Recently, researchers proposed various low-precision gradient compression, for efficient communication in large-scale distributed optimization. Based on these work, we try to reduce the communication complexity from a new direction. We pursue an ideal bijective mapping between two spaces of gradient distribution, so that the mapped gradient carries greater information entropy after the compression. In our setting, all servers should share a reference gradient in advance, and they communicate via the normalized gradients, which are the subtraction or quotient, between current gradients and the reference. To obtain a reference vector that yields a stronger signal-to-noise ratio, dynamically in each iteration, we extract and fuse information from the past trajectory in hindsight, and search for an optimal reference for compression. We name this to be the trajectory-based normalized gradients (TNG). It bridges the research from different societies, like coding, optimization, systems, and learning. It is easy to implement and can universally combine with existing algorithms. Our experiments on benchmarking hard non-convex functions, convex problems like logistic regression demonstrate that TNG is more compression-efficient for communication of distributed optimization of general functions.
Researchers proposed protocols from other perspectives to reduce communication. A prevailing method is to average parameter occasionally, but not too frequent @cite_25 @cite_43 , or just one round of averaging over final parameters @cite_29 . If the problems require the servers to frequently synchronized, we can use an asynchronous protocol like parameter servers @cite_28 @cite_6 , where each server requests the latest parameter from the main server or contributes its gradients, passively or aggressively, based on the network condition; the decentralized optimization algorithms @cite_4 @cite_27 @cite_39 view every servers equally, to avoid the congestion of communication since the main server takes over most of the requests and causing unbalance. Efficiently using a large batch-size @cite_17 @cite_26 @cite_34 @cite_21 or the second-order gradient will reduce the communication since the overall number of iterations, and therefore reduce commnunication.the model synchronization can also be formulated as a global consensus problem @cite_18 with penalty of delay. Besides, the normalization idea was also used in other areas, like normalized gradient descent for general convex or quasi-convex optimization @cite_19 @cite_7 ; on different subjects, normalization helps to stablize the feature or gradient distribution in neural networks @cite_44 @cite_30 @cite_0 @cite_2 .
@cite_30 @cite_29 @cite_44 @cite_43 @cite_2 @cite_18 @cite_4 @cite_21 @cite_39 @cite_17 @cite_26 @cite_7 @cite_28 @cite_6 @cite_19 @cite_27 @cite_34 @cite_25 @cite_0
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We consider distributed plurality consensus in a complete graph of size @math with @math initial opinions. We design an efficient and simple protocol in the asynchronous communication model that ensures that all nodes eventually agree on the initially most frequent opinion. In this model, each node is equipped with a random Poisson clock with parameter @math . Whenever a node's clock ticks, it samples some neighbors, uniformly at random and with replacement, and adjusts its opinion according to the sample. A prominent example is the so-called two-choices algorithm in the synchronous model, where in each round, every node chooses two neighbors uniformly at random, and if the two sampled opinions coincide, then that opinion is adopted. This protocol is very efficient and well-studied when @math . If @math for some small @math , we show that it converges to the initial plurality opinion within @math rounds, w.h.p., as long as the initial difference between the largest and second largest opinion is @math . On the other side, we show that there are cases in which @math rounds are needed, w.h.p. One can beat this lower bound in the synchronous model by combining the two-choices protocol with randomized broadcasting. Our main contribution is a non-trivial adaptation of this approach to the asynchronous model. If the support of the most frequent opinion is at least @math times that of the second-most frequent one and @math , then our protocol achieves the best possible run time of @math , w.h.p. We relax full synchronicity by allowing @math nodes to be poorly synchronized, and the well synchronized nodes are only required to be within a certain time difference from one another. We enforce this synchronicity by introducing a novel gadget into the protocol. We revisit the classic problem of spreading a piece of information in a group of @math n fully connected processors. By suitably adding a small dose of randomness to the protocol of Gasieniec and Pelc (Parallel Comput 22:903---912, 1996), we derive for the first time protocols that (i) use a linear number of messages, (ii) are correct even when an arbitrary number of adversarially chosen processors does not participate in the process, and (iii) with high probability have the asymptotically optimal runtime of @math O(logn) when at least an arbitrarily small constant fraction of the processors are working. In addition, our protocols do not require that the system is synchronized nor that all processors are simultaneously woken up at time zero, they are fully based on push-operations, and they do not need an a priori estimate on the number of failed nodes. Our protocols thus overcome the typical disadvantages of the two known approaches, algorithms based on random gossip (typically needing a large number of messages due to their unorganized nature) and algorithms based on fair workload splitting (which are either not time-efficient or require intricate preprocessing steps plus synchronization). We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes (local workers), is based on an elastic force which links the parameters they compute with a center variable stored by the parameter server (master). The algorithm enables the local workers to perform more exploration, i.e. the algorithm allows the local variables to fluctuate further from the center variable by reducing the amount of communication between local workers and the master. We empirically demonstrate that in the deep learning setting, due to the existence of many local optima, allowing more exploration can lead to the improved performance. We propose synchronous and asynchronous variants of the new algorithm. We provide the stability analysis of the asynchronous variant in the round-robin scheme and compare it with the more common parallelized method ADMM. We show that the stability of EASGD is guaranteed when a simple stability condition is satisfied, which is not the case for ADMM. We additionally propose the momentum-based version of our algorithm that can be applied in both synchronous and asynchronous settings. Asynchronous variant of the algorithm is applied to train convolutional neural networks for image classification on the CIFAR and ImageNet datasets. Experiments demonstrate that the new algorithm accelerates the training of deep architectures compared to DOWNPOUR and other common baseline approaches and furthermore is very communication efficient. We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes (local workers), is based on an elastic force which links the parameters they compute with a center variable stored by the parameter server (master). The algorithm enables the local workers to perform more exploration, i.e. the algorithm allows the local variables to fluctuate further from the center variable by reducing the amount of communication between local workers and the master. We empirically demonstrate that in the deep learning setting, due to the existence of many local optima, allowing more exploration can lead to the improved performance. We propose synchronous and asynchronous variants of the new algorithm. We provide the stability analysis of the asynchronous variant in the round-robin scheme and compare it with the more common parallelized method ADMM. We show that the stability of EASGD is guaranteed when a simple stability condition is satisfied, which is not the case for ADMM. We additionally propose the momentum-based version of our algorithm that can be applied in both synchronous and asynchronous settings. Asynchronous variant of the algorithm is applied to train convolutional neural networks for image classification on the CIFAR and ImageNet datasets. Experiments demonstrate that the new algorithm accelerates the training of deep architectures compared to DOWNPOUR and other common baseline approaches and furthermore is very communication efficient.