| import math |
| import torch |
| from torch import Tensor |
| from .optimizer import Optimizer |
| from typing import List, Optional |
| |
| __all__ = ['NAdam', 'nadam'] |
| |
| class NAdam(Optimizer): |
| r"""Implements NAdam algorithm. |
| |
| .. 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) |
| foreach (bool, optional): whether foreach implementation of optimizer |
| is used (default: None) |
| |
| .. _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, foreach: Optional[bool] = None): |
| 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, |
| foreach=foreach) |
| super(NAdam, self).__init__(params, defaults) |
| |
| def __setstate__(self, state): |
| super().__setstate__(state) |
| for group in self.param_groups: |
| group.setdefault('foreach', None) |
| state_values = list(self.state.values()) |
| step_is_tensor = (len(state_values) != 0) and torch.is_tensor(state_values[0]['step']) |
| if not step_is_tensor: |
| for s in state_values: |
| s['step'] = torch.tensor(float(s['step'])) |
| mu_product_is_tensor = (len(state_values) != 0) and torch.is_tensor(state_values[0]['mu_product']) |
| if not mu_product_is_tensor: |
| for s in state_values: |
| s['mu_product'] = torch.tensor(s['mu_product']) |
| |
| @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 = [] |
| mu_products = [] |
| 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('NAdam does not support sparse gradients') |
| grads.append(p.grad) |
| |
| state = self.state[p] |
| # Lazy state initialization |
| if len(state) == 0: |
| state['step'] = torch.tensor(0.) |
| state['mu_product'] = torch.tensor(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']) |
| state_steps.append(state['step']) |
| |
| nadam(params_with_grad, |
| grads, |
| 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'], |
| foreach=group['foreach']) |
| |
| return loss |
| |
| |
| def nadam(params: List[Tensor], |
| grads: List[Tensor], |
| exp_avgs: List[Tensor], |
| exp_avg_sqs: List[Tensor], |
| mu_products: List[Tensor], |
| state_steps: List[Tensor], |
| # kwonly args with defaults are not supported by functions compiled with torchscript issue #70627 |
| # setting this as kwarg for now as functional API is compiled by torch/distributed/optim |
| foreach: bool = None, |
| *, |
| beta1: float, |
| beta2: float, |
| lr: float, |
| weight_decay: float, |
| momentum_decay: float, |
| eps: float): |
| r"""Functional API that performs NAdam algorithm computation. |
| |
| See :class:`~torch.optim.NAdam` for details. |
| """ |
| |
| if not all(isinstance(t, torch.Tensor) for t in state_steps): |
| raise RuntimeError("API has changed, `state_steps` argument must contain a list of singleton tensors") |
| |
| if not all(isinstance(t, torch.Tensor) for t in mu_products): |
| raise RuntimeError("API has changed, `mu_products` argument must contain a list of singleton tensors") |
| |
| if foreach is None: |
| # Placeholder for more complex foreach logic to be added when value is not set |
| foreach = False |
| |
| if foreach and torch.jit.is_scripting(): |
| raise RuntimeError('torch.jit.script not supported with foreach optimizers') |
| |
| if foreach and not torch.jit.is_scripting(): |
| func = _multi_tensor_nadam |
| else: |
| func = _single_tensor_nadam |
| |
| func(params, |
| grads, |
| exp_avgs, |
| exp_avg_sqs, |
| mu_products, |
| state_steps, |
| beta1=beta1, |
| beta2=beta2, |
| lr=lr, |
| weight_decay=weight_decay, |
| momentum_decay=momentum_decay, |
| eps=eps) |
| |
| |
| def _single_tensor_nadam(params: List[Tensor], |
| grads: List[Tensor], |
| exp_avgs: List[Tensor], |
| exp_avg_sqs: List[Tensor], |
| mu_products: List[Tensor], |
| state_steps: List[Tensor], |
| *, |
| beta1: float, |
| beta2: float, |
| lr: float, |
| weight_decay: float, |
| momentum_decay: float, |
| eps: float): |
| |
| for i, param in enumerate(params): |
| grad = grads[i] |
| exp_avg = exp_avgs[i] |
| exp_avg_sq = exp_avg_sqs[i] |
| mu_product = mu_products[i] |
| step_t = state_steps[i] |
| # update step |
| step_t += 1 |
| step = step_t.item() |
| |
| bias_correction2 = 1 - beta2 ** step |
| |
| if weight_decay != 0: |
| grad = grad.add(param, alpha=weight_decay) |
| |
| # calculate the momentum cache \mu^{t} and \mu^{t+1} |
| mu = beta1 * (1. - 0.5 * (0.96 ** (step * momentum_decay))) |
| mu_next = beta1 * (1. - 0.5 * (0.96 ** ((step + 1) * momentum_decay))) |
| |
| # update mu_product |
| mu_product *= mu |
| mu_product_next = mu_product * mu * mu_next |
| |
| # decay the first and second moment running average coefficient |
| exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1) |
| exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2) |
| |
| denom = exp_avg_sq.div(bias_correction2).sqrt().add_(eps) |
| param.addcdiv_(grad, denom, value=-lr * (1. - mu) / (1. - mu_product.item())) |
| param.addcdiv_(exp_avg, denom, value=-lr * mu_next / (1. - mu_product_next.item())) |
| |
| |
| def _multi_tensor_nadam(params: List[Tensor], |
| grads: List[Tensor], |
| exp_avgs: List[Tensor], |
| exp_avg_sqs: List[Tensor], |
| mu_products: List[Tensor], |
| state_steps: List[Tensor], |
| *, |
| beta1: float, |
| beta2: float, |
| lr: float, |
| weight_decay: float, |
| momentum_decay: float, |
| eps: float): |
| |
| if len(params) == 0: |
| return |
| |
| # update steps |
| torch._foreach_add_(state_steps, 1) |
| |
| bias_correction1 = [1 - beta1 ** step.item() for step in state_steps] |
| bias_correction2 = [1 - beta2 ** step.item() for step in state_steps] |
| mus = [beta1 * (1. - 0.5 * (0.96 ** (step.item() * momentum_decay))) for step in state_steps] |
| mu_nexts = [beta1 * (1. - 0.5 * (0.96 ** ((step.item() + 1) * momentum_decay))) |
| for step in state_steps] |
| |
| # update mu_products |
| torch._foreach_mul_(mu_products, mus) |
| |
| if weight_decay != 0: |
| torch._foreach_add_(grads, params, alpha=weight_decay) |
| |
| # Decay the first and second moment running average coefficient |
| torch._foreach_mul_(exp_avgs, beta1) |
| torch._foreach_add_(exp_avgs, grads, alpha=1 - beta1) |
| |
| torch._foreach_mul_(exp_avg_sqs, beta2) |
| torch._foreach_addcmul_(exp_avg_sqs, grads, grads, 1 - beta2) |
| |
| exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs) |
| bias_correction_sqrt = [math.sqrt(bc) for bc in bias_correction2] |
| torch._foreach_div_(exp_avg_sq_sqrt, bias_correction_sqrt) |
| denom = torch._foreach_add(exp_avg_sq_sqrt, eps) |
| |
| step_size_grads = [(lr * (1. - mu) / (1. - mu_product.item())) * -1 |
| for mu_product, mu in zip(mu_products, mus)] |
| step_size_expavg = [(lr * mu_next / (1. - mu_product.item() * mu_next)) * -1 |
| for mu_product, mu_next in zip(mu_products, mu_nexts)] |
| torch._foreach_addcdiv_(params, grads, denom, step_size_grads) |
| torch._foreach_addcdiv_(params, exp_avgs, denom, step_size_expavg) |
