| import torch |
| from . import _functional as F |
| from .optimizer import Optimizer |
| |
| |
| class Adam(Optimizer): |
| r"""Implements Adam algorithm. |
| |
| .. 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)} \\ |
| &\hspace{13mm} \lambda \text{ (weight decay)}, \: \textit{amsgrad}, |
| \:\textit{maximize} \\ |
| &\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)}, |
| v_0\leftarrow 0 \text{ (second moment)},\: \widehat{v_0}^{max}\leftarrow 0\\[-1.ex] |
| &\rule{110mm}{0.4pt} \\ |
| &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ |
| |
| &\hspace{5mm}\textbf{if} \: \textit{maximize}: \\ |
| &\hspace{10mm}g_t \leftarrow -\nabla_{\theta} f_t (\theta_{t-1}) \\ |
| &\hspace{5mm}\textbf{else} \\ |
| &\hspace{10mm}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{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 m_t/\big(1-\beta_1^t \big) \\ |
| &\hspace{5mm}\widehat{v_t} \leftarrow v_t/\big(1-\beta_2^t \big) \\ |
| &\hspace{5mm}\textbf{if} \: amsgrad \\ |
| &\hspace{10mm}\widehat{v_t}^{max} \leftarrow \mathrm{max}(\widehat{v_t}^{max}, |
| \widehat{v_t}) \\ |
| &\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/ |
| \big(\sqrt{\widehat{v_t}^{max}} + \epsilon \big) \\ |
| &\hspace{5mm}\textbf{else} \\ |
| &\hspace{10mm}\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 `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: 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) |
| amsgrad (boolean, optional): whether to use the AMSGrad variant of this |
| algorithm from the paper `On the Convergence of Adam and Beyond`_ |
| (default: False) |
| maximize (bool, optional): maximize the params based on the objective, instead of |
| minimizing (default: False) |
| |
| .. _Adam\: A Method for Stochastic Optimization: |
| https://arxiv.org/abs/1412.6980 |
| .. _On the Convergence of Adam and Beyond: |
| https://openreview.net/forum?id=ryQu7f-RZ |
| """ |
| |
| def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, |
| weight_decay=0, amsgrad=False, *, maximize: bool = False): |
| 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, amsgrad=amsgrad, maximize=maximize) |
| super(Adam, self).__init__(params, defaults) |
| |
| def __setstate__(self, state): |
| super(Adam, self).__setstate__(state) |
| for group in self.param_groups: |
| group.setdefault('amsgrad', False) |
| group.setdefault('maximize', False) |
| |
| @torch.no_grad() |
| 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: |
| with torch.enable_grad(): |
| loss = closure() |
| |
| for group in self.param_groups: |
| params_with_grad = [] |
| grads = [] |
| exp_avgs = [] |
| exp_avg_sqs = [] |
| max_exp_avg_sqs = [] |
| state_steps = [] |
| beta1, beta2 = group['betas'] |
| |
| for p in group['params']: |
| if p.grad is not None: |
| params_with_grad.append(p) |
| if p.grad.is_sparse: |
| raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead') |
| grads.append(p.grad) |
| |
| 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) |
| if group['amsgrad']: |
| # Maintains max of all exp. moving avg. of sq. grad. values |
| state['max_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']) |
| |
| if group['amsgrad']: |
| max_exp_avg_sqs.append(state['max_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']) |
| |
| F.adam(params_with_grad, |
| grads, |
| exp_avgs, |
| exp_avg_sqs, |
| max_exp_avg_sqs, |
| state_steps, |
| amsgrad=group['amsgrad'], |
| beta1=beta1, |
| beta2=beta2, |
| lr=group['lr'], |
| weight_decay=group['weight_decay'], |
| eps=group['eps'], |
| maximize=group['maximize']) |
| return loss |
