| import math |
| import torch |
| from torch import Tensor |
| |
| from .optimizer import Optimizer, _use_grad_for_differentiable |
| from typing import List, Optional |
| |
| __all__ = ['RAdam', 'radam'] |
| |
| class RAdam(Optimizer): |
| r"""Implements RAdam 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)}, \: |
| \lambda \text{ (weightdecay)}, \\ |
| &\hspace{13mm} \epsilon \text{ (epsilon)} \\ |
| &\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)}, |
| v_0 \leftarrow 0 \text{ ( second moment)}, \\ |
| &\hspace{18mm} \rho_{\infty} \leftarrow 2/(1-\beta_2) -1 \\[-1.ex] |
| &\rule{110mm}{0.4pt} \\ |
| &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ |
| &\hspace{6mm}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{6mm}m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\ |
| &\hspace{6mm}v_t \leftarrow \beta_2 v_{t-1} + (1-\beta_2) g^2_t \\ |
| &\hspace{6mm}\widehat{m_t} \leftarrow m_t/\big(1-\beta_1^t \big) \\ |
| &\hspace{6mm}\rho_t \leftarrow \rho_{\infty} - |
| 2 t \beta^t_2 /\big(1-\beta_2^t \big) \\[0.1.ex] |
| &\hspace{6mm}\textbf{if} \: \rho_t > 5 \\ |
| &\hspace{12mm} l_t \leftarrow \sqrt{ (1-\beta^t_2) / \big( v_t +\epsilon \big) } \\ |
| &\hspace{12mm} r_t \leftarrow |
| \sqrt{\frac{(\rho_t-4)(\rho_t-2)\rho_{\infty}}{(\rho_{\infty}-4)(\rho_{\infty}-2) \rho_t}} \\ |
| &\hspace{12mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t} r_t l_t \\ |
| &\hspace{6mm}\textbf{else} \\ |
| &\hspace{12mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_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 `On the variance of the adaptive learning rate and beyond`_. |
| |
| 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) |
| foreach (bool, optional): whether foreach implementation of optimizer |
| is used (default: None) |
| |
| .. _On the variance of the adaptive learning rate and beyond: |
| https://arxiv.org/abs/1908.03265 |
| """ |
| |
| def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, |
| weight_decay=0, *, foreach: Optional[bool] = None, |
| differentiable: 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, |
| foreach=foreach, differentiable=differentiable) |
| super(RAdam, self).__init__(params, defaults) |
| |
| def __setstate__(self, state): |
| super().__setstate__(state) |
| for group in self.param_groups: |
| group.setdefault('foreach', None) |
| group.setdefault('differentiable', False) |
| 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'])) |
| |
| @_use_grad_for_differentiable |
| 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 = [] |
| 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('RAdam 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.) |
| # 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']) |
| state_steps.append(state['step']) |
| |
| radam(params_with_grad, |
| grads, |
| exp_avgs, |
| exp_avg_sqs, |
| state_steps, |
| beta1=beta1, |
| beta2=beta2, |
| lr=group['lr'], |
| weight_decay=group['weight_decay'], |
| eps=group['eps'], |
| foreach=group['foreach'], |
| differentiable=group['differentiable']) |
| |
| return loss |
| |
| |
| def radam(params: List[Tensor], |
| grads: List[Tensor], |
| exp_avgs: List[Tensor], |
| exp_avg_sqs: 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, |
| differentiable: bool = False, |
| *, |
| beta1: float, |
| beta2: float, |
| lr: float, |
| weight_decay: float, |
| eps: float): |
| r"""Functional API that performs RAdam algorithm computation. |
| |
| See :class:`~torch.optim.RAdam` 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 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_radam |
| else: |
| func = _single_tensor_radam |
| |
| func(params, |
| grads, |
| exp_avgs, |
| exp_avg_sqs, |
| state_steps, |
| beta1=beta1, |
| beta2=beta2, |
| lr=lr, |
| weight_decay=weight_decay, |
| eps=eps, |
| differentiable=differentiable) |
| |
| |
| def _single_tensor_radam(params: List[Tensor], |
| grads: List[Tensor], |
| exp_avgs: List[Tensor], |
| exp_avg_sqs: List[Tensor], |
| state_steps: List[Tensor], |
| *, |
| beta1: float, |
| beta2: float, |
| lr: float, |
| weight_decay: float, |
| eps: float, |
| differentiable: bool): |
| |
| for i, param in enumerate(params): |
| grad = grads[i] |
| exp_avg = exp_avgs[i] |
| exp_avg_sq = exp_avg_sqs[i] |
| step_t = state_steps[i] |
| # update step |
| step_t += 1 |
| step = step_t.item() |
| |
| bias_correction1 = 1 - beta1 ** step |
| bias_correction2 = 1 - beta2 ** step |
| |
| if weight_decay != 0: |
| grad = grad.add(param, alpha=weight_decay) |
| |
| # 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) |
| |
| # correcting bias for the first moving moment |
| bias_corrected_exp_avg = exp_avg / bias_correction1 |
| |
| # maximum length of the approximated SMA |
| rho_inf = 2 / (1 - beta2) - 1 |
| # compute the length of the approximated SMA |
| rho_t = rho_inf - 2 * step * (beta2 ** step) / bias_correction2 |
| |
| if rho_t > 5.: |
| # Compute the variance rectification term and update parameters accordingly |
| rect = math.sqrt((rho_t - 4) * (rho_t - 2) * rho_inf / ((rho_inf - 4) * (rho_inf - 2) * rho_t)) |
| exp_avg_sq_sqrt = exp_avg_sq.sqrt() |
| if differentiable: |
| exp_avg_sq_sqrt = exp_avg_sq_sqrt.add(eps) |
| else: |
| exp_avg_sq_sqrt = exp_avg_sq_sqrt.add_(eps) |
| adaptive_lr = math.sqrt(bias_correction2) / exp_avg_sq_sqrt |
| param.add_(bias_corrected_exp_avg * lr * adaptive_lr * rect, alpha=-1.0) |
| else: |
| param.add_(bias_corrected_exp_avg * lr, alpha=-1.0) |
| |
| |
| def _multi_tensor_radam(params: List[Tensor], |
| grads: List[Tensor], |
| exp_avgs: List[Tensor], |
| exp_avg_sqs: List[Tensor], |
| state_steps: List[Tensor], |
| *, |
| beta1: float, |
| beta2: float, |
| lr: float, |
| weight_decay: float, |
| eps: float, |
| differentiable: bool): |
| |
| if len(params) == 0: |
| return |
| |
| assert not differentiable, "_foreach ops don't support autograd" |
| |
| # Update steps |
| torch._foreach_add_(state_steps, 1) |
| |
| # maximum length of the approximated SMA |
| rho_inf = 2 / (1 - beta2) - 1 |
| # compute the length of the approximated SMA |
| rho_t_list = [rho_inf - 2 * step.item() * (beta2 ** step.item()) / (1 - beta2 ** step.item()) for step in state_steps] |
| |
| bias_correction1 = [1 - beta1 ** step.item() for step in state_steps] |
| bias_correction2 = [1 - beta2 ** step.item() for step in state_steps] |
| 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) |
| |
| rect = [math.sqrt((rho_t - 4) * (rho_t - 2) * rho_inf / ((rho_inf - 4) * (rho_inf - 2) * rho_t)) |
| if rho_t > 5 else 0 for rho_t in rho_t_list] |
| unrectified = [0 if rect > 0 else 1. for rect in rect] |
| |
| exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs) |
| bias_correction_sqrt = [math.sqrt(bc) for bc in bias_correction2] |
| denom = torch._foreach_div(exp_avg_sq_sqrt, bias_correction_sqrt) |
| step_size = [(lr * rect / bc) * -1 for rect, bc in zip(rect, bias_correction1)] |
| torch._foreach_addcdiv_(params, exp_avgs, denom, step_size) |
| |
| denom = [torch.ones_like(exp_av, memory_format=torch.preserve_format) for exp_av in exp_avgs] |
| step_size = [(lr * rect / bc) * -1 for rect, bc in zip(unrectified, bias_correction1)] |
| torch._foreach_addcdiv_(params, exp_avgs, denom, step_size) |
