分布式机器学习:异步SGD和Hogwild!算法(Pytorch)

时间:2023-02-14 07:10:05

我们在博客《分布式机器学习:同步并行SGD算法的实现与复杂度分析(PySpark)》和博客《分布式机器学习:模型平均MA与弹性平均EASGD(PySpark) 》中介绍的都是同步算法。同步算法的共性是所有的节点会以一定的频率进行全局同步。然而,当工作节点的计算性能存在差异,或者某些工作节点无法正常工作(比如死机)的时候,分布式系统的整体运行效率不好,甚至无法完成训练任务。为了解决此问题,人们提出了异步的并行算法。在异步的通信模式下,各个工作节点不需要互相等待,而是以一个或多个全局服务器做为中介,实现对全局模型的更新和读取。这样可以显著减少通信时间,从而获得更好的多机扩展性。

2 异步SGD

2.1 算法描述与实现

异步SGD[9]是最基础的异步算法,其流畅如下图所示。粗略地讲,ASGD的参数更新发生在工作节点,而模型的更新发生在服务器端。当参数服务器接收到来自某个工作节点的参数梯度时,就直接将其加到全局模型上,而无需等待其它工作节点的梯度信息。

分布式机器学习:异步SGD和Hogwild!算法(Pytorch)

下面我们用Pytorch实现的训练代码(采用RPC进行进程间通信)。首先,我们设置初始化多个进程,其中0号进程做为参数服务器,其余进程做为worker来对模型进行训练,则总的通信域(world_size)大小为workers的数量+1。这里我们设置参数服务器IP地址为localhost,端口号29500

def run(rank, world_size):
    os.environ['MASTER_ADDR'] = 'localhost'
    os.environ['MASTER_PORT'] = '29500'
    options=rpc.TensorPipeRpcBackendOptions(
        num_worker_threads=16,
        rpc_timeout=0  # infinite timeout
     )
    if rank == 0:
        rpc.init_rpc(
            "ps",
            rank=rank,
            world_size=world_size,
            rpc_backend_options=options
        )
        run_ps([f"trainer{r}" for r in range(1, world_size)])
    else:
        rpc.init_rpc(
            f"trainer{rank}",
            rank=rank,
            world_size=world_size,
            rpc_backend_options=options
        )
        # trainer passively waiting for ps to kick off training iterations

    # block until all rpcs finish
    rpc.shutdown()


if __name__=="__main__":
    world_size = n_workers + 1
    mp.spawn(run, args=(world_size, ), nprocs=world_size, join=True)

下面我们定义参数服务器的所要完成工作流程,包括将训练数据划分到各个worker,异步调用所有worker的训练流程,最后训练完毕后在参数服务器完成对模型的评估。

def run_trainer(ps_rref, train_dataset):
    trainer = Trainer(ps_rref)
    trainer.train(train_dataset)


def run_ps(trainers):
    transform=transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
    ])
    train_dataset = datasets.MNIST('./data', train=True, download=True,
                       transform=transform)
    local_train_datasets = dataset_split(train_dataset, n_workers)    
    
    
    print(f"{datetime.now().strftime('%H:%M:%S')} Start training")
    ps = ParameterServer()
    ps_rref = rpc.RRef(ps)
    futs = []
    for idx, trainer in enumerate(trainers):
        futs.append(
            rpc.rpc_async(trainer, run_trainer, args=(ps_rref, local_train_datasets[idx]))
        )

    torch.futures.wait_all(futs)
    print(f"{datetime.now().strftime('%H:%M:%S')} Finish training")
    ps.evaluation()

这里数据集的划分代码采用我们在《Pytorch:单卡多进程并行训练》中所述的数据划分方式:

class CustomSubset(Subset):
    '''A custom subset class with customizable data transformation'''
    def __init__(self, dataset, indices, subset_transform=None):
        super().__init__(dataset, indices)
        self.subset_transform = subset_transform

    def __getitem__(self, idx):
        x, y = self.dataset[self.indices[idx]]
        if self.subset_transform:
            x = self.subset_transform(x)
        return x, y   

    def __len__(self):
        return len(self.indices)

    
def dataset_split(dataset, n_workers):
    n_samples = len(dataset)
    n_sample_per_workers = n_samples // n_workers
    local_datasets = []
    for w_id in range(n_workers):
        if w_id < n_workers - 1:
            local_datasets.append(CustomSubset(dataset, range(w_id * n_sample_per_workers, (w_id + 1) * n_sample_per_workers)))
        else:
            local_datasets.append(CustomSubset(dataset, range(w_id * n_sample_per_workers, n_samples)))
    return local_datasets    

以下是参数服务器类ParameterServer的定义:

class ParameterServer(object):

    def __init__(self, n_workers=n_workers):
        self.model = Net().to(device)
        self.lock = threading.Lock()
        self.future_model = torch.futures.Future()
        self.n_workers = n_workers
        self.curr_update_size = 0
        self.optimizer = optim.SGD(self.model.parameters(), lr=0.001, momentum=0.9)
        for p in self.model.parameters():
            p.grad = torch.zeros_like(p)
        self.test_loader = torch.utils.data.DataLoader(
            datasets.MNIST('../data', train=False,
                           transform=transforms.Compose([
                               transforms.ToTensor(),
                               transforms.Normalize((0.1307,), (0.3081,))
                           ])),
            batch_size=32, shuffle=True)


    def get_model(self):
        # TensorPipe RPC backend only supports CPU tensors, 
        # so we move your tensors to CPU before sending them over RPC
        return self.model.to("cpu")

    @staticmethod
    @rpc.functions.async_execution
    def update_and_fetch_model(ps_rref, grads):
        self = ps_rref.local_value()
        for p, g in zip(self.model.parameters(), grads):
            p.grad += g
        with self.lock:
            self.curr_update_size += 1
            fut = self.future_model

            if self.curr_update_size >= self.n_workers:
                for p in self.model.parameters():
                    p.grad /= self.n_workers
                self.curr_update_size = 0
                self.optimizer.step()
                self.optimizer.zero_grad()
                fut.set_result(self.model)
                self.future_model = torch.futures.Future()

        return fut

    def evaluation(self):
        self.model.eval()
        self.model = self.model.to(device)
        test_loss = 0
        correct = 0
        with torch.no_grad():
            for data, target in self.test_loader:
                output = self.model(data.to(device))
                test_loss += F.nll_loss(output, target.to(device), reduction='sum').item() # sum up batch loss
                pred = output.max(1)[1] # get the index of the max log-probability
                correct += pred.eq(target.to(device)).sum().item()

        test_loss /= len(self.test_loader.dataset)
        print('\nTest result - Accuracy: {}/{} ({:.0f}%)\n'.format(
            correct, len(self.test_loader.dataset), 100. * correct / len(self.test_loader.dataset)))  

以下是Trainer类的定义:

class Trainer(object):

    def __init__(self, ps_rref):
        self.ps_rref = ps_rref
        self.model = Net().to(device) 

    def train(self, train_dataset):
        train_loader = torch.utils.data.DataLoader(train_dataset, batch_size=batch_size, shuffle=True)
        model = self.ps_rref.rpc_sync().get_model().cuda()
        pid = os.getpid()
        for epoch in range(epochs):
            for batch_idx, (data, target) in enumerate(train_loader):
                output = model(data.to(device))
                loss = F.nll_loss(output, target.to(device))
                loss.backward()
                model = rpc.rpc_sync(
                    self.ps_rref.owner(),
                    ParameterServer.update_and_fetch_model,
                    args=(self.ps_rref, [p.grad for p in model.cpu().parameters()]),
                ).cuda()
                if batch_idx % log_interval == 0:
                    print('{}\tTrain Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                        pid, epoch + 1, batch_idx * len(data), len(train_loader.dataset),
                        100. * batch_idx / len(train_loader), loss.item()))

完整代码我已经上传到了GitHub仓库 [Distributed-Algorithm-PySpark],感兴趣的童鞋可以前往查看。

运行该代码得到的评估结果为:

Test result - Accuracy: 9696/10000 (97%)

可见该训练算法是收敛的,但在10个epoch下在测试集上只能达到97%的精度,不如我们下面提到的在10个epoch就能在测试集上达到99%精度的Hogwild!算法。注意,ASGD和Hogwild都是异步算法,但ASGD是分布式算法(当然我们这里是单机多进程模拟),进程间采用RPC通信,不会出现同步错误的问题,根本不需要考虑加不加锁。而Hogwild!算法是单机算法,进程/线程间采用共享内存通信,需要考虑加不加锁的问题,不过Hogwild!算法为了提高训练过程中的数据吞吐量,直接采用了无锁的全局内存访问。

2.2 收敛性分析

ASGD避开了同步开销,但会给模型更新增加一些延迟。我们下面将ASGD的工作流程用下图加以剖析来解释这一点。用\(\text{worker}(k)\)来代表第\(k\)个工作节点,用\(w^t\)来代表第\(t\)轮迭代时服务端的全局模型。按照时间顺序,首先\(\text{worker}(k)\)先从参数服务器获取全局模型\(w^t\),再根据本地数据计算模型梯度\(g(w_t)\)并将其发往参数服务器。一段时间后,\(\text{worker}(k')\)也从参数服务器取回当时的全局模型\(w^{t+1}\),并同样依据它的本地数据计算模型的梯度\(f(w^{t+1})\)。注意,在\(\text{worker}(k')\)取回参数并进行计算的过程中,其它工作节点(比如\(\text{worker}(k)\))可能已经将它的梯度提交给服务器并进行更新了。所以当\(\text{worker}(k')\)将其梯度\(g(w^{t+1})\)发给服务器时,全局模型已经不再是\(w^{t+1}\),而已经是被更新过的版本。

分布式机器学习:异步SGD和Hogwild!算法(Pytorch)

我们将上面这种现象称为梯度和模型的失配,也即我们用一个比较旧的参数计算了梯度,而将这个“延迟”的梯度更新到了模型参数上。这种延迟使得ASGD和SGD之间在参数更新规则上存在偏差,可能导致模型在某些特定的更新点上出现严重抖动,设置优化过程出错,无法收敛。后面我们会介绍克服延迟问题的手段。

3 Hogwild!算法

3.1 算法描述与实现

异步并行算法既可以在多机集群上开展,也可以在多核系统下通过多线程开展。当我们把ASGD算法应用在多线程环境中时,因为不再有参数服务器这一角色,算法的细节会发生一些变化。特别地,因为全局模型存储在共享内存中,所以当异步的模型更新发生时,我们需要讨论是否将内存加锁,以保证模型写入的一致性。

Hogwild!算法[2]为了提高训练过程中的数据吞吐量,选择了无锁的全局模型访问,其工作逻辑如下所示:

分布式机器学习:异步SGD和Hogwild!算法(Pytorch)

这里使用我们在《Pytorch:单卡多进程并行训练》所提到的torch.multiprocessing来进行多进程并行训练。多进程原本内存空间是独立的,这里我们显式调用model.share_memory()来讲模型设置在共享内存中以进行进程间通信。不过注意,如果我们采用GPU训练,则GPU直接就做为了多进程的共享内存,此时model.share_memory()实际上为空操作(no-op)。

我们用Pytorch实现的训练代码如下:

from __future__ import print_function
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.multiprocessing as mp
from torchvision import datasets, transforms
import os
import torch
import torch.optim as optim
import torch.nn.functional as F


batch_size = 64 # input batch size for training
test_batch_size = 1000 # input batch size for testing
epochs = 10 # number of global epochs to train
lr = 0.01 # learning rate
momentum = 0.5 # SGD momentum
seed = 1 # random seed
log_interval = 10 # how many batches to wait before logging training status
n_workers = 4 # how many training processes to use
cuda = True # enables CUDA training
mps = False # enables macOS GPU training
dry_run = False # quickly check a single pass


def train(rank, model, device, dataset, dataloader_kwargs):
    torch.manual_seed(seed + rank)

    train_loader = torch.utils.data.DataLoader(dataset, **dataloader_kwargs)

    optimizer = optim.SGD(model.parameters(), lr=lr, momentum=momentum)
    for epoch in range(1, epochs + 1):
        model.train()
        pid = os.getpid()
        for batch_idx, (data, target) in enumerate(train_loader):
            optimizer.zero_grad()
            output = model(data.to(device))
            loss = F.nll_loss(output, target.to(device))
            loss.backward()
            optimizer.step()
            if batch_idx % log_interval == 0:
                print('{}\tTrain Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                    pid, epoch, batch_idx * len(data), len(train_loader.dataset),
                    100. * batch_idx / len(train_loader), loss.item()))
                if dry_run:
                    break


def test(model, device, dataset, dataloader_kwargs):
    torch.manual_seed(seed)
    test_loader = torch.utils.data.DataLoader(dataset, **dataloader_kwargs)

    model.eval()
    test_loss = 0
    correct = 0
    with torch.no_grad():
        for data, target in test_loader:
            output = model(data.to(device))
            test_loss += F.nll_loss(output, target.to(device), reduction='sum').item() # sum up batch loss
            pred = output.max(1)[1] # get the index of the max log-probability
            correct += pred.eq(target.to(device)).sum().item()

    test_loss /= len(test_loader.dataset)
    print('\nTest set: Global loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
        test_loss, correct, len(test_loader.dataset),
        100. * correct / len(test_loader.dataset)))  
    

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        self.conv2_drop = nn.Dropout2d()
        self.fc1 = nn.Linear(320, 50)
        self.fc2 = nn.Linear(50, 10)

    def forward(self, x):
        x = F.relu(F.max_pool2d(self.conv1(x), 2))
        x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2))
        x = x.view(-1, 320)
        x = F.relu(self.fc1(x))
        x = F.dropout(x, training=self.training)
        x = self.fc2(x)
        return F.log_softmax(x, dim=1)
    
    
if __name__ == '__main__':
    use_cuda = cuda and torch.cuda.is_available()
    use_mps = mps and torch.backends.mps.is_available()
    if use_cuda:
        device = torch.device("cuda")
    elif use_mps:
        device = torch.device("mps")
    else:
        device = torch.device("cpu")

    print(device)
    
    transform=transforms.Compose([
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
        ])
    train_dataset = datasets.MNIST('../data', train=True, download=True,
                       transform=transform)
    test_dataset = datasets.MNIST('../data', train=False,
                       transform=transform)
    kwargs = {'batch_size': batch_size,
              'shuffle': True}
    if use_cuda:
        kwargs.update({'num_workers': 1,
                       'pin_memory': True,
                      })

    torch.manual_seed(seed)
    mp.set_start_method('spawn', force=True)

    model = Net().to(device)
    model.share_memory() # gradients are allocated lazily, so they are not shared here

    processes = []
    for rank in range(n_workers):
        p = mp.Process(target=train, args=(rank, model, device,
                                           train_dataset, kwargs))
        # We first train the model across `n_workers` processes
        p.start()
        processes.append(p)
        
    for p in processes:
        p.join()
        
    # Once training is complete, we can test the model
    test(model, device, test_dataset, kwargs)

运行得到的评估结果为:

Test set: Global loss: 0.0325, Accuracy: 9898/10000 (99%)

可见该训练算法是收敛的。

3.2 收敛性分析

当采用不带锁的多线程的写入(即在更新\(w_j\)的时候不用先获取对\(w_j\)的访问权限),而这可能会导致导致同步错误[10]的问题。比如在线程\(1\)加载全局参数\(w^t_j\)之后,线程\(2\)还没等线程\(1\)存储全局参数更新后的值,就也对全局参数\(w^t_j\)进行加载,这样导致每个线程都会存储值为\(w^t_j - \eta^t g(w^t_j)\)的更新后的全局参数值,这样就导致其中一个线程的更新实际上在做“无用功”。直观的感觉是这应该会对学习的过程产生负面影响。不过,当我们对模型访问的稀疏性(sparity)做一定的限定后,这种访问冲突实际上是非常有限的。这正是Hogwild!算法收敛性存在的理论依据。

假设我们要最小化的损失函数为\(l: \mathcal{W}\rightarrow \mathbb{R}\),对于特定的训练样本集合,损失函数\(l\)是由一系列稀疏子函数组合而来的:

\[l(w) = \sum_{e\in E}f_e(w_e) \]

也就是说,实际的学习过程中,每个训练样本涉及的参数组合\(e\)只是全体参数集合中的一个很小的子集。我们可以用一个超图\(G=(V, E)\)来表述这个学习过程中参数和参数之间的关系,其中节点\(v\)表示参数,而超边\(e\)表示训练样本涉及的参数组合。那么,稀疏性可以用下面几个统计量加以表示:

\[\Omega:=\max_{e\in E}|e|\\ \Delta:=\frac{\underset{1\leqslant v \leqslant n}{\max}|\{e\in E: v\in e\}|}{|E|}\\ \rho:=\frac{\underset{e\in E}{\max}|\{\hat{e}\in E: \hat{e}\cap e \neq \emptyset \}|}{|E|} \]

其中,\(\Omega\)表达了最大超边的大小,也就是单个样本最多涉及的参数个数;\(\Delta\)反映的是一个参数最多可以涉及多少个不同的超边;而\(\rho\)则反映了给定任意一个超边,与其共享参数的超边个数。这三个值的取值越小,则优化问题越稀疏。在\(\Omega\)\(\Delta\)\(\rho\)都比较小的条件下,Hogwild!算法的收敛性保证还需要假设损失函数是凸函数,并且是Lipschitz连续的,详细的理论证明和定量关系请参考文献[2]

参考

  • [1] Agarwal A, Duchi J C. Distributed delayed stochastic optimization[J]. Advances in neural information processing systems, 2011, 24.

  • [2] Recht B, Re C, Wright S, et al. Hogwild!: A lock-free approach to parallelizing stochastic gradient descent[J]. Advances in neural information processing systems, 2011, 24.

  • [3] 刘浩洋,户将等. 最优化:建模、算法与理论[M]. 高教出版社, 2020.

  • [4] 刘铁岩,陈薇等. 分布式机器学习:算法、理论与实践[M]. 机械工业出版社, 2018.

  • [5] Stanford CME 323: Distributed Algorithms and Optimization (Lecture 7)

  • [6] Bryant R E等.《深入理解计算机系统》[M]. 机械工业出版社, 2015.