Source code for torch.optim.adam

from typing import List, Optional

import torch
from torch import Tensor
from .optimizer import (Optimizer, _use_grad_for_differentiable, _get_value, _stack_if_compiling,
                        _dispatch_sqrt, _default_to_fused_or_foreach, _capturable_doc,
                        _differentiable_doc, _foreach_doc, _fused_doc, _maximize_doc)
from torch.utils._foreach_utils import _group_tensors_by_device_and_dtype

__all__ = ['Adam', 'adam']


class Adam(Optimizer):
    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0, amsgrad=False, *, foreach: Optional[bool] = None,
                 maximize: bool = False, capturable: bool = False,
                 differentiable: bool = False, fused: 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))

        defaults = dict(lr=lr, betas=betas, eps=eps,
                        weight_decay=weight_decay, amsgrad=amsgrad,
                        maximize=maximize, foreach=foreach, capturable=capturable,
                        differentiable=differentiable, fused=fused)
        super().__init__(params, defaults)

        if fused:
            if differentiable:
                raise RuntimeError("`fused` does not support `differentiable`")
            self._step_supports_amp_scaling = True
            # TODO(crcrpar): [low prec params & their higher prec copy]
            # Suppor AMP with FP16/BF16 model params which would need
            # higher prec copy of params to do update math in higher prec to
            # alleviate the loss of information.
            if not all(
                p.is_cuda and torch.is_floating_point(p)
                for pg in self.param_groups for p in pg['params']
            ):
                raise RuntimeError("`fused=True` requires all the params to be CUDA, floating point Tensor")
            if foreach:
                raise RuntimeError("`fused` and `foreach` cannot be `True` together.")

    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)
            group.setdefault('differentiable', False)
            group.setdefault('fused', 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']))

    def _init_group(
        self,
        group,
        params_with_grad,
        grads,
        exp_avgs,
        exp_avg_sqs,
        max_exp_avg_sqs,
        state_steps
    ):
        for p in group['params']:
            if p.grad is not None:
                params_with_grad.append(p)
                if p.grad.is_sparse:
                    raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
                grads.append(p.grad)

                state = self.state[p]
                # Lazy state initialization
                if len(state) == 0:
                    state['step'] = (
                        torch.zeros((1,), dtype=torch.float, device=p.device)
                        if group['capturable'] or group['fused']
                        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 group['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 group['amsgrad']:
                    max_exp_avg_sqs.append(state['max_exp_avg_sq'])
                if group['differentiable'] and state['step'].requires_grad:
                    raise RuntimeError('`requires_grad` is not supported for `step` in differentiable mode')
                state_steps.append(state['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.
        """
        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 = []
            beta1, beta2 = group['betas']

            self._init_group(
                group,
                params_with_grad,
                grads,
                exp_avgs,
                exp_avg_sqs,
                max_exp_avg_sqs,
                state_steps)

            adam(
                params_with_grad,
                grads,
                exp_avgs,
                exp_avg_sqs,
                max_exp_avg_sqs,
                state_steps,
                amsgrad=group['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'],
                differentiable=group['differentiable'],
                fused=group['fused'],
                grad_scale=getattr(self, "grad_scale", None),
                found_inf=getattr(self, "found_inf", None),
            )

        return loss


Adam.__doc__ = r"""Implements Adam 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)}          \\
            &\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}\textbf{if} \: \lambda \neq 0                                           \\
            &\hspace{10mm} g_t \leftarrow g_t + \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-1} - \gamma \widehat{m_t}/
                \big(\sqrt{\widehat{v_t}^{max}} + \epsilon \big)                                 \\
            &\hspace{5mm}\textbf{else}                                                           \\
            &\hspace{10mm}\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 `Adam: A Method for Stochastic Optimization`_.
    """ + r"""
    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)
        amsgrad (bool, optional): whether to use the AMSGrad variant of this
            algorithm from the paper `On the Convergence of Adam and Beyond`_
            (default: False)
        {foreach}
        {maximize}
        {capturable}
        {differentiable}
        {fused}
    .. _Adam\: A Method for Stochastic Optimization:
        https://arxiv.org/abs/1412.6980
    .. _On the Convergence of Adam and Beyond:
        https://openreview.net/forum?id=ryQu7f-RZ

    """.format(foreach=_foreach_doc, maximize=_maximize_doc, capturable=_capturable_doc,
               differentiable=_differentiable_doc, fused=_fused_doc)


def adam(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: Optional[bool] = None,
         capturable: bool = False,
         differentiable: bool = False,
         fused: Optional[bool] = None,
         grad_scale: Optional[Tensor] = None,
         found_inf: Optional[Tensor] = None,
         *,
         amsgrad: bool,
         beta1: float,
         beta2: float,
         lr: float,
         weight_decay: float,
         eps: float,
         maximize: bool):
    r"""Functional API that performs Adam algorithm computation.
    See :class:`~torch.optim.Adam` for details.
    """

    # Respect when the user inputs False/True for foreach or fused. We only want to change
    # the default when neither have been user-specified. Note that we default to foreach
    # and pass False to use_fused. This is not a mistake--we want to give the fused impl
    # bake-in time before making it the default, even if it is typically faster.
    if fused is None and foreach is None:
        _, foreach = _default_to_fused_or_foreach(params, differentiable, use_fused=False)
    if fused is None:
        fused = False
    if foreach is None:
        foreach = False

    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 and torch.jit.is_scripting():
        raise RuntimeError('torch.jit.script not supported with foreach optimizers')

    if fused and not torch.jit.is_scripting():
        func = _fused_adam
    elif foreach and not torch.jit.is_scripting():
        func = _multi_tensor_adam
    else:
        func = _single_tensor_adam

    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,
         differentiable=differentiable,
         grad_scale=grad_scale,
         found_inf=found_inf)


def _single_tensor_adam(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],
                        grad_scale: Optional[Tensor],
                        found_inf: Optional[Tensor],
                        *,
                        amsgrad: bool,
                        beta1: float,
                        beta2: float,
                        lr: float,
                        weight_decay: float,
                        eps: float,
                        maximize: bool,
                        capturable: bool,
                        differentiable: bool):

    assert grad_scale is None and found_inf is None

    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

        if weight_decay != 0:
            grad = grad.add(param, alpha=weight_decay)

        if torch.is_complex(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)
            param = torch.view_as_real(param)

        # 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.conj(), value=1 - beta2)

        if capturable or differentiable:
            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
                if differentiable:
                    max_exp_avg_sqs_i = max_exp_avg_sqs[i].clone()
                else:
                    max_exp_avg_sqs_i = max_exp_avg_sqs[i]
                max_exp_avg_sqs[i].copy_(torch.maximum(max_exp_avg_sqs_i, exp_avg_sq))
                # 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 = _get_value(step_t)

            bias_correction1 = 1 - beta1 ** step
            bias_correction2 = 1 - beta2 ** step

            step_size = lr / bias_correction1

            bias_correction2_sqrt = _dispatch_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_adam(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],
                       grad_scale: Optional[Tensor],
                       found_inf: Optional[Tensor],
                       *,
                       amsgrad: bool,
                       beta1: float,
                       beta2: float,
                       lr: float,
                       weight_decay: float,
                       eps: float,
                       maximize: bool,
                       capturable: bool,
                       differentiable: 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."

    assert grad_scale is None and found_inf is None

    assert not differentiable, "_foreach ops don't support autograd"

    grouped_tensors = _group_tensors_by_device_and_dtype([params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps])
    for (device_params, device_grads, device_exp_avgs, device_exp_avg_sqs,
         device_max_exp_avg_sqs, device_state_steps) in grouped_tensors.values():

        if maximize:
            device_grads = torch._foreach_neg(tuple(device_grads))  # type: ignore[assignment]

        # Handle complex parameters
        device_grads = [torch.view_as_real(x) if torch.is_complex(x) else x for x in device_grads]
        device_exp_avgs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in device_exp_avgs]
        device_exp_avg_sqs = [torch.view_as_real(x) if torch.is_complex(x) else x for x in device_exp_avg_sqs]
        params_ = [torch.view_as_real(x) if torch.is_complex(x) else x for x in device_params]

        # update steps
        torch._foreach_add_(device_state_steps, 1)

        if weight_decay != 0:
            device_grads = torch._foreach_add(device_grads, device_params, alpha=weight_decay)

        # Decay the first and second moment running average coefficient
        torch._foreach_mul_(device_exp_avgs, beta1)
        torch._foreach_add_(device_exp_avgs, device_grads, alpha=1 - beta1)

        torch._foreach_mul_(device_exp_avg_sqs, beta2)
        torch._foreach_addcmul_(device_exp_avg_sqs, device_grads, device_grads, 1 - beta2)

        if capturable:
            # TODO: use foreach_pow if/when foreach_pow is added
            bias_correction1 = [torch.pow(beta1, step) for step in device_state_steps]
            bias_correction2 = [torch.pow(beta2, step) for step in device_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
                torch._foreach_maximum_(device_max_exp_avg_sqs, device_exp_avg_sqs)  # type: ignore[assignment]

                # Use the max. for normalizing running avg. of gradient
                max_exp_avg_sq_sqrt = torch._foreach_sqrt(device_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(device_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_, device_exp_avgs, denom)
        else:
            bias_correction1 = [1 - beta1 ** _get_value(step) for step in device_state_steps]
            bias_correction2 = [1 - beta2 ** _get_value(step) for step in device_state_steps]

            step_size = _stack_if_compiling([(lr / bc) * -1 for bc in bias_correction1])

            bias_correction2_sqrt = [_dispatch_sqrt(bc) for bc in bias_correction2]

            if amsgrad:
                # Maintains the maximum of all 2nd moment running avg. till now
                torch._foreach_maximum_(device_max_exp_avg_sqs, device_exp_avg_sqs)

                # Use the max. for normalizing running avg. of gradient
                max_exp_avg_sq_sqrt = torch._foreach_sqrt(device_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(device_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_, device_exp_avgs, denom, step_size)


def _fused_adam(
    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],
    grad_scale: Optional[Tensor],
    found_inf: Optional[Tensor],
    *,
    amsgrad: bool,
    beta1: float,
    beta2: float,
    lr: float,
    weight_decay: float,
    eps: float,
    maximize: bool,
    capturable: bool,  # Needed for consistency.
    differentiable: bool,
) -> None:
    grad_scale_dict = {grad_scale.device: grad_scale} if grad_scale is not None else None
    found_inf_dict = {found_inf.device: found_inf} if found_inf is not None else None
    grouped_tensors = _group_tensors_by_device_and_dtype([params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps])
    for (device, dtype) in grouped_tensors:
        (
            device_params,
            device_grads,
            device_exp_avgs,
            device_exp_avg_sqs,
            device_max_exp_avg_sqs,
            device_state_steps,
        ) = grouped_tensors[(device, dtype)]
        device_grad_scale, device_found_inf = None, None
        if grad_scale is not None:
            if device not in grad_scale_dict:
                grad_scale_dict[device] = grad_scale.to(device, non_blocking=True)
            device_grad_scale = grad_scale_dict[device]
        if found_inf is not None:
            if found_inf not in found_inf_dict:
                found_inf_dict[device] = found_inf.to(device, non_blocking=True)
            device_found_inf = found_inf_dict[device]
        torch._foreach_add_(device_state_steps, 1)
        torch._fused_adam_(
            device_params,
            device_grads,
            device_exp_avgs,
            device_exp_avg_sqs,
            device_max_exp_avg_sqs,
            device_state_steps,
            amsgrad=amsgrad,
            lr=lr,
            beta1=beta1,
            beta2=beta2,
            weight_decay=weight_decay,
            eps=eps,
            maximize=maximize,
            grad_scale=device_grad_scale,
            found_inf=device_found_inf,
        )
        if device_found_inf is not None:
            torch._foreach_sub_(device_state_steps, [device_found_inf] * len(device_state_steps))