import math import torch from torch import Tensor from .optimizer import Optimizer from typing import List, Optional 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)