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# Source code for torch.optim.adamax

import torch
from . import _functional as F
from .optimizer import Optimizer

r"""Implements Adamax algorithm (a variant of Adam based on infinity norm).

.. 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{ (weight decay)},                                                \\
&\hspace{13mm}    \epsilon \text{ (epsilon)}                                          \\
&\textbf{initialize} :  m_0 \leftarrow 0 \text{ ( first moment)},
u_0 \leftarrow 0 \text{ ( infinity norm)}                                 \\[-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}m_t      \leftarrow   \beta_1 m_{t-1} + (1 - \beta_1) g_t               \\
&\hspace{5mm}u_t      \leftarrow   \mathrm{max}(\beta_2 u_{t-1}, |g_{t}|+\epsilon)   \\
&\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \frac{\gamma m_t}{(1-\beta^t_1) u_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 Adam: A Method for Stochastic Optimization_.

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
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)

.. _Adam\: A Method for Stochastic Optimization:
https://arxiv.org/abs/1412.6980
"""

def __init__(self, params, lr=2e-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_infs = []
state_steps = []

beta1, beta2 = group['betas']
eps = group['eps']
lr = group['lr']
weight_decay = group['weight_decay']

for p in group['params']:
if p.grad is None:
continue
raise RuntimeError('Adamax does not support sparse gradients')

state = self.state[p]

# State initialization
if len(state) == 0:
state['step'] = 0
state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
state['exp_inf'] = torch.zeros_like(p, memory_format=torch.preserve_format)

exp_avgs.append(state['exp_avg'])
exp_infs.append(state['exp_inf'])

state['step'] += 1
state_steps.append(state['step'])

exp_avgs,
exp_infs,
state_steps,
eps=eps,
beta1=beta1,
beta2=beta2,
lr=lr,
weight_decay=weight_decay)

return loss


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