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import torch

from . import _functional as F
from .optimizer import Optimizer

.. 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
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)

https://arxiv.org/abs/1212.5701
"""

def __init__(self, params, lr=1.0, rho=0.9, eps=1e-6, weight_decay=0):
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)

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:
loss = closure()

for group in self.param_groups:
square_avgs = []
acc_deltas = []
lr, rho, eps, weight_decay = group['lr'], group['rho'], group['eps'], group['weight_decay']

for p in group['params']:
continue

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

square_avgs,
acc_deltas,
lr=lr,
rho=rho,
eps=eps,
weight_decay=weight_decay)

return loss


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