - 2 * _get_value(step) * (beta2 ** _get_value(step)) /
(1 - beta2 ** _get_value(step)) for step in grouped_state_steps]
if weight_decay != 0:
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)
# Delete the local intermediate since it won't be used anymore to save on peak memory
del grouped_grads
rect = [
_dispatch_sqrt(
(rho_t - 4)
* (rho_t - 2)
* rho_inf
/ ((rho_inf - 4) * (rho_inf - 2) * rho_t)
)
if rho_t > 5
else 0
for rho_t in rho_t_list
]
unrectified = [0 if rect > 0 else 1.0 for rect in rect]
bias_correction1 = [1 - beta1 ** _get_value(step) for step in grouped_state_steps]
unrect_step_size = _stack_if_compiling([(lr * rect / bc) * -1 for rect, bc in zip(unrectified, bias_correction1)])
bias_correction2_sqrt_times_rect_step_size = [
_dispatch_sqrt(1 - beta2 ** _get_value(step)) * (lr * rect / bc) * -1
for step, rect, bc in zip(grouped_state_steps, rect, bias_correction1)
]
buffer = torch._foreach_sqrt(grouped_exp_avg_sqs)
torch._foreach_add_(buffer, eps)
torch._foreach_div_(buffer, bias_correction2_sqrt_times_rect_step_size)
torch._foreach_reciprocal_(buffer)
torch._foreach_add_(buffer, unrect_step_size)
# Here, buffer = sqrt(1 - beta2^t) * rect_step_size / (sqrt(v) + eps) + unrect_step_size
torch._foreach_addcmul_(grouped_params, grouped_exp_avgs, buffer)
