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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)}, \: \lambda \text{ (weight decay)},                          \\
&\hspace{12mm}    \tau \text{ (initial accumulator value)}, \: \eta\text{ (lr decay)}\\
&\textbf{initialize} :  state\_sum_0 \leftarrow 0                             \\[-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} \tilde{\gamma}    \leftarrow \gamma / (1 +(t-1) \eta)                  \\
&\hspace{5mm} \textbf{if} \: \lambda \neq 0                                          \\
&\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1}                             \\
&\hspace{5mm}state\_sum_t  \leftarrow  state\_sum_{t-1} + g^2_t                      \\
&\hspace{5mm}\theta_t \leftarrow
\theta_{t-1}- \tilde{\gamma} \frac{g_t}{\sqrt{state\_sum_t}+\epsilon}            \\
&\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 Adaptive Subgradient Methods for Online Learning
and Stochastic Optimization_.

Args:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): learning rate (default: 1e-2)
lr_decay (float, optional): learning rate decay (default: 0)
weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
eps (float, optional): term added to the denominator to improve
numerical stability (default: 1e-10)

Optimization: http://jmlr.org/papers/v12/duchi11a.html
"""

def __init__(self, params, lr=1e-2, lr_decay=0, weight_decay=0, initial_accumulator_value=0, eps=1e-10):
if not 0.0 <= lr:
raise ValueError("Invalid learning rate: {}".format(lr))
if not 0.0 <= lr_decay:
raise ValueError("Invalid lr_decay value: {}".format(lr_decay))
if not 0.0 <= weight_decay:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
if not 0.0 <= initial_accumulator_value:
raise ValueError("Invalid initial_accumulator_value value: {}".format(initial_accumulator_value))
if not 0.0 <= eps:
raise ValueError("Invalid epsilon value: {}".format(eps))

defaults = dict(lr=lr, lr_decay=lr_decay, eps=eps, weight_decay=weight_decay,
initial_accumulator_value=initial_accumulator_value)

for group in self.param_groups:
for p in group['params']:
state = self.state[p]
state['step'] = 0
init_value = complex(initial_accumulator_value, initial_accumulator_value) if torch.is_complex(p) \
else initial_accumulator_value
state['sum'] = torch.full_like(p, init_value, memory_format=torch.preserve_format)

def share_memory(self):
for group in self.param_groups:
for p in group['params']:
state = self.state[p]
state['sum'].share_memory_()

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:
state_sums = []
state_steps = []

for p in group['params']:
state = self.state[p]
state_sums.append(state['sum'])
# update the steps for each param group update
state['step'] += 1
# record the step after step update
state_steps.append(state['step'])

state_sums,
state_steps,
lr=group['lr'],
weight_decay=group['weight_decay'],
lr_decay=group['lr_decay'],
eps=group['eps'])

return loss


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