# Copyright (c) 2020 Mobvoi Inc (Binbin Zhang) # 2022 Ximalaya Inc (Yuguang Yang) # 2024 Alibaba Inc (authors: Xiang Lyu) # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # Modified from ESPnet(https://github.com/espnet/espnet) # NeMo(https://github.com/NVIDIA/NeMo) from typing import Union import math import warnings import torch from torch.optim.lr_scheduler import _LRScheduler class WarmupLR(_LRScheduler): """The WarmupLR scheduler This scheduler is almost same as NoamLR Scheduler except for following difference: NoamLR: lr = optimizer.lr * model_size ** -0.5 * min(step ** -0.5, step * warmup_step ** -1.5) WarmupLR: lr = optimizer.lr * warmup_step ** 0.5 * min(step ** -0.5, step * warmup_step ** -1.5) Note that the maximum lr equals to optimizer.lr in this scheduler. """ def __init__( self, optimizer: torch.optim.Optimizer, warmup_steps: Union[int, float] = 25000, last_epoch: int = -1, ): self.warmup_steps = warmup_steps # __init__() must be invoked before setting field # because step() is also invoked in __init__() super().__init__(optimizer, last_epoch) def __repr__(self): return f"{self.__class__.__name__}(warmup_steps={self.warmup_steps})" def get_lr(self): step_num = self.last_epoch + 1 if self.warmup_steps == 0: return [lr * step_num**-0.5 for lr in self.base_lrs] else: return [ lr * self.warmup_steps**0.5 * min(step_num**-0.5, step_num * self.warmup_steps**-1.5) for lr in self.base_lrs ] def set_step(self, step: int): self.last_epoch = step class WarmupPolicy(_LRScheduler): """Adds warmup kwargs and warmup logic to lr policy. All arguments should be passed as kwargs for clarity, Args: warmup_steps: Number of training steps in warmup stage warmup_ratio: Ratio of warmup steps to total steps max_steps: Total number of steps while training or `None` for infinite training """ def __init__(self, optimizer, *, warmup_steps=None, warmup_ratio=None, max_steps=None, min_lr=0.0, last_epoch=-1): assert not (warmup_steps is not None and warmup_ratio is not None),\ "Either use particular number of step or ratio" assert warmup_ratio is None or max_steps is not None, \ "If there is a ratio, there should be a total steps" # It is necessary to assign all attributes *before* __init__, # as class is wrapped by an inner class. self.max_steps = max_steps if warmup_steps is not None: self.warmup_steps = warmup_steps elif warmup_ratio is not None: self.warmup_steps = int(warmup_ratio * max_steps) else: self.warmup_steps = 0 self.min_lr = min_lr super().__init__(optimizer, last_epoch) def get_lr(self): if not self._get_lr_called_within_step: warnings.warn( "To get the last learning rate computed " "by the scheduler, please use `get_last_lr()`.", UserWarning, stacklevel=2) step = self.last_epoch if step <= self.warmup_steps and self.warmup_steps > 0: return self._get_warmup_lr(step) if step > self.max_steps: return [self.min_lr for _ in self.base_lrs] return self._get_lr(step) def _get_warmup_lr(self, step): lr_val = (step + 1) / (self.warmup_steps + 1) return [initial_lr * lr_val for initial_lr in self.base_lrs] def _get_lr(self, step): """Simple const lr policy""" return self.base_lrs class SquareRootConstantPolicy(_LRScheduler): """Adds warmup kwargs and warmup logic to lr policy. All arguments should be passed as kwargs for clarity, Args: warmup_steps: Number of training steps in warmup stage warmup_ratio: Ratio of warmup steps to total steps max_steps: Total number of steps while training or `None` for infinite training """ def __init__(self, optimizer, *, constant_steps=None, constant_ratio=None, max_steps=None, min_lr=0.0, last_epoch=-1): assert not (constant_steps is not None and constant_ratio is not None), \ "Either use particular number of step or ratio" assert constant_ratio is None or max_steps is not None, \ "If there is a ratio, there should be a total steps" # It is necessary to assign all attributes *before* __init__, # as class is wrapped by an inner class. self.max_steps = max_steps if constant_steps is not None: self.constant_steps = constant_steps elif constant_ratio is not None: self.constant_steps = int(constant_ratio * max_steps) else: self.constant_steps = 0 self.constant_lr = 1 / (constant_steps**0.5) self.min_lr = min_lr super().__init__(optimizer, last_epoch) def get_lr(self): if not self._get_lr_called_within_step: warnings.warn( "To get the last learning rate computed " "by the scheduler, please use `get_last_lr()`.", UserWarning, stacklevel=2) step = self.last_epoch if step <= self.constant_steps: return [self.constant_lr for _ in self.base_lrs] if step > self.max_steps: return [self.min_lr for _ in self.base_lrs] return self._get_lr(step) def _get_lr(self, step): """Simple const lr policy""" return self.base_lrs class WarmupHoldPolicy(WarmupPolicy): """Variant of WarmupPolicy which maintains high learning rate for a defined number of steps. All arguments should be passed as kwargs for clarity, Args: warmup_steps: Number of training steps in warmup stage warmup_ratio: Ratio of warmup steps to total steps hold_steps: Number of training steps to hold the learning rate after warm up hold_ratio: Ratio of hold steps to total steps max_steps: Total number of steps while training or `None` for infinite training """ def __init__( self, optimizer, *, warmup_steps=None, warmup_ratio=None, hold_steps=None, hold_ratio=None, max_steps=None, min_lr=0.0, last_epoch=-1, ): assert not (hold_steps is not None and hold_ratio is not None), \ "Either use particular number of step or ratio" assert hold_ratio is None or max_steps is not None, \ "If there is a ratio, there should be a total steps" self.min_lr = min_lr self._last_warmup_lr = 0.0 # Necessary to duplicate as class attributes are hidden in inner class self.max_steps = max_steps if warmup_steps is not None: self.warmup_steps = warmup_steps elif warmup_ratio is not None: self.warmup_steps = int(warmup_ratio * max_steps) else: self.warmup_steps = 0 if hold_steps is not None: self.hold_steps = hold_steps + self.warmup_steps elif hold_ratio is not None: self.hold_steps = int(hold_ratio * max_steps) + self.warmup_steps else: self.hold_steps = 0 super().__init__( optimizer, warmup_steps=warmup_steps, warmup_ratio=warmup_ratio, max_steps=max_steps, last_epoch=last_epoch, min_lr=min_lr, ) def get_lr(self): if not self._get_lr_called_within_step: warnings.warn( "To get the last learning rate computed by the scheduler," " " "please use `get_last_lr()`.", UserWarning, stacklevel=2) step = self.last_epoch # Warmup phase if step <= self.warmup_steps and self.warmup_steps > 0: return self._get_warmup_lr(step) # Hold phase if (step >= self.warmup_steps) and (step < self.hold_steps): return self.base_lrs if step > self.max_steps: return [self.min_lr for _ in self.base_lrs] return self._get_lr(step) class WarmupAnnealHoldPolicy(_LRScheduler): """Adds warmup kwargs and warmup logic to lr policy. All arguments should be passed as kwargs for clarity, Args: warmup_steps: Number of training steps in warmup stage warmup_ratio: Ratio of warmup steps to total steps max_steps: Total number of steps while training or `None` for infinite training min_lr: Minimum lr to hold the learning rate after decay at. constant_steps: Number of steps to keep lr constant at. constant_ratio: Ratio of steps to keep lr constant. """ def __init__( self, optimizer, *, warmup_steps=None, warmup_ratio=None, constant_steps=None, constant_ratio=None, max_steps=None, min_lr=0.0, last_epoch=-1, ): assert not (warmup_steps is not None and warmup_ratio is not None), \ "Either use particular number of step or ratio" assert not (constant_steps is not None and constant_ratio is not None), \ "Either use constant_steps or constant_ratio" assert warmup_ratio is None or max_steps is not None, \ "If there is a ratio, there should be a total steps" # It is necessary to assign all attributes *before* __init__, # as class is wrapped by an inner class. self.max_steps = max_steps if warmup_steps is not None: self.warmup_steps = warmup_steps elif warmup_ratio is not None: self.warmup_steps = int(warmup_ratio * max_steps) else: self.warmup_steps = 0 if constant_steps is not None: self.constant_steps = constant_steps elif constant_ratio is not None: self.constant_steps = int(constant_ratio * max_steps) else: self.constant_steps = 0 self.decay_steps = max_steps - (self.constant_steps + self.warmup_steps) self.min_lr = min_lr super().__init__(optimizer, last_epoch) def get_lr(self): if not self._get_lr_called_within_step: warnings.warn( "To get the last learning rate computed " "by the scheduler, please use `get_last_lr()`.", UserWarning, stacklevel=2) step = self.last_epoch # Warmup steps if self.warmup_steps > 0 and step <= self.warmup_steps: return self._get_warmup_lr(step) # Constant steps after warmup and decay if self.constant_steps > 0 and ( self.warmup_steps + self.decay_steps) < step <= self.max_steps: return self._get_constant_lr(step) # Min lr after max steps of updates if step > self.max_steps: return [self.min_lr for _ in self.base_lrs] return self._get_lr(step) def _get_warmup_lr(self, step): lr_val = (step + 1) / (self.warmup_steps + 1) return [initial_lr * lr_val for initial_lr in self.base_lrs] def _get_constant_lr(self, step): return [self.min_lr for _ in self.base_lrs] def _get_lr(self, step): """Simple const lr policy""" return self.base_lrs def _squareroot_annealing(initial_lr, step, max_steps, min_lr): mult = ((max_steps - step) / max_steps)**0.5 out_lr = initial_lr * mult out_lr = max(out_lr, min_lr) return out_lr def _square_annealing(initial_lr, step, max_steps, min_lr): mult = ((max_steps - step) / max_steps)**2 out_lr = initial_lr * mult out_lr = max(out_lr, min_lr) return out_lr def _cosine_annealing(initial_lr, step, max_steps, min_lr): mult = 0.5 * (1 + math.cos(math.pi * step / max_steps)) out_lr = (initial_lr - min_lr) * mult + min_lr return out_lr def _linear_warmup_with_cosine_annealing(max_lr, warmup_steps, step, decay_steps, min_lr): assert max_lr > min_lr # Use linear warmup for the initial part. if warmup_steps > 0 and step <= warmup_steps: return max_lr * float(step) / float(warmup_steps) # For any steps larger than `decay_steps`, use `min_lr`. if step > warmup_steps + decay_steps: return min_lr # If we are done with the warmup period, use the decay style. num_steps_ = step - warmup_steps decay_steps_ = decay_steps decay_ratio = float(num_steps_) / float(decay_steps_) assert decay_ratio >= 0.0 assert decay_ratio <= 1.0 delta_lr = max_lr - min_lr coeff = 0.5 * (math.cos(math.pi * decay_ratio) + 1.0) return min_lr + coeff * delta_lr def _poly_decay(initial_lr, step, decay_steps, power, min_lr, cycle): if cycle: multiplier = 1.0 if step == 0 else math.ceil(step / decay_steps) decay_steps *= multiplier else: step = min(step, decay_steps) p = step / decay_steps lr = (initial_lr - min_lr) * math.pow(1.0 - p, power) lr += min_lr return lr def _noam_hold_annealing(initial_lr, step, warmup_steps, hold_steps, decay_rate, min_lr): # hold_steps = total number of steps # to hold the LR, not the warmup + hold steps. T_warmup_decay = max(1, warmup_steps**decay_rate) T_hold_decay = max(1, (step - hold_steps)**decay_rate) lr = (initial_lr * T_warmup_decay) / T_hold_decay lr = max(lr, min_lr) return lr class SquareAnnealing(WarmupPolicy): def __init__(self, optimizer, *, max_steps, min_lr=1e-5, last_epoch=-1, **kwargs): super().__init__(optimizer=optimizer, max_steps=max_steps, last_epoch=last_epoch, min_lr=min_lr, **kwargs) def _get_lr(self, step): new_lrs = [ _square_annealing( initial_lr=initial_lr, step=step - self.warmup_steps, max_steps=self.max_steps - self.warmup_steps, min_lr=self.min_lr, ) for initial_lr in self.base_lrs ] return new_lrs class SquareRootAnnealing(WarmupPolicy): def __init__(self, optimizer, *, max_steps, min_lr=0, last_epoch=-1, **kwargs): super().__init__(optimizer=optimizer, max_steps=max_steps, last_epoch=last_epoch, min_lr=min_lr, **kwargs) def _get_lr(self, step): new_lrs = [ _squareroot_annealing(initial_lr=initial_lr, step=step, max_steps=self.max_steps, min_lr=self.min_lr) for initial_lr in self.base_lrs ] return new_lrs class CosineAnnealing(WarmupAnnealHoldPolicy): def __init__(self, optimizer, *, max_steps, min_lr=0, last_epoch=-1, **kwargs): super().__init__(optimizer=optimizer, max_steps=max_steps, last_epoch=last_epoch, min_lr=min_lr, **kwargs) def _get_lr(self, step): for initial_lr in self.base_lrs: if initial_lr < self.min_lr: raise ValueError( f"{self} received an initial learning rate " f"that was lower than the minimum learning rate.") if self.constant_steps is None or self.constant_steps == 0: new_lrs = [ _cosine_annealing( initial_lr=initial_lr, step=step - self.warmup_steps, max_steps=self.max_steps - self.warmup_steps, min_lr=self.min_lr, ) for initial_lr in self.base_lrs ] else: new_lrs = self._get_linear_warmup_with_cosine_annealing_lr(step) return new_lrs def _get_warmup_lr(self, step): if self.constant_steps is None or self.constant_steps == 0: return super()._get_warmup_lr(step) else: # Use linear warmup for the initial part. return self._get_linear_warmup_with_cosine_annealing_lr(step) def _get_constant_lr(self, step): # Only called when `constant_steps` > 0. return self._get_linear_warmup_with_cosine_annealing_lr(step) def _get_linear_warmup_with_cosine_annealing_lr(self, step): # Cosine Schedule for Megatron LM, # slightly different warmup schedule + constant LR at the end. new_lrs = [ _linear_warmup_with_cosine_annealing( max_lr=self.base_lrs[0], warmup_steps=self.warmup_steps, step=step, decay_steps=self.decay_steps, min_lr=self.min_lr, ) for _ in self.base_lrs ] return new_lrs class NoamAnnealing(_LRScheduler): def __init__(self, optimizer, *, d_model, warmup_steps=None, warmup_ratio=None, max_steps=None, min_lr=0.0, last_epoch=-1): self._normalize = d_model**(-0.5) assert not (warmup_steps is not None and warmup_ratio is not None), \ "Either use particular number of step or ratio" assert warmup_ratio is None or max_steps is not None, \ "If there is a ratio, there should be a total steps" # It is necessary to assign all attributes *before* __init__, # as class is wrapped by an inner class. self.max_steps = max_steps if warmup_steps is not None: self.warmup_steps = warmup_steps elif warmup_ratio is not None: self.warmup_steps = int(warmup_ratio * max_steps) else: self.warmup_steps = 0 self.min_lr = min_lr super().__init__(optimizer, last_epoch) def get_lr(self): if not self._get_lr_called_within_step: warnings.warn( "To get the last learning rate computed " "by the scheduler, please use `get_last_lr()`.", UserWarning, stacklevel=2) step = max(1, self.last_epoch) for initial_lr in self.base_lrs: if initial_lr < self.min_lr: raise ValueError( f"{self} received an initial learning rate " f"that was lower than the minimum learning rate.") new_lrs = [ self._noam_annealing(initial_lr=initial_lr, step=step) for initial_lr in self.base_lrs ] return new_lrs def _noam_annealing(self, initial_lr, step): if self.warmup_steps > 0: mult = self._normalize * min(step**(-0.5), step * (self.warmup_steps**(-1.5))) else: mult = self._normalize * step**(-0.5) out_lr = initial_lr * mult if step > self.warmup_steps: out_lr = max(out_lr, self.min_lr) return out_lr class NoamHoldAnnealing(WarmupHoldPolicy): def __init__(self, optimizer, *, max_steps, decay_rate=0.5, min_lr=0.0, last_epoch=-1, **kwargs): """ From Nemo: Implementation of the Noam Hold Annealing policy from the SqueezeFormer paper. Unlike NoamAnnealing, the peak learning rate can be explicitly set for this scheduler. The schedule first performs linear warmup, then holds the peak LR, then decays with some schedule for the remainder of the steps. Therefore the min-lr is still dependent on the hyper parameters selected. It's schedule is determined by three factors- Warmup Steps: Initial stage, where linear warmup occurs uptil the peak LR is reached. Unlike NoamAnnealing, the peak LR is explicitly stated here instead of a scaling factor. Hold Steps: Intermediate stage, where the peak LR is maintained for some number of steps. In this region, the high peak LR allows the model to converge faster if training is stable. However the high LR may also cause instability during training. Should usually be a significant fraction of training steps (around 30-40% of the entire training steps). Decay Steps: Final stage, where the LR rapidly decays with some scaling rate (set by decay rate). To attain Noam decay, use 0.5, for Squeezeformer recommended decay, use 1.0. The fast decay after prolonged high LR during hold phase allows for rapid convergence. References: - [Squeezeformer: An Efficient Transformer for Automatic Speech Recognition] (https://arxiv.org/abs/2206.00888) Args: optimizer: Pytorch compatible Optimizer object. warmup_steps: Number of training steps in warmup stage warmup_ratio: Ratio of warmup steps to total steps hold_steps: Number of training steps to hold the learning rate after warm up hold_ratio: Ratio of hold steps to total steps max_steps: Total number of steps while training or `None` for infinite training decay_rate: Float value describing the polynomial decay after the hold period. Default value of 0.5 corresponds to Noam decay. min_lr: Minimum learning rate. """ self.decay_rate = decay_rate super().__init__(optimizer=optimizer, max_steps=max_steps, last_epoch=last_epoch, min_lr=min_lr, **kwargs) def _get_lr(self, step): if self.warmup_steps is None or self.warmup_steps == 0: raise ValueError( "Noam scheduler cannot be used without warmup steps") if self.hold_steps > 0: hold_steps = self.hold_steps - self.warmup_steps else: hold_steps = 0 new_lrs = [ _noam_hold_annealing( initial_lr, step=step, warmup_steps=self.warmup_steps, hold_steps=hold_steps, decay_rate=self.decay_rate, min_lr=self.min_lr, ) for initial_lr in self.base_lrs ] return new_lrs def set_step(self, step: int): self.last_epoch = step class ConstantLR(_LRScheduler): """The ConstantLR scheduler This scheduler keeps a constant lr """ def __init__( self, optimizer: torch.optim.Optimizer, ): # __init__() must be invoked before setting field # because step() is also invoked in __init__() super().__init__(optimizer) def get_lr(self): return self.base_lrs def set_step(self, step: int): self.last_epoch = step