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Title: Stochastic Gradient Push for Distributed Deep Learning

Paper content:
Large mini-batch parallel SGD is commonly used for distributed training of deep networks.
Approaches that use tightly-coupled exact distributed averaging based on AllReduce are sensitive to slow nodes and high-latency communication.
In this work we show the applicability of Stochastic Gradient Push (SGP) for distributed training.
SGP uses a gossip algorithm called PushSum for approximate distributed averaging, allowing for much more loosely coupled communications which can be beneficial in high-latency or high-variability scenarios.
The tradeoff is that approximate distributed averaging injects additional noise in the gradient which can affect the train and test accuracies.
We prove that SGP converges to a stationary point of smooth, non-convex objective functions.
Furthermore, we validate empirically the potential of SGP.
For example, using 32 nodes with 8 GPUs per node to train ResNet-50 on ImageNet, where nodes communicate over 10Gbps Ethernet, SGP completes 90 epochs in around 1.5 hours while AllReduce SGD takes over 5 hours, and the top-1 validation accuracy of SGP remains within 1.2% of that obtained using AllReduce SGD.
Deep Neural Networks (DNNs) are the state-of-the art machine learning approach in many application areas, including image recognition (He et al., 2016) and natural language processing (Vaswani et al., 2017) .
Stochastic Gradient Descent (SGD) is the current workhorse for training neural networks.
The algorithm optimizes the network parameters, x, to minimize a loss function, f (·), through gradient descent, where the loss function's gradients are approximated using a subset of training examples (a mini-batch).
DNNs often require large amounts of training data and trainable parameters, necessitating non-trivial computational requirements (Wu et al., 2016; Mahajan et al., 2018) .
There is a need for efficient methods to train DNNs in large-scale computing environments.A parallel version of SGD is usually adopted for large-scale, distributed training (Goyal et al., 2017; Li et al., 2014) .
Worker nodes compute local mini-batch gradients of the loss function on different subsets of the data, and then calculate an exact inter-node average gradient using either the ALLRE-DUCE communication primitive, in synchronous implementations (Goyal et al., 2017) , or using a central parameter server, in asynchronous implementations (Dean et al., 2012) .
Using a parameter server to aggregate gradients introduces a potential bottleneck and a central point of failure (Lian et al., 2017) .
The ALLREDUCE primitive computes the exact average gradient at all workers in a decentralized manner, avoiding issues associated with centralized communication and computation.However, exact averaging algorithms like ALLREDUCE are not robust in high-latency or highvariability platforms, e.g., where the network bandwidth may be a significant bottleneck, because they involve tightly-coupled, blocking communication (i.e., the call does not return until all nodes have finished aggregating).
Moreover, aggregating gradients across all the nodes in the network can introduce non-trivial computational overhead when there are many nodes, or when the gradients themselves are large.
This issue motivates the investigation of a decentralized and inexact version of SGD to reduce the overhead associated with distributed training.There have been numerous decentralized optimization algorithms proposed and studied in the control-systems literature that leverage consensus-based approaches to aggregate information; see the recent survey Nedić et al. (2018) and references therein.
Rather than exactly aggregating gradi-ents (as with ALLREDUCE), this line of work uses less-coupled message passing algorithms which compute inexact distributed averages.Most previous work in this area has focused on theoretical convergence analysis assuming convex objectives.
Recent work has begun to investigate their applicability to large-scale training of DNNs (Lian et al., 2017; Jiang et al., 2017) .
However, these papers study methods based on communication patterns which are static (the same at every iteration) and symmetric (if i sends to j, then i must also receive from j before proceeding).
Such methods inherently require blocking and communication overhead.
State-of-the-art consensus optimization methods build on the PUSHSUM algorithm for approximate distributed averaging (Kempe et al., 2003; Nedić et al., 2018) , which allows for non-blocking, time-varying, and directed (asymmetric) communication.
Since SGD already uses stochastic mini-batches, the hope is that an inexact average mini-batch will be as useful as the exact one if the averaging error is sufficiently small relative to the variability in the stochastic gradient.
This paper studies the use of Stochastic Gradient Push (SGP), an algorithm blending SGD and PUSHSUM, for distributed training of deep neural networks.
We provide a theoretical analysis of SGP, showing it converges for smooth non-convex objectives.
We also evaluate SGP experimentally, training ResNets on ImageNet using up to 32 nodes, each with 8 GPUs (i.e., 256 GPUs in total).
Our main contributions are summarized as follows:• We provide the first convergence analysis for Stochastic Gradient Push when the objective function is smooth and non-convex.
We show that, for an appropriate choice of the step size, SGP converges to a stationary point at a rate of O 1/ √ nK , where n is the number of nodes and K is the number of iterations.•
In a high-latency scenario, where nodes communicate over 10Gbps Ethernet, SGP runs up to 3× faster than ALLREDUCE SGD and exhibits 88.6% scaling efficiency over the range from 4-32 nodes.•
The top-1 validation accuracy of SGP matches that of ALLREDUCE SGD for up to 8 nodes (64 GPUs), and remains within 1.2% of ALLREDUCE SGD for larger networks.•
In a low-latency scenario, where nodes communicate over a 100Gbps InfiniBand network supporting GPUDirect, SGP is on par with ALLREDUCE SGD in terms of running time, and SGP exhibits 92.4% scaling efficiency.•
In comparison to other synchronous decentralized consensus-based approaches that require symmetric messaging, SGP runs faster and it produces models with better validation accuracy.

assistant: text: For distributed training over high-latency networks, use gossip-based approximate distributed averaging instead of exact distribute averaging like AllReduce.