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import torch
from torch import Tensor
from .optimizer import Optimizer
from typing import List, Optional
__all__ = ['Adadelta', 'adadelta']
class Adadelta(Optimizer):
r"""Implements Adadelta algorithm.
.. math::
\begin{aligned}
&\rule{110mm}{0.4pt} \\
&\textbf{input} : \gamma \text{ (lr)}, \: \theta_0 \text{ (params)},
\: f(\theta) \text{ (objective)}, \: \rho \text{ (decay)},
\: \lambda \text{ (weight decay)} \\
&\textbf{initialize} : v_0 \leftarrow 0 \: \text{ (square avg)},
\: u_0 \leftarrow 0 \: \text{ (accumulate variables)} \\[-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}if \: \lambda \neq 0 \\
&\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\
&\hspace{5mm} v_t \leftarrow v_{t-1} \rho + g^2_t (1 - \rho) \\
&\hspace{5mm}\Delta x_t \leftarrow \frac{\sqrt{u_{t-1} +
\epsilon }}{ \sqrt{v_t + \epsilon} }g_t \hspace{21mm} \\
&\hspace{5mm} u_t \leftarrow u_{t-1} \rho +
\Delta x^2_t (1 - \rho) \\
&\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \gamma \Delta x_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 `ADADELTA: An Adaptive Learning Rate Method`_.
Args:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
rho (float, optional): coefficient used for computing a running average
of squared gradients (default: 0.9)
eps (float, optional): term added to the denominator to improve
numerical stability (default: 1e-6)
lr (float, optional): coefficient that scale delta before it is applied
to the parameters (default: 1.0)
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
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)
.. _ADADELTA\: An Adaptive Learning Rate Method:
https://arxiv.org/abs/1212.5701
"""
def __init__(self, params, lr=1.0, rho=0.9, eps=1e-6, weight_decay=0,
foreach: Optional[bool] = None, *, maximize: bool = False):
if not 0.0 <= lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <= rho <= 1.0:
raise ValueError("Invalid rho value: {}".format(rho))
if not 0.0 <= eps:
raise ValueError("Invalid epsilon value: {}".format(eps))
if not 0.0 <= weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults = dict(lr=lr, rho=rho, eps=eps, weight_decay=weight_decay,
maximize=maximize, foreach=foreach)
super(Adadelta, self).__init__(params, defaults)
def __setstate__(self, state):
super().__setstate__(state)
for group in self.param_groups:
group.setdefault('foreach', None)
group.setdefault('maximize', False)
@torch.no_grad()
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 = []
square_avgs = []
acc_deltas = []
lr, rho, eps, weight_decay, foreach, maximize = (group['lr'],
group['rho'],
group['eps'],
group['weight_decay'],
group['foreach'],
group['maximize'])
for p in group['params']:
if p.grad is None:
continue
params_with_grad.append(p)
if p.grad.is_sparse:
raise RuntimeError('Adadelta does not support sparse gradients')
grads.append(p.grad)
state = self.state[p]
# Lazy state initialization
if len(state) == 0:
state['step'] = 0
state['square_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
state['acc_delta'] = torch.zeros_like(p, memory_format=torch.preserve_format)
square_avgs.append(state['square_avg'])
acc_deltas.append(state['acc_delta'])
state['step'] += 1
adadelta(params_with_grad,
grads,
square_avgs,
acc_deltas,
lr=lr,
rho=rho,
eps=eps,
weight_decay=weight_decay,
foreach=foreach,
maximize=maximize)
return loss
def adadelta(params: List[Tensor],
grads: List[Tensor],
square_avgs: List[Tensor],
acc_deltas: 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: bool = None,
*,
lr: float,
rho: float,
eps: float,
weight_decay: float,
maximize: bool):
r"""Functional API that performs Adadelta algorithm computation.
See :class:`~torch.optim.Adadelta` for details.
"""
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_adadelta
else:
func = _single_tensor_adadelta
func(params,
grads,
square_avgs,
acc_deltas,
lr=lr,
rho=rho,
eps=eps,
weight_decay=weight_decay,
maximize=maximize)
def _single_tensor_adadelta(params: List[Tensor],
grads: List[Tensor],
square_avgs: List[Tensor],
acc_deltas: List[Tensor],
*,
lr: float,
rho: float,
eps: float,
weight_decay: float,
maximize: bool):
for (param, grad, square_avg, acc_delta) in zip(params, grads, square_avgs, acc_deltas):
grad = grad if not maximize else -grad
if weight_decay != 0:
grad = grad.add(param, alpha=weight_decay)
if torch.is_complex(param):
square_avg = torch.view_as_real(square_avg)
acc_delta = torch.view_as_real(acc_delta)
grad = torch.view_as_real(grad)
square_avg.mul_(rho).addcmul_(grad, grad, value=1 - rho)
std = square_avg.add(eps).sqrt_()
delta = acc_delta.add(eps).sqrt_().div_(std).mul_(grad)
acc_delta.mul_(rho).addcmul_(delta, delta, value=1 - rho)
if torch.is_complex(param):
delta = torch.view_as_complex(delta)
param.add_(delta, alpha=-lr)
def _multi_tensor_adadelta(params: List[Tensor],
grads: List[Tensor],
square_avgs: List[Tensor],
acc_deltas: List[Tensor],
*,
lr: float,
weight_decay: float,
rho: float,
eps: float,
maximize: bool):
if len(params) == 0:
return
if maximize:
grads = torch._foreach_neg(grads)
if weight_decay != 0:
torch._foreach_add_(grads, params, alpha=weight_decay)
torch._foreach_mul_(square_avgs, rho)
torch._foreach_addcmul_(square_avgs, grads, grads, value=1 - rho)
std = torch._foreach_add(square_avgs, eps)
torch._foreach_sqrt_(std)
deltas = torch._foreach_add(acc_deltas, eps)
torch._foreach_sqrt_(deltas)
torch._foreach_div_(deltas, std)
torch._foreach_mul_(deltas, grads)
torch._foreach_add_(params, deltas, alpha=-lr)
torch._foreach_mul_(acc_deltas, rho)
torch._foreach_addcmul_(acc_deltas, deltas, deltas, value=1 - rho)
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