Asynchronous Stochastic Gradient Descent with Delay Compensation (1609.08326v6)

Abstract: With the fast development of deep learning, it has become common to learn big neural networks using massive training data. Asynchronous Stochastic Gradient Descent (ASGD) is widely adopted to fulfill this task for its efficiency, which is, however, known to suffer from the problem of delayed gradients. That is, when a local worker adds its gradient to the global model, the global model may have been updated by other workers and this gradient becomes "delayed". We propose a novel technology to compensate this delay, so as to make the optimization behavior of ASGD closer to that of sequential SGD. This is achieved by leveraging Taylor expansion of the gradient function and efficient approximation to the Hessian matrix of the loss function. We call the new algorithm Delay Compensated ASGD (DC-ASGD). We evaluated the proposed algorithm on CIFAR-10 and ImageNet datasets, and the experimental results demonstrate that DC-ASGD outperforms both synchronous SGD and asynchronous SGD, and nearly approaches the performance of sequential SGD.

Asynchronous Stochastic Gradient Descent with Delay Compensation

The paper "Asynchronous Stochastic Gradient Descent with Delay Compensation" introduces an advanced methodology designed to address a notorious challenge associated with asynchronous stochastic gradient descent (ASGD) in distributed deep learning systems: the delay of gradient updates. The proposed solution, Delay Compensated ASGD (DC-ASGD), seeks to enhance the efficiency and accuracy of ASGD by compensating for the delay using Taylor expansion and an efficient approximation of the Hessian matrix of the loss function.

Problem Context and Motivation

The ongoing evolution of deep neural networks (DNNs) demands scalable optimization techniques capable of handling extensive datasets across distributed computational architectures. ASGD stands out for its efficiency by allowing updates without synchronization constraints, unlike its synchronous counterpart, SSGD. However, ASGD attempts to integrate gradients based on stale model parameters, leading to potentially incoherent gradient updates. These delayed gradients can impair convergence speed and accuracy, presenting a formidable obstacle in realizing the full potential of distributed deep learning.

DC-ASGD: Methodological Contributions

The authors propose DC-ASGD to mitigate the adverse effects of delayed gradients. The method is built upon the observation that gradients computed at stale parameters can be adjusted using higher-order information derived from Taylor expansion. Specifically, the first-order Taylor approximation is employed to refine these gradients more accurately, using additional terms that require estimating the Hessian matrix. Given the computational challenge inherent in directly computing the Hessian matrix in high-dimensional spaces typical of DNNs, the authors develop a computationally feasible approximation.

1. Gradient Decomposition via Taylor Expansion: The core of DC-ASGD is employing a Taylor series expansion to approximate the gradient at the current parameter configuration. This approach aligns the optimization steps more closely with the intended ASGD trajectory by incorporating compensation terms that address the delay.
2. Efficient Hessian Approximation: Recognizing the prohibitive cost of direct Hessian computation, the authors introduce a technique using the outer product of gradients. This substitute captures the essential curvature information, enabling effective delay compensation without excessive computational overhead. The paper demonstrates that with adequate scaling, this approximation minimizes both bias and variance in gradient estimates.

Theoretical and Empirical Validation

The paper provides a rigorous theoretical foundation for DC-ASGD, proving that the method maintains convergence rates akin to those of sequential SGD under bounded delay conditions. Empirically, DC-ASGD outperformed existing algorithms on CIFAR-10 and ImageNet tasks, demonstrating superior convergence speed and accuracy. It notably achieves comparability with, and occasionally surpasses, sequential SGD in terms of model accuracy, particularly when adaptive techniques are employed to stabilize gradient variance.

Implications and Future Directions

While the proposed DC-ASGD algorithm bridges the performance gaps caused by delayed gradients in ASGD, its implications extend beyond immediate improvements in convergence rates. By demonstrating how higher-order gradient information can be effectively utilized in distributed settings, the paper suggests pathways for integrating more complex optimization strategies within existing frameworks without incurring prohibitive computational costs.

Further exploration is warranted to extend this methodology to even larger computational clusters where latency and resource allocation are of greater concern. Additionally, integrating higher-order compensations and exploring adaptive schemes that adjust the degree of approximation dynamically could lead to even more robust distributed optimization methods in neural network training.

In summary, DC-ASGD represents a significant step forward in overcoming some of the fundamental challenges associated with distributed asynchronous optimization in deep learning. Through sophisticated mathematical modeling and empirical validation, the paper enriches the toolkit available for researchers and practitioners seeking to leverage large-scale distributed environments for training complex neural networks.