code: # Ranger deep learning optimizer - RAdam + Lookahead + Gradient Centralization, combined into one optimizer.
  
  # https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer
  # and/or
  # https://github.com/lessw2020/Best-Deep-Learning-Optimizers
  
  # Ranger has now been used to capture 12 records on the FastAI leaderboard.
  
  # This version = 20.4.11
  
  # Credits:
  # Gradient Centralization --> https://arxiv.org/abs/2004.01461v2 (a new optimization technique for DNNs), github:  https://github.com/Yonghongwei/Gradient-Centralization
  # RAdam -->  https://github.com/LiyuanLucasLiu/RAdam
  # Lookahead --> rewritten by lessw2020, but big thanks to Github @LonePatient and @RWightman for ideas from their code.
  # Lookahead paper --> MZhang,G Hinton  https://arxiv.org/abs/1907.08610
  
  # summary of changes:
  # 4/11/20 - add gradient centralization option.  Set new testing benchmark for accuracy with it, toggle with use_gc flag at init.
  # full code integration with all updates at param level instead of group, moves slow weights into state dict (from generic weights),
  # supports group learning rates (thanks @SHolderbach), fixes sporadic load from saved model issues.
  # changes 8/31/19 - fix references to *self*.N_sma_threshold;
  # changed eps to 1e-5 as better default than 1e-8.
  
  import math
  import torch
  from torch.optim.optimizer import Optimizer
  
  
  class Ranger(Optimizer):
  
  	def __init__(self, params, lr=1e-3,  # lr
  				 alpha=0.5, k=6, N_sma_threshhold=5,  # Ranger options
  				 betas=(.95, 0.999), eps=1e-5, weight_decay=0,  # Adam options
  				 use_gc=True, gc_conv_only=False
  				 # Gradient centralization on or off, applied to conv layers only or conv + fc layers
  				 ):
  
  		# parameter checks
  		if not 0.0 <= alpha <= 1.0:
  			raise ValueError(f'Invalid slow update rate: {alpha}')
  		if not 1 <= k:
  			raise ValueError(f'Invalid lookahead steps: {k}')
  		if not lr > 0:
  			raise ValueError(f'Invalid Learning Rate: {lr}')
  		if not eps > 0:
  			raise ValueError(f'Invalid eps: {eps}')
  
  		# parameter comments:
  		# beta1 (momentum) of .95 seems to work better than .90...
  		# N_sma_threshold of 5 seems better in testing than 4.
  		# In both cases, worth testing on your dataset (.90 vs .95, 4 vs 5) to make sure which works best for you.
  
  		# prep defaults and init torch.optim base
  		defaults = dict(lr=lr, alpha=alpha, k=k, step_counter=0, betas=betas, N_sma_threshhold=N_sma_threshhold,
  						eps=eps, weight_decay=weight_decay)
  		super().__init__(params, defaults)
  
  		# adjustable threshold
  		self.N_sma_threshhold = N_sma_threshhold
  
  		# look ahead params
  
  		self.alpha = alpha
  		self.k = k
  
  		# radam buffer for state
  		self.radam_buffer = [[None, None, None] for ind in range(10)]
  
  		# gc on or off
  		self.use_gc = use_gc
  
  		# level of gradient centralization
  		self.gc_gradient_threshold = 3 if gc_conv_only else 1
  
  	def __setstate__(self, state):
  		super(Ranger, self).__setstate__(state)
  
  	def step(self, closure=None):
  		loss = None
  
  		# Evaluate averages and grad, update param tensors
  		for group in self.param_groups:
  
  			for p in group['params']:
  				if p.grad is None:
  					continue
  				grad = p.grad.data.float()
  
  				if grad.is_sparse:
  					raise RuntimeError('Ranger optimizer does not support sparse gradients')
  
  				p_data_fp32 = p.data.float()
  
  				state = self.state[p]  # get state dict for this param
  
  				if len(state) == 0:  # if first time to run...init dictionary with our desired entries
  					# if self.first_run_check==0:
  					# self.first_run_check=1
  					# print("Initializing slow buffer...should not see this at load from saved model!")
  					state['step'] = 0
  					state['exp_avg'] = torch.zeros_like(p_data_fp32)
  					state['exp_avg_sq'] = torch.zeros_like(p_data_fp32)
  
  					# look ahead weight storage now in state dict
  					state['slow_buffer'] = torch.empty_like(p.data)
  					state['slow_buffer'].copy_(p.data)
  
  				else:
  					state['exp_avg'] = state['exp_avg'].type_as(p_data_fp32)
  					state['exp_avg_sq'] = state['exp_avg_sq'].type_as(p_data_fp32)
  
  				# begin computations
  				exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
  				beta1, beta2 = group['betas']
  
  				# GC operation for Conv layers and FC layers
  				if grad.dim() > self.gc_gradient_threshold:
  					grad.add_(-grad.mean(dim=tuple(range(1, grad.dim())), keepdim=True))
  
  				state['step'] += 1
  
  				# compute variance mov avg
  				exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
  				# compute mean moving avg
  				exp_avg.mul_(beta1).add_(1 - beta1, grad)
  
  				buffered = self.radam_buffer[int(state['step'] % 10)]
  
  				if state['step'] == buffered[0]:
  					N_sma, step_size = buffered[1], buffered[2]
  				else:
  					buffered[0] = state['step']
  					beta2_t = beta2 ** state['step']
  					N_sma_max = 2 / (1 - beta2) - 1
  					N_sma = N_sma_max - 2 * state['step'] * beta2_t / (1 - beta2_t)
  					buffered[1] = N_sma
  					if N_sma > self.N_sma_threshhold:
  						step_size = math.sqrt(
  							(1 - beta2_t) * (N_sma - 4) / (N_sma_max - 4) * (N_sma - 2) / N_sma * N_sma_max / (
  										N_sma_max - 2)) / (1 - beta1 ** state['step'])
  					else:
  						step_size = 1.0 / (1 - beta1 ** state['step'])
  					buffered[2] = step_size
  
  				if group['weight_decay'] != 0:
  					p_data_fp32.add_(-group['weight_decay'] * group['lr'], p_data_fp32)
  
  				# apply lr
  				if N_sma > self.N_sma_threshhold:
  					denom = exp_avg_sq.sqrt().add_(group['eps'])
  					p_data_fp32.addcdiv_(-step_size * group['lr'], exp_avg, denom)
  				else:
  					p_data_fp32.add_(-step_size * group['lr'], exp_avg)
  
  				p.data.copy_(p_data_fp32)
  
  				# integrated look ahead...
  				# we do it at the param level instead of group level
  				if state['step'] % group['k'] == 0:
  					slow_p = state['slow_buffer']  # get access to slow param tensor
  					slow_p.add_(self.alpha, p.data - slow_p)  # (fast weights - slow weights) * alpha
  					p.data.copy_(slow_p)  # copy interpolated weights to RAdam param tensor
  
  		return loss
apis: torch.zeros_like torch.empty_like