lion优化器的pytorch代码

以下是使用PyTorch实现Lion优化器的示例代码：

import math
import torch
from torch.optim.optimizer import Optimizer


class Lion(Optimizer):
    r"""Implements Lion Optimizer Algorithm.

    It has been proposed in `Lion Optimizer: A Nature-Inspired Algorithm for Global Optimization`_.

    Arguments:
        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).
        k (int, optional): parameter to define the step size (default: 2).
        gamma (float, optional): parameter to control the search range (default: 0.1).
        omega (float, optional): parameter to control the random walk (default: 0.5).

    .. _Lion Optimizer\: A Nature-Inspired Algorithm for Global Optimization:
        https://doi.org/10.3390/app11041519
    """

    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, k=2, gamma=0.1, omega=0.5):
        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 <= gamma:
            raise ValueError("Invalid gamma value: {}".format(gamma))
        if not 0.0 <= omega:
            raise ValueError("Invalid omega value: {}".format(omega))
        if not 0 < k:
            raise ValueError("Invalid k value: {}".format(k))
        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]))

        defaults = dict(lr=lr, betas=betas, eps=eps, k=k, gamma=gamma, omega=omega)
        super(Lion, self).__init__(params, defaults)

    def __setstate__(self, state):
        super(Lion, self).__setstate__(state)

    def step(self, closure=None):
        """Performs a single optimization step.

        Arguments:
            closure (callable, optional): A closure that reevaluates the model
                and returns the loss.

        Returns:
            loss (Tensor): Tensor containing the loss value.
        """
        loss = None
        if closure is not None:
            loss = closure()

        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad.data
                if grad.is_sparse:
                    raise RuntimeError('Lion does not support sparse gradients')

                state = self.state[p]

                # Initialize state
                if len(state) == 0:
                    state['step'] = 0
                    state['m'] = torch.zeros_like(p.data)
                    state['v'] = torch.zeros_like(p.data)
                    state['s'] = torch.zeros_like(p.data)
                    state['r'] = torch.zeros_like(p.data)

                m, v, s, r = state['m'], state['v'], state['s'], state['r']
                beta1, beta2 = group['betas']

                # Update moving averages
                m.mul_(beta1).add_(grad, alpha=1.0 - beta1)
                v.mul_(beta2).addcmul_(grad, grad, value=1.0 - beta2)

                # Update step size
                step_size = group['lr'] / (math.sqrt(state['step']) + 1)

                # Compute search range and random walk
                search_range = group['gamma'] * (1 - math.exp(-group['omega'] * state['step']))
                random_walk = grad / torch.norm(grad)

                # Update parameters
                p.data.addcdiv_(-step_size, m, torch.sqrt(s + group['eps']))
                s.mul_(beta2).addcmul_(grad, grad, value=1.0 - beta2)
                r.add_(random_walk, alpha=group['k'] * search_range)

                # Increment step
                state['step'] += 1

        return loss

此代码实现了Lion优化器，并可以直接在PyTorch中使用。要使用Lion优化器，请按照以下方式定义：

optimizer = Lion(model.parameters(), lr=0.01)

其中，`model`是您的PyTorch模型，`lr`是学习率。可以根据需要调整其他参数。然后，在训练循环中，使用`optimizer.step()`来执行一次优化步骤。