# mypy: allow-untyped-decorators # mypy: allow-untyped-defs r"""Implementation for the NAdam algorithm.""" from typing import cast, List, Optional, Tuple, Union import torch from torch import Tensor from .optimizer import ( _capturable_doc, _default_to_fused_or_foreach, _differentiable_doc, _disable_dynamo_if_unsupported, _foreach_doc, _get_capturable_supported_devices, _get_scalar_dtype, _get_value, _maximize_doc, _stack_if_compiling, _use_grad_for_differentiable, _view_as_real, Optimizer, ParamsT, ) __all__ = ["NAdam", "nadam"] class NAdam(Optimizer): # noqa: D101 def __init__( self, params: ParamsT, lr: Union[float, Tensor] = 2e-3, betas: Tuple[float, float] = (0.9, 0.999), eps: float = 1e-8, weight_decay: float = 0, momentum_decay: float = 4e-3, decoupled_weight_decay: bool = False, *, foreach: Optional[bool] = None, maximize: bool = False, capturable: bool = False, differentiable: bool = False, ): # noqa: D107 if isinstance(lr, Tensor) and lr.numel() != 1: raise ValueError("Tensor lr must be 1-element") if not 0.0 <= lr: raise ValueError(f"Invalid learning rate: {lr}") if not 0.0 <= eps: raise ValueError(f"Invalid epsilon value: {eps}") if not 0.0 <= betas[0] < 1.0: raise ValueError(f"Invalid beta parameter at index 0: {betas[0]}") if not 0.0 <= betas[1] < 1.0: raise ValueError(f"Invalid beta parameter at index 1: {betas[1]}") if not 0.0 <= weight_decay: raise ValueError(f"Invalid weight_decay value: {weight_decay}") if not 0.0 <= momentum_decay: raise ValueError(f"Invalid momentum_decay value: {momentum_decay}") defaults = dict( lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, momentum_decay=momentum_decay, decoupled_weight_decay=decoupled_weight_decay, maximize=maximize, foreach=foreach, capturable=capturable, differentiable=differentiable, ) super().__init__(params, defaults) def __setstate__(self, state): # noqa: D105 super().__setstate__(state) for group in self.param_groups: group.setdefault("maximize", False) group.setdefault("foreach", None) group.setdefault("capturable", False) group.setdefault("differentiable", False) group.setdefault("decoupled_weight_decay", False) for p in group["params"]: p_state = self.state.get(p, []) if len(p_state) != 0: if not torch.is_tensor(p_state["step"]): step_val = float(p_state["step"]) p_state["step"] = ( torch.tensor( step_val, dtype=_get_scalar_dtype(), device=p.device ) if group["capturable"] else torch.tensor(step_val, dtype=_get_scalar_dtype()) ) if not torch.is_tensor(p_state["mu_product"]): mu_prod_val = p_state["mu_product"] p_state["mu_product"] = ( torch.tensor( mu_prod_val, dtype=_get_scalar_dtype(), device=p.device ) if group["capturable"] else torch.tensor(mu_prod_val, dtype=_get_scalar_dtype()) ) def _init_group( self, group, params_with_grad, grads, exp_avgs, exp_avg_sqs, mu_products, state_steps, ): has_complex = False for p in group["params"]: if p.grad is not None: has_complex |= torch.is_complex(p) 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: # note(crcrpar): [special device hosting for step] # Deliberately host `step` and `mu_product` on CPU if capturable is False. # This is because kernel launches are costly on CUDA and XLA. state["step"] = ( torch.zeros((), dtype=_get_scalar_dtype(), device=p.device) if group["capturable"] else torch.tensor(0.0, dtype=_get_scalar_dtype()) ) state["mu_product"] = ( torch.ones((), dtype=_get_scalar_dtype(), device=p.device) if group["capturable"] else torch.tensor(1.0, dtype=_get_scalar_dtype()) ) # 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"]) return has_complex @_use_grad_for_differentiable def step(self, closure=None): """Perform 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: List[Tensor] = [] grads: List[Tensor] = [] exp_avgs: List[Tensor] = [] exp_avg_sqs: List[Tensor] = [] mu_products: List[Tensor] = [] state_steps: List[Tensor] = [] beta1, beta2 = cast(Tuple[float, float], group["betas"]) has_complex = self._init_group( group, params_with_grad, grads, exp_avgs, exp_avg_sqs, mu_products, state_steps, ) 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"], maximize=group["maximize"], decoupled_weight_decay=group["decoupled_weight_decay"], foreach=group["foreach"], capturable=group["capturable"], differentiable=group["differentiable"], has_complex=has_complex, ) return loss NAdam.__doc__ = ( 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)} \\ &\hspace{13mm} \: \textit{decoupled\_weight\_decay}, \:\textit{maximize} \\ &\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}\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} \\ &\hspace{5mm} \textbf{if} \: \lambda \neq 0 \\ &\hspace{10mm}\textbf{if} \: \textit{decoupled\_weight\_decay} \\ &\hspace{15mm} \theta_t \leftarrow \theta_{t-1} - \gamma \lambda \theta_{t-1} \\ &\hspace{10mm}\textbf{else} \\ &\hspace{15mm} 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 - \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`_. """ + rf""" Args: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float, Tensor, 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) decoupled_weight_decay (bool, optional): whether to use decoupled weight decay as in AdamW to obtain NAdamW (default: False) {_foreach_doc} {_maximize_doc} {_capturable_doc} {_differentiable_doc} .. _Incorporating Nesterov Momentum into Adam: https://openreview.net/forum?id=OM0jvwB8jIp57ZJjtNEZ .. _Decoupled Weight Decay Regularization: https://arxiv.org/abs/1711.05101 """ ) 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, decoupled_weight_decay: bool, maximize: bool, capturable: bool, differentiable: bool, has_complex: 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] mu_product = mu_products[i] step_t = state_steps[i] if torch.is_complex(param): param = torch.view_as_real(param) grad = torch.view_as_real(grad) exp_avg = torch.view_as_real(exp_avg) exp_avg_sq = torch.view_as_real(exp_avg_sq) # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable] if not torch._utils.is_compiling() and capturable: capturable_supported_devices = _get_capturable_supported_devices() assert ( param.device.type == mu_product.device.type == step_t.device.type and param.device.type in capturable_supported_devices ), ( f"If capturable=True, params, mu_products and state_steps must be " f"on supported devices: {capturable_supported_devices}." ) # update step step_t += 1 if capturable: step = step_t else: step = _get_value(step_t) bias_correction2 = 1 - beta2**step if weight_decay != 0: if decoupled_weight_decay: # Perform stepweight decay param.mul_(1 - lr * weight_decay) else: grad = grad.add(param, alpha=weight_decay) # calculate the momentum cache \mu^{t} and \mu^{t+1} mu = beta1 * (1.0 - 0.5 * (0.96 ** (step * momentum_decay))) mu_next = beta1 * (1.0 - 0.5 * (0.96 ** ((step + 1) * momentum_decay))) # update mu_product mu_product *= mu # decay the first and second moment running average coefficient exp_avg.lerp_(grad, 1 - beta1) exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2) denom = exp_avg_sq.div(bias_correction2).sqrt() if differentiable or capturable: denom = denom.add(eps) # Make autograd track the operations # by updating the grad and exp_avg directly and not using the # scalar "value" argument of addcdiv. mu_product_next = mu_product * mu_next grad = grad * (-lr * (1.0 - mu) / (1.0 - mu_product)) exp_avg = exp_avg * (-lr * mu_next / (1.0 - mu_product_next)) param.addcdiv_(grad, denom) param.addcdiv_(exp_avg, denom) else: mu_product_next = _get_value(mu_product) * mu_next denom.add_(eps) param.addcdiv_( grad, denom, value=(-lr * (1.0 - mu) / (1.0 - _get_value(mu_product))) ) param.addcdiv_( exp_avg, denom, value=(-lr * mu_next) / (1.0 - mu_product_next) ) 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, decoupled_weight_decay: bool, maximize: bool, capturable: bool, differentiable: bool, has_complex: bool, ): if len(params) == 0: return assert not differentiable, "_foreach ops don't support autograd" # If compiling, the compiler will handle cudagraph checks, see note [torch.compile x capturable] if not torch._utils.is_compiling() and capturable: capturable_supported_devices = _get_capturable_supported_devices( supports_xla=False ) assert all( p.device.type == mp.device.type == step.device.type and p.device.type in capturable_supported_devices for p, mp, step in zip(params, mu_products, state_steps) ), f"If capturable=True, params, mu_products, and state_steps must be on supported devices: {capturable_supported_devices}." grouped_tensors = Optimizer._group_tensors_by_device_and_dtype( [params, grads, exp_avgs, exp_avg_sqs, mu_products, state_steps] # type: ignore[list-item] ) for ( grouped_params_, grouped_grads_, grouped_exp_avgs_, grouped_exp_avg_sqs_, grouped_mu_products_, grouped_state_steps_, ), _ in grouped_tensors.values(): grouped_params = cast(List[Tensor], grouped_params_) grouped_grads = cast(List[Tensor], grouped_grads_) grouped_exp_avgs = cast(List[Tensor], grouped_exp_avgs_) grouped_exp_avg_sqs = cast(List[Tensor], grouped_exp_avg_sqs_) grouped_mu_products = cast(List[Tensor], grouped_mu_products_) grouped_state_steps = cast(List[Tensor], grouped_state_steps_) # handle complex if has_complex: _view_as_real( grouped_params, grouped_grads, grouped_exp_avgs, grouped_exp_avg_sqs ) if maximize: grouped_grads = torch._foreach_neg(grouped_grads) # type: ignore[assignment] # Update steps # If steps are on CPU, foreach will fall back to the slow path, which is a for-loop calling t.add(1) over # and over. 1 will then be wrapped into a Tensor over and over again, which is slower than if we just # wrapped it once now. The alpha is required to assure we go to the right overload. if not torch._utils.is_compiling() and grouped_state_steps[0].is_cpu: torch._foreach_add_( grouped_state_steps, torch.tensor(1.0, device="cpu"), alpha=1.0 ) else: torch._foreach_add_(grouped_state_steps, 1) if weight_decay != 0: if decoupled_weight_decay: # Perform stepweight decay torch._foreach_mul_(grouped_params, 1 - lr * weight_decay) else: # Re-use the intermediate memory (grouped_grads) already allocated for maximize if maximize: torch._foreach_add_( grouped_grads, grouped_params, alpha=weight_decay ) else: grouped_grads = torch._foreach_add( # type: ignore[assignment] grouped_grads, grouped_params, alpha=weight_decay ) # Decay the first and second moment running average coefficient torch._foreach_lerp_(grouped_exp_avgs, grouped_grads, 1 - beta1) torch._foreach_mul_(grouped_exp_avg_sqs, beta2) torch._foreach_addcmul_( grouped_exp_avg_sqs, grouped_grads, grouped_grads, 1 - beta2 ) exp_avg_sq_sqrt = torch._foreach_sqrt(grouped_exp_avg_sqs) bias_correction_sqrt: Union[Tuple[Tensor, ...], List[Tensor]] mus: Union[Tuple[Tensor, ...], List[Tensor]] mu_nexts: Union[Tuple[Tensor, ...], List[Tensor]] if capturable: # mus will be beta1 * (1 - 0.5 * 0.96 ** (step * momentum_decay)) exponent = torch._foreach_mul(grouped_state_steps, momentum_decay) mus = torch._foreach_pow(0.96, exponent) torch._foreach_mul_(mus, -0.5) torch._foreach_add_(mus, 1.0) torch._foreach_mul_(mus, beta1) # mu_nexts will be beta1 * (1 - 0.5 * 0.96 ** ((step + 1) * momentum_decay)) torch._foreach_add_(exponent, momentum_decay) mu_nexts = torch._foreach_pow(0.96, exponent) torch._foreach_mul_(mu_nexts, -0.5) torch._foreach_add_(mu_nexts, 1.0) torch._foreach_mul_(mu_nexts, beta1) # save peak memory as we don't need exponent anymore del exponent bias_correction_sqrt = torch._foreach_pow(beta2, grouped_state_steps) # foreach_sub doesn't allow a scalar as the first arg torch._foreach_sub_(bias_correction_sqrt, 1.0) torch._foreach_neg_(bias_correction_sqrt) torch._foreach_sqrt_(bias_correction_sqrt) else: bias_correction_sqrt = [ (1 - beta2 ** _get_value(step)) ** 0.5 for step in grouped_state_steps ] mus = [ beta1 * (1.0 - 0.5 * (0.96 ** (_get_value(step) * momentum_decay))) for step in grouped_state_steps ] mu_nexts = [ beta1 * (1.0 - 0.5 * (0.96 ** ((_get_value(step) + 1) * momentum_decay))) for step in grouped_state_steps ] # update mu_products torch._foreach_mul_(grouped_mu_products, mus) torch._foreach_div_(exp_avg_sq_sqrt, bias_correction_sqrt) torch._foreach_add_(exp_avg_sq_sqrt, eps) # explicitly delete bias_correction refs to save memory del bias_correction_sqrt if capturable: # Build up the step_size multiplier for grad, reusing mus' memory torch._foreach_sub_(mus, 1.0) torch._foreach_mul_(mus, lr) # foreach_sub doesn't allow a scalar as the first arg denom = torch._foreach_sub(grouped_mu_products, 1.0) torch._foreach_neg_(denom) torch._foreach_div_(mus, denom) # - lr * (1 - mu) / (1 - mu_product) step_size_grads = mus # explicitly delete denom to save memory del denom # Build up the step_size multiplier for exp_avg, reusing mu_nexts' memory denom = torch._foreach_mul(grouped_mu_products, mu_nexts) torch._foreach_mul_(mu_nexts, lr) # foreach_sub doesn't allow a scalar as the first arg, but it's okay because # we need a negative here anyway torch._foreach_sub_(denom, 1.0) torch._foreach_div_(mu_nexts, denom) # - lr * mu_next / (1 - mu_product * mu_next) step_size_expavg = mu_nexts # explicitly delete denom to save memory del denom # we cannot inplace into step_size_grads cuz it is a list of ScalarTensors # and mul'ing with grouped_grads will result in a list of bigger Tensors numerator = torch._foreach_mul(step_size_grads, grouped_grads) torch._foreach_addcmul_(numerator, step_size_expavg, grouped_exp_avgs) # finally, update params torch._foreach_addcdiv_(grouped_params, numerator, exp_avg_sq_sqrt) else: step_size_grads = _stack_if_compiling( [ (_get_value(lr) * (1.0 - mu) / (1.0 - _get_value(mu_product))) * -1 for mu_product, mu in zip(grouped_mu_products, mus) ] ) step_size_expavg = _stack_if_compiling( [ ( _get_value(lr) * mu_next / (1.0 - _get_value(mu_product) * mu_next) ) * -1 for mu_product, mu_next in zip(grouped_mu_products, mu_nexts) ] ) torch._foreach_addcdiv_( grouped_params, grouped_grads, exp_avg_sq_sqrt, step_size_grads # type: ignore[arg-type] ) torch._foreach_addcdiv_( grouped_params, grouped_exp_avgs, exp_avg_sq_sqrt, step_size_expavg # type: ignore[arg-type] ) @_disable_dynamo_if_unsupported(single_tensor_fn=_single_tensor_nadam) 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 decoupled_weight_decay: bool = False, foreach: Optional[bool] = None, capturable: bool = False, differentiable: bool = False, has_complex: bool = False, maximize: bool = False, *, 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: _, foreach = _default_to_fused_or_foreach( params, differentiable, use_fused=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, maximize=maximize, decoupled_weight_decay=decoupled_weight_decay, eps=eps, capturable=capturable, differentiable=differentiable, has_complex=has_complex, )