# Copyright (c) Microsoft Corporation. # Licensed under the MIT License. """MS-AMP pure-python AdamW optimizer.""" import math from typing import List, Union import torch from torch import Tensor from msamp.common.dtype import Dtypes from msamp.common.tensor import ScalingTensor from msamp.optim import LBOptimizer class LBAdamWBase(LBOptimizer): r"""Implements AdamW algorithm using pure python functions. .. 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) exp_avg_dtype(torch.dtype, optional): dtype for the first moment (default: torch.uint8) exp_avg_sq_dtype(torch.dtype, optional): dtype for the second moment (default: torch.float16) .. _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, bias_correction=True, betas=(0.9, 0.999), eps=1e-8, weight_decay=1e-2, amsgrad=False, *, maximize: bool = False, exp_avg_dtype=torch.uint8, exp_avg_sq_dtype=torch.float16, ): """Constructor. See class docstring for details.""" 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) self.bias_correction = bias_correction self.exp_avg_dtype = exp_avg_dtype self.exp_avg_sq_dtype = exp_avg_sq_dtype self.use_adam = False super().__init__(params, defaults) def __setstate__(self, state): """Set state of the optimizer. Args: state (dict): state of the optimizer. """ super().__setstate__(state) for group in self.param_groups: group.setdefault('amsgrad', False) group.setdefault('maximize', False) def _get_state_tensor(self, state, dtype): """Get the state tensor of the given dtype. Args: state (torch.Tensor): the orignal state tensor. dtype (torch.dtype): the dtype of the state tensor. Returns: ScalingTensor: the state tensor. """ if dtype != torch.float32: if dtype not in [torch.uint8, torch.int8, torch.float16]: raise TypeError('Unsupported dtype: {}'.format(dtype)) qtype = Dtypes.dtype_to_qtype[dtype] state = state.cast(qtype) return state def _update_lp_tensor(self, lp, hp): """Update the low precision tensor with the value high precision tensor. Args: lp (torch.Tensor or ScalingTensor): the low precision tensor. hp (torch.Tensor): the high precision tensor. """ # hp -> lp if id(lp) == id(hp): return if isinstance(lp, ScalingTensor): lp.copy_(hp.cast(lp.qtype)) else: lp.copy_(hp) @torch.no_grad() def lb_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 = [] max_exp_avg_sqs = [] state_steps = [] amsgrad = group['amsgrad'] beta1, beta2 = group['betas'] for p in group['params']: grad = p.grad if grad is None: continue if grad.is_sparse: raise RuntimeError('AdamW does not support sparse gradients') params_with_grad.append(p) grads.append(grad) state = self.state[p] # State initialization if len(state) == 0: state['step'] = 0 # Exponential moving average of gradient values state['exp_avg'] = self._get_state_tensor( torch.zeros_like(p, memory_format=torch.preserve_format, dtype=torch.float32), self.exp_avg_dtype ) # Exponential moving average of squared gradient values state['exp_avg_sq'] = self._get_state_tensor( torch.zeros_like(p, memory_format=torch.preserve_format, dtype=torch.float32), self.exp_avg_sq_dtype ) if amsgrad: # Maintains max of all exp. moving avg. of sq. grad. values state['max_exp_avg_sq'] = self._get_state_tensor( torch.zeros_like(p, memory_format=torch.preserve_format, dtype=torch.float32), self.state_dtype ) 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']) # update the steps for each param group update state['step'] += 1 # record the step after step update state_steps.append(state['step']) self.adamw_fn( 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'], ) return loss def adamw_fn( self, params: List[Union[Tensor, ScalingTensor]], grads: List[Union[Tensor, ScalingTensor]], exp_avgs: List[Union[Tensor, ScalingTensor]], exp_avg_sqs: List[Union[Tensor, ScalingTensor]], max_exp_avg_sqs: List[Union[Tensor, ScalingTensor]], state_steps: List[int], *, amsgrad: bool, beta1: float, beta2: float, lr: float, weight_decay: float, eps: float, maximize: bool ): """Functional API that performs AdamW algorithm computation. Args: params (List[Union[Tensor, ScalingTensor]]): list of parameters. grads (List[Union[Tensor, ScalingTensor]]): list of gradients. exp_avgs (List[Union[Tensor, ScalingTensor]]): list of exponential moving average of gradient. exp_avg_sqs (List[Union[Tensor, ScalingTensor]]): list of exponential moving average of squared gradient. max_exp_avg_sqs (List[Union[Tensor, ScalingTensor]]): list of maximum exponential moving average of squared gradient. state_steps (List[int]): list of steps, currently not supported. amsgrad (bool): whether to use the AMSGrad variant of this algorithm, currently only support True. beta1 (float): coefficient used for computing running averages of gradient. beta2 (float): coefficient used for computing running averages of squared gradient. lr (float): learning rate. weight_decay (float): weight decay coefficient. eps (float): term added to the denominator to improve numerical stability. maximize (bool): maximize the params based on the objective, instead of minimizing. """ if amsgrad: raise ValueError('Only amsgrad=False is supported for now.') for i, param_lp in enumerate(params): grad_lp = grads[i] if not maximize else -grads[i] exp_avg_lp = exp_avgs[i] exp_avg_sq_lp = exp_avg_sqs[i] step = state_steps[i] grad = grad_lp.float() param = param_lp.float() if weight_decay != 0: if self.use_adam: grad = grad.add(param, alpha=weight_decay) else: param.mul_(1 - lr * weight_decay) assert param.is_contiguous() assert grad.is_contiguous() exp_avg = exp_avg_lp.float() exp_avg_sq = exp_avg_sq_lp.float() if self.bias_correction: bias_correction1 = 1 - beta1**step bias_correction2 = 1 - beta2**step else: bias_correction1 = bias_correction2 = 1.0 step_size = lr / bias_correction1 # 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) denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(eps) param.addcdiv_(exp_avg, denom, value=-step_size) # Parameter self._update_lp_tensor(param_lp, param) # momentum 1 self._update_lp_tensor(exp_avg_lp, exp_avg) # momentum 2 self._update_lp_tensor(exp_avg_sq_lp, exp_avg_sq)