import math import torch from torch import Tensor from .optimizer import Optimizer from typing import List, Optional class AdamW(Optimizer): r"""Implements AdamW 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)}, \: \epsilon \text{ (epsilon)} \\ &\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} \theta_t \leftarrow \theta_{t-1} - \gamma \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 - \gamma \widehat{m_t}/ \big(\sqrt{\widehat{v_t}^{max}} + \epsilon \big) \\ &\hspace{5mm}\textbf{else} \\ &\hspace{10mm}\theta_t \leftarrow \theta_t - \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 `Decoupled Weight Decay Regularization`_. 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 coefficient (default: 1e-2) 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) foreach (bool, optional): whether foreach implementation of optimizer is used (default: None) capturable (bool, optional): whether this instance is safe to capture in a CUDA graph. Passing True can impair ungraphed performance, so if you don't intend to graph capture this instance, leave it False (default: False) .. _Decoupled Weight Decay Regularization: https://arxiv.org/abs/1711.05101 .. _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=1e-2, amsgrad=False, *, maximize: bool = False, foreach: Optional[bool] = None, capturable: 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, foreach=foreach, maximize=maximize, capturable=capturable) super(AdamW, self).__init__(params, defaults) def __setstate__(self, state): super().__setstate__(state) for group in self.param_groups: group.setdefault('amsgrad', False) group.setdefault('maximize', False) group.setdefault('foreach', None) group.setdefault('capturable', 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'])) @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. """ self._cuda_graph_capture_health_check() 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 = [] amsgrad = group['amsgrad'] beta1, beta2 = group['betas'] for p in group['params']: if p.grad is None: continue params_with_grad.append(p) if p.grad.is_sparse: raise RuntimeError('AdamW does not support sparse gradients') grads.append(p.grad) state = self.state[p] # State initialization if len(state) == 0: state['step'] = torch.zeros((1,), dtype=torch.float, device=p.device) \ if self.defaults['capturable'] else 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) if 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 amsgrad: max_exp_avg_sqs.append(state['max_exp_avg_sq']) state_steps.append(state['step']) adamw(params_with_grad, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps, amsgrad=amsgrad, beta1=beta1, beta2=beta2, lr=group['lr'], weight_decay=group['weight_decay'], eps=group['eps'], maximize=group['maximize'], foreach=group['foreach'], capturable=group['capturable']) return loss def adamw(params: List[Tensor], grads: List[Tensor], exp_avgs: List[Tensor], exp_avg_sqs: List[Tensor], max_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, capturable: bool = False, *, amsgrad: bool, beta1: float, beta2: float, lr: float, weight_decay: float, eps: float, maximize: bool): r"""Functional API that performs AdamW algorithm computation. See :class:`~torch.optim.AdamW` 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_adamw else: func = _single_tensor_adamw func(params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps, amsgrad=amsgrad, beta1=beta1, beta2=beta2, lr=lr, weight_decay=weight_decay, eps=eps, maximize=maximize, capturable=capturable) def _single_tensor_adamw(params: List[Tensor], grads: List[Tensor], exp_avgs: List[Tensor], exp_avg_sqs: List[Tensor], max_exp_avg_sqs: List[Tensor], state_steps: List[Tensor], *, amsgrad: bool, beta1: float, beta2: float, lr: float, weight_decay: float, eps: float, maximize: bool, capturable: bool): for i, param in enumerate(params): grad = grads[i] if not maximize else -grads[i] exp_avg = exp_avgs[i] exp_avg_sq = exp_avg_sqs[i] step_t = state_steps[i] if capturable: assert param.is_cuda and step_t.is_cuda, "If capturable=True, params and state_steps must be CUDA tensors." # update step step_t += 1 # Perform stepweight decay param.mul_(1 - lr * 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) if capturable: step = step_t # 1 - beta1 ** step can't be captured in a CUDA graph, even if step is a CUDA tensor # (incurs "RuntimeError: CUDA error: operation not permitted when stream is capturing") bias_correction1 = 1 - torch.pow(beta1, step) bias_correction2 = 1 - torch.pow(beta2, step) step_size = lr / bias_correction1 step_size_neg = step_size.neg() bias_correction2_sqrt = bias_correction2.sqrt() if amsgrad: # Maintains the maximum of all 2nd moment running avg. till now torch.maximum(max_exp_avg_sqs[i], exp_avg_sq, out=max_exp_avg_sqs[i]) # Uses the max. for normalizing running avg. of gradient # Folds in (admittedly ugly) 1-elem step_size math here to avoid extra param-set-sized read+write # (can't fold it into addcdiv_ below because addcdiv_ requires value is a Number, not a Tensor) denom = (max_exp_avg_sqs[i].sqrt() / (bias_correction2_sqrt * step_size_neg)).add_(eps / step_size_neg) else: denom = (exp_avg_sq.sqrt() / (bias_correction2_sqrt * step_size_neg)).add_(eps / step_size_neg) param.addcdiv_(exp_avg, denom) else: step = step_t.item() bias_correction1 = 1 - beta1 ** step bias_correction2 = 1 - beta2 ** step step_size = lr / bias_correction1 bias_correction2_sqrt = math.sqrt(bias_correction2) if amsgrad: # Maintains the maximum of all 2nd moment running avg. till now torch.maximum(max_exp_avg_sqs[i], exp_avg_sq, out=max_exp_avg_sqs[i]) # Use the max. for normalizing running avg. of gradient denom = (max_exp_avg_sqs[i].sqrt() / bias_correction2_sqrt).add_(eps) else: denom = (exp_avg_sq.sqrt() / bias_correction2_sqrt).add_(eps) param.addcdiv_(exp_avg, denom, value=-step_size) def _multi_tensor_adamw(params: List[Tensor], grads: List[Tensor], exp_avgs: List[Tensor], exp_avg_sqs: List[Tensor], max_exp_avg_sqs: List[Tensor], state_steps: List[Tensor], *, amsgrad: bool, beta1: float, beta2: float, lr: float, weight_decay: float, eps: float, maximize: bool, capturable: bool): if len(params) == 0: return if capturable: assert all(p.is_cuda and step.is_cuda for p, step in zip(params, state_steps)), \ "If capturable=True, params and state_steps must be CUDA tensors." if maximize: grads = torch._foreach_neg(tuple(grads)) # type: ignore[assignment] # update steps torch._foreach_add_(state_steps, 1) # Perform stepweight decay torch._foreach_mul_(params, 1 - lr * 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) if capturable: # TODO: use foreach_pow if/when foreach_pow is added bias_correction1 = [torch.pow(beta1, step) for step in state_steps] bias_correction2 = [torch.pow(beta2, step) for step in state_steps] # foreach_sub doesn't allow a scalar as the first arg torch._foreach_sub_(bias_correction1, 1) torch._foreach_sub_(bias_correction2, 1) torch._foreach_neg_(bias_correction1) torch._foreach_neg_(bias_correction2) # foreach_div doesn't allow a scalar as the first arg step_size = torch._foreach_div(bias_correction1, lr) torch._foreach_reciprocal_(step_size) torch._foreach_neg_(step_size) bias_correction2_sqrt = torch._foreach_sqrt(bias_correction2) if amsgrad: # Maintains the maximum of all 2nd moment running avg. till now max_exp_avg_sqs = torch._foreach_maximum(max_exp_avg_sqs, exp_avg_sqs) # type: ignore[assignment] # Use the max. for normalizing running avg. of gradient max_exp_avg_sq_sqrt = torch._foreach_sqrt(max_exp_avg_sqs) # Folds in (admittedly ugly) 1-elem step_size math here to avoid extra param-set-sized read+write # (can't fold it into addcdiv_ below because addcdiv_ requires value is a Number, not a Tensor) torch._foreach_div_(max_exp_avg_sq_sqrt, torch._foreach_mul(bias_correction2_sqrt, step_size)) eps_over_step_size = torch._foreach_div(step_size, eps) torch._foreach_reciprocal_(eps_over_step_size) denom = torch._foreach_add(max_exp_avg_sq_sqrt, eps_over_step_size) else: exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs) torch._foreach_div_(exp_avg_sq_sqrt, torch._foreach_mul(bias_correction2_sqrt, step_size)) eps_over_step_size = torch._foreach_div(step_size, eps) torch._foreach_reciprocal_(eps_over_step_size) denom = torch._foreach_add(exp_avg_sq_sqrt, eps_over_step_size) torch._foreach_addcdiv_(params, exp_avgs, denom) else: bias_correction1 = [1 - beta1 ** step.item() for step in state_steps] bias_correction2 = [1 - beta2 ** step.item() for step in state_steps] step_size = [(lr / bc) * -1 for bc in bias_correction1] bias_correction2_sqrt = [math.sqrt(bc) for bc in bias_correction2] if amsgrad: # Maintains the maximum of all 2nd moment running avg. till now max_exp_avg_sqs = torch._foreach_maximum(max_exp_avg_sqs, exp_avg_sqs) # type: ignore[assignment] # Use the max. for normalizing running avg. of gradient max_exp_avg_sq_sqrt = torch._foreach_sqrt(max_exp_avg_sqs) torch._foreach_div_(max_exp_avg_sq_sqrt, bias_correction2_sqrt) denom = torch._foreach_add(max_exp_avg_sq_sqrt, eps) else: exp_avg_sq_sqrt = torch._foreach_sqrt(exp_avg_sqs) torch._foreach_div_(exp_avg_sq_sqrt, bias_correction2_sqrt) denom = torch._foreach_add(exp_avg_sq_sqrt, eps) torch._foreach_addcdiv_(params, exp_avgs, denom, step_size)