# mypy: allow-untyped-decorators # mypy: allow-untyped-defs r"""Implementation for the RAdam 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, _use_grad_for_differentiable, _view_as_real, Optimizer, ParamsT, ) __all__ = ["RAdam", "radam"] class RAdam(Optimizer): # noqa: D101 def __init__( self, params: ParamsT, lr: Union[float, Tensor] = 1e-3, betas: Tuple[float, float] = (0.9, 0.999), eps: float = 1e-8, weight_decay: float = 0, 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}") defaults = dict( lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, maximize=maximize, foreach=foreach, capturable=capturable, decoupled_weight_decay=decoupled_weight_decay, differentiable=differentiable, ) super().__init__(params, defaults) def __setstate__(self, state): # noqa: D105 super().__setstate__(state) for group in self.param_groups: group.setdefault("foreach", None) group.setdefault("maximize", False) group.setdefault("differentiable", False) group.setdefault("decoupled_weight_decay", False) group.setdefault("capturable", False) for p in group["params"]: p_state = self.state.get(p, []) if len(p_state) != 0 and 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()) ) def _init_group( self, group, params_with_grad, grads, exp_avgs, exp_avg_sqs, 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("RAdam does not support sparse gradients") grads.append(p.grad) state = self.state[p] # Lazy state initialization if len(state) == 0: state["step"] = ( torch.zeros((), dtype=_get_scalar_dtype(), device=p.device) if group["capturable"] else torch.tensor(0.0, 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"]) 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] = [] 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, state_steps ) 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"], maximize=group["maximize"], foreach=group["foreach"], capturable=group["capturable"], differentiable=group["differentiable"], decoupled_weight_decay=group["decoupled_weight_decay"], has_complex=has_complex, ) return loss RAdam.__doc__ = ( 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)}, \:\textit{maximize} \\ &\hspace{13mm} \epsilon \text{ (epsilon)}, \textit{decoupled\_weight\_decay} \\ &\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}\textbf{if} \: \textit{maximize}: \\ &\hspace{12mm}g_t \leftarrow -\nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{6mm}\textbf{else} \\ &\hspace{12mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{6mm} \theta_t \leftarrow \theta_{t-1} \\ &\hspace{6mm} \textbf{if} \: \lambda \neq 0 \\ &\hspace{12mm}\textbf{if} \: \textit{decoupled\_weight\_decay} \\ &\hspace{18mm} \theta_t \leftarrow \theta_{t} - \gamma \lambda \theta_{t} \\ &\hspace{12mm}\textbf{else} \\ &\hspace{18mm} g_t \leftarrow g_t + \lambda \theta_{t} \\ &\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 \frac{\sqrt{ (1-\beta^t_2) }}{ \sqrt{v_t} +\epsilon } \\ &\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 - \gamma \widehat{m_t} r_t l_t \\ &\hspace{6mm}\textbf{else} \\ &\hspace{12mm}\theta_t \leftarrow \theta_t - \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`_. This implementation provides an option to use either the original weight_decay implementation as in Adam (where the weight_decay is applied to the gradient) or the one from AdamW (where weight_decay is applied to the weight) through the decoupled_weight_decay option. When decoupled_weight_decay is set to False (default), it uses the original Adam style weight decay, otherwise, it uses the AdamW style which corresponds more closely to the `author's implementation`_ in the RAdam paper. Further information about decoupled weight decay can be found in `Decoupled Weight Decay Regularization`_. """ + rf""" Args: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float, Tensor, 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) decoupled_weight_decay (bool, optional): whether to use decoupled weight decay as in AdamW to obtain RAdamW (default: False) {_foreach_doc} {_maximize_doc} {_differentiable_doc} {_capturable_doc} .. _On the variance of the adaptive learning rate and beyond: https://arxiv.org/abs/1908.03265 .. _author's implementation: https://github.com/LiyuanLucasLiu/RAdam .. _Decoupled Weight Decay Regularization: https://arxiv.org/abs/1711.05101 """ ) 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, decoupled_weight_decay: bool, differentiable: bool, maximize: bool, capturable: 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] step_t = state_steps[i] # 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 == step_t.device.type and param.device.type in capturable_supported_devices ), f"If capturable=True, params and state_steps must be on supported devices: {capturable_supported_devices}." 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) # update step step_t += 1 step = step_t if capturable else _get_value(step_t) if weight_decay != 0: if decoupled_weight_decay: param.mul_(1 - lr * weight_decay) else: grad = grad.add(param, alpha=weight_decay) # 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) bias_correction1 = 1 - beta1**step bias_correction2 = 1 - beta2**step # 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 def _compute_rect(): return ( (rho_t - 4) * (rho_t - 2) * rho_inf / ((rho_inf - 4) * (rho_inf - 2) * rho_t) ) ** 0.5 def _compute_adaptive_lr(): 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) return (bias_correction2**0.5) / exp_avg_sq_sqrt # Compute the variance rectification term and update parameters accordingly if capturable: update = torch.where( rho_t > 5.0, _compute_rect() * _compute_adaptive_lr(), 1.0 ) param.add_(bias_corrected_exp_avg * lr * update, alpha=-1.0) else: if rho_t > 5.0: param.add_( bias_corrected_exp_avg * lr * _compute_adaptive_lr() * _compute_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, decoupled_weight_decay: bool, differentiable: bool, maximize: bool, capturable: 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 == step.device.type and p.device.type in capturable_supported_devices for p, step in zip(params, state_steps) ), f"If capturable=True, params 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, state_steps] # type: ignore[list-item] ) for ( grouped_params_, grouped_grads_, grouped_exp_avgs_, grouped_exp_avg_sqs_, 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_state_steps = cast(List[Tensor], grouped_state_steps_) # 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 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] # maximum length of the approximated SMA rho_inf = 2 / (1 - beta2) - 1 # compute the length of the approximated SMA bias_correction1: Union[Tuple[Tensor, ...], List[Tensor]] bias_correction2: Union[Tuple[Tensor, ...], List[Tensor]] rho_t_list: Union[Tuple[Tensor, ...], List[Tensor]] if capturable: bias_correction1 = torch._foreach_pow(beta2, grouped_state_steps) torch._foreach_neg_(bias_correction1) torch._foreach_add_(bias_correction1, 1) bias_correction2 = torch._foreach_pow(beta2, grouped_state_steps) torch._foreach_mul_(bias_correction2, grouped_state_steps) torch._foreach_mul_(bias_correction2, 2) torch._foreach_div_(bias_correction2, bias_correction1) torch._foreach_neg_(bias_correction2) torch._foreach_add_(bias_correction2, rho_inf) rho_t_list = bias_correction2 else: rho_t_list = [ rho_inf - 2 * _get_value(step) * (beta2 ** _get_value(step)) / (1 - beta2 ** _get_value(step)) for step in grouped_state_steps ] if weight_decay != 0: if decoupled_weight_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 ) # Delete the local intermediate since it won't be used anymore to save on peak memory del grouped_grads if capturable: num = torch._foreach_sub(rho_t_list, 4) sub2 = torch._foreach_sub(rho_t_list, 2) torch._foreach_mul_(num, sub2) del sub2 torch._foreach_mul_(num, rho_inf) rho_inf = (rho_inf - 4) * (rho_inf - 2) denom = torch._foreach_mul(rho_t_list, rho_inf) torch._foreach_div_(num, denom) del denom torch._foreach_sqrt_(num) # TODO(mlazos): we should try and get a foreach_where op https://github.com/pytorch/pytorch/issues/117884 rect = [ torch.where(rho_t > 5.0, n, 0.0) for n, rho_t in zip(num, rho_t_list) ] del num del rho_t_list unrect_step_size = [torch.where(rect > 0, 0.0, 1.0) for rect in rect] torch._foreach_mul_(unrect_step_size, lr) bias_correction1 = torch._foreach_pow(beta1, grouped_state_steps) torch._foreach_neg_(bias_correction1) torch._foreach_add_(bias_correction1, 1) torch._foreach_div_(unrect_step_size, bias_correction1) torch._foreach_neg_(unrect_step_size) bias_correction2 = torch._foreach_pow(beta2, grouped_state_steps) torch._foreach_neg_(bias_correction2) torch._foreach_add_(bias_correction2, 1) torch._foreach_sqrt_(bias_correction2) torch._foreach_mul_(bias_correction2, lr) torch._foreach_mul_(bias_correction2, rect) del rect torch._foreach_neg_(bias_correction2) torch._foreach_div_(bias_correction2, bias_correction1) del bias_correction1 else: rect = [ ( (rho_t - 4) # type: ignore[arg-type] * (rho_t - 2) * rho_inf / ((rho_inf - 4) * (rho_inf - 2) * rho_t) ) ** 0.5 if rho_t > 5 else 0 for rho_t in rho_t_list ] unrectified = [0 if rect > 0 else 1.0 for rect in rect] bias_correction1 = [ 1 - beta1 ** _get_value(step) for step in grouped_state_steps ] unrect_step_size = [ (lr * rect / bc) * -1 for rect, bc in zip(unrectified, bias_correction1) ] bias_correction2 = [ ((1 - beta2 ** _get_value(step)) ** 0.5) * (lr * rect / bc) * -1 for step, rect, bc in zip(grouped_state_steps, rect, bias_correction1) ] buffer = torch._foreach_sqrt(grouped_exp_avg_sqs) torch._foreach_add_(buffer, eps) torch._foreach_div_(buffer, bias_correction2) torch._foreach_reciprocal_(buffer) torch._foreach_add_(buffer, unrect_step_size) # Here, buffer = sqrt(1 - beta2^t) * rect_step_size / (sqrt(v) + eps) + unrect_step_size torch._foreach_addcmul_(grouped_params, grouped_exp_avgs, buffer) @_disable_dynamo_if_unsupported(single_tensor_fn=_single_tensor_radam) 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 decoupled_weight_decay: bool = False, foreach: Optional[bool] = None, differentiable: bool = False, capturable: bool = False, has_complex: bool = False, maximize: 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: _, 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_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, maximize=maximize, decoupled_weight_decay=decoupled_weight_decay, differentiable=differentiable, capturable=capturable, has_complex=has_complex, )