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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_t \text{ (lr)}, \: \beta_1,\beta_2 \text{ (betas)},
\: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)}                   \\
&\hspace{13mm} \: \lambda \text{ (weight decay)}, \:\psi \text{ (momentum decay)}    \\
&\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
v_0 \leftarrow 0 \text{ ( second moment)}                                 \\[-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} \mu_t \leftarrow \beta_1 \big(1 - \frac{1}{2}  0.96^{t \psi} \big)     \\
&\hspace{5mm} \mu_{t+1} \leftarrow \beta_1 \big(1 - \frac{1}{2} 0.96^{(t+1)\psi}\big)\\
&\hspace{5mm}m_t           \leftarrow   \beta_1 m_{t-1} + (1 - \beta_1) g_t          \\
&\hspace{5mm}v_t           \leftarrow   \beta_2 v_{t-1} + (1-\beta_2) g^2_t          \\
&\hspace{5mm}\widehat{m_t} \leftarrow \mu_{t+1} m_t/(1-\prod_{i=1}^{t+1}\mu_i)\\[-1.ex]
& \hspace{11mm} + (1-\mu_t) g_t /(1-\prod_{i=1}^{t} \mu_{i})                         \\
&\hspace{5mm}\widehat{v_t} \leftarrow   v_t/\big(1-\beta_2^t \big)                   \\
&\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/
\big(\sqrt{\widehat{v_t}} + \epsilon \big)                                       \\
&\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 Incorporating Nesterov Momentum into Adam_.

Args:
params (iterable): iterable of parameters to optimize or dicts defining
parameter groups
lr (float, optional): learning rate (default: 2e-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)
momentum_decay (float, optional): momentum momentum_decay (default: 4e-3)

.. _Incorporating Nesterov Momentum into Adam:
https://openreview.net/forum?id=OM0jvwB8jIp57ZJjtNEZ
"""

def __init__(self, params, lr=2e-3, betas=(0.9, 0.999), eps=1e-8,
weight_decay=0, momentum_decay=4e-3):
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))
if not 0.0 <= momentum_decay:
raise ValueError("Invalid momentum_decay value: {}".format(momentum_decay))
defaults = dict(lr=lr, betas=betas, eps=eps,
weight_decay=weight_decay, momentum_decay=momentum_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 = []
mu_products = []
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
state['mu_product'] = 1.
# 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'])
mu_products.append(state['mu_product'])

# 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,
mu_products,
state_steps,
beta1=beta1,
beta2=beta2,
lr=group['lr'],
weight_decay=group['weight_decay'],
momentum_decay=group['momentum_decay'],
eps=group['eps'])

# update mu_product
for p, mu_product in zip(params_with_grad, mu_products):
state = self.state[p]
state['mu_product'] = state['mu_product'] * beta1 * \
(1. - 0.5 * (0.96 ** (state['step'] * group['momentum_decay'])))

return loss


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