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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)}, \: \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 \sqrt{ (1-\beta^t_2) / \big( v_t +\epsilon \big) }     \\
&\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_.

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)

.. _On the variance of the adaptive learning rate and beyond:
https://arxiv.org/abs/1908.03265
"""

def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
weight_decay=0):
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)

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:
exp_avgs = []
exp_avg_sqs = []
max_exp_avg_sqs = []
state_steps = []
beta1, beta2 = group['betas']

for p in group['params']:

state = self.state[p]
# Lazy state initialization
if len(state) == 0:
state['step'] = 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'])

# update the steps for each param group update
state['step'] += 1
# record the step after step update
state_steps.append(state['step'])

exp_avgs,
exp_avg_sqs,
state_steps,
beta1=beta1,
beta2=beta2,
lr=group['lr'],
weight_decay=group['weight_decay'],
eps=group['eps'])
return loss


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