import torch from torch import Tensor from .optimizer import Optimizer from typing import List, Optional class Adamax(Optimizer): r"""Implements Adamax algorithm (a variant of Adam based on infinity norm). .. 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{ (weight decay)}, \\ &\hspace{13mm} \epsilon \text{ (epsilon)} \\ &\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)}, u_0 \leftarrow 0 \text{ ( infinity norm)} \\[-1.ex] &\rule{110mm}{0.4pt} \\ &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ &\hspace{5mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}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}u_t \leftarrow \mathrm{max}(\beta_2 u_{t-1}, |g_{t}|+\epsilon) \\ &\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \frac{\gamma m_t}{(1-\beta^t_1) u_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 `Adam: A Method for Stochastic Optimization`_. Args: params (iterable): iterable of parameters to optimize or dicts defining parameter groups lr (float, optional): learning rate (default: 2e-3) betas (Tuple[float, float], optional): coefficients used for computing running averages of gradient and its square 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) foreach (bool, optional): whether foreach implementation of optimizer is used (default: None) maximize (bool, optional): maximize the params based on the objective, instead of minimizing (default: False) .. _Adam\: A Method for Stochastic Optimization: https://arxiv.org/abs/1412.6980 """ def __init__(self, params, lr=2e-3, betas=(0.9, 0.999), eps=1e-8, weight_decay=0, foreach: Optional[bool] = None, *, maximize: bool = False): 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, foreach=foreach, maximize=maximize) super(Adamax, self).__init__(params, defaults) def __setstate__(self, state): super().__setstate__(state) for group in self.param_groups: group.setdefault('foreach', None) group.setdefault('maximize', False) 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'])) @torch.no_grad() def 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_infs = [] state_steps = [] beta1, beta2 = group['betas'] eps = group['eps'] lr = group['lr'] weight_decay = group['weight_decay'] foreach = group['foreach'] maximize = group['maximize'] for p in group['params']: if p.grad is None: continue params_with_grad.append(p) if p.grad.is_sparse: raise RuntimeError('Adamax does not support sparse gradients') grads.append(p.grad) state = self.state[p] # State initialization if len(state) == 0: state['step'] = torch.tensor(0.) state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format) state['exp_inf'] = torch.zeros_like(p, memory_format=torch.preserve_format) exp_avgs.append(state['exp_avg']) exp_infs.append(state['exp_inf']) state_steps.append(state['step']) adamax(params_with_grad, grads, exp_avgs, exp_infs, state_steps, eps=eps, beta1=beta1, beta2=beta2, lr=lr, weight_decay=weight_decay, foreach=foreach, maximize=maximize) return loss def adamax(params: List[Tensor], grads: List[Tensor], exp_avgs: List[Tensor], exp_infs: 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: bool = None, maximize: bool = False, *, eps: float, beta1: float, beta2: float, lr: float, weight_decay: float): r"""Functional API that performs adamax algorithm computation. See :class:`~torch.optim.Adamax` 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: # Placeholder for more complex foreach logic to be added when value is not set foreach = 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_adamax else: func = _single_tensor_adamax func(params, grads, exp_avgs, exp_infs, state_steps, eps=eps, beta1=beta1, beta2=beta2, lr=lr, weight_decay=weight_decay, maximize=maximize) def _single_tensor_adamax(params: List[Tensor], grads: List[Tensor], exp_avgs: List[Tensor], exp_infs: List[Tensor], state_steps: List[Tensor], *, eps: float, beta1: float, beta2: float, lr: float, weight_decay: float, maximize: bool): for i, param in enumerate(params): grad = grads[i] grad = grad if not maximize else -grad exp_avg = exp_avgs[i] exp_inf = exp_infs[i] step_t = state_steps[i] # update step step_t += 1 step = step_t.item() if weight_decay != 0: grad = grad.add(param, alpha=weight_decay) # Update biased first moment estimate. exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1) # Update the exponentially weighted infinity norm. norm_buf = torch.cat([ exp_inf.mul_(beta2).unsqueeze(0), grad.abs().add_(eps).unsqueeze_(0) ], 0) torch.amax(norm_buf, 0, keepdim=False, out=exp_inf) bias_correction = 1 - beta1 ** step clr = lr / bias_correction param.addcdiv_(exp_avg, exp_inf, value=-clr) def _multi_tensor_adamax(params: List[Tensor], grads: List[Tensor], exp_avgs: List[Tensor], exp_infs: List[Tensor], state_steps: List[Tensor], *, beta1: float, beta2: float, lr: float, weight_decay: float, eps: float, maximize: bool): if len(params) == 0: return if maximize: grads = torch._foreach_neg(grads) # Update steps torch._foreach_add_(state_steps, 1) if weight_decay != 0: torch._foreach_add_(grads, params, alpha=weight_decay) # Update biased first moment estimate. torch._foreach_mul_(exp_avgs, beta1) torch._foreach_add_(exp_avgs, grads, alpha=1 - beta1) # Update the exponentially weighted infinity norm. torch._foreach_mul_(exp_infs, beta2) for exp_inf, grad in zip(exp_infs, grads): norm_buf = torch.cat([ exp_inf.unsqueeze(0), grad.abs().add_(eps).unsqueeze_(0) ], 0) torch.max(norm_buf, 0, keepdim=False, out=(exp_inf, exp_inf.new().long())) bias_corrections = [1 - beta1 ** step.item() for step in state_steps] clr = [-1 * (lr / bias_correction) for bias_correction in bias_corrections] torch._foreach_addcdiv_(params, exp_avgs, exp_infs, clr)