Error Feedback Fixes SignSGD and other Gradient Compression Schemes (1901.09847v2)

Abstract: Sign-based algorithms (e.g. signSGD) have been proposed as a biased gradient compression technique to alleviate the communication bottleneck in training large neural networks across multiple workers. We show simple convex counter-examples where signSGD does not converge to the optimum. Further, even when it does converge, signSGD may generalize poorly when compared with SGD. These issues arise because of the biased nature of the sign compression operator. We then show that using error-feedback, i.e. incorporating the error made by the compression operator into the next step, overcomes these issues. We prove that our algorithm EF-SGD with arbitrary compression operator achieves the same rate of convergence as SGD without any additional assumptions. Thus EF-SGD achieves gradient compression for free. Our experiments thoroughly substantiate the theory and show that error-feedback improves both convergence and generalization. Code can be found at \url{https://github.com/epfml/error-feedback-SGD}.

• The paper reveals that signSGD fails to converge due to biased gradient compression, supported by clear counterexamples.
• The error feedback mechanism recovers lost gradient information, enabling convergence rates comparable to full SGD.
• Empirical results on benchmarks like CIFAR-10 validate enhanced generalization and reduced communication costs.

An Analysis of Error Feedback in Gradient Compression Schemes

The paper "Error Feedback Fixes SignSGD and other Gradient Compression Schemes" by Karimireddy et al. explores the efficacy of sign-based algorithms and proposes a refined approach to alleviate the communication bottleneck in distributed training of large neural networks. Through meticulous exploration, the authors contend both theoretically and experimentally that the application of error feedback significantly enhances the convergence and generalization of gradient-based methods that utilize biased compression schemes.

Overview of the Research

Sign-based algorithms such as signSGD have garnered attention due to their potential to compress gradients effectively. However, the authors identify crucial shortcomings of these methods—most notably, their inability to consistently converge to optimal solutions. To exemplify these claims, the authors construct simple convex counterexamples where signSGD fails to converge. Furthermore, even when convergence is achieved, signSGD may exhibit poor generalization compared to SGD owing to the biased nature of the sign compression operator.

The authors propose error feedback as a solution—an approach of integrating previously discarded error into the subsequent gradient updates. This method, denoted as ef-SGD, applies corrections that enable it to achieve convergence rates comparable to SGD without further assumptions. The suggested method achieves gradient compression "for free," meaning it retains the computational efficiency of gradient compression while addressing the convergence and generalization issues.

Key Contributions

1. Counterexamples and Non-Convergence: The paper illustrates that signSGD is flawed due to its inherent bias, failing to converge under certain conditions. The provision of specific convex and non-convex examples extends the understanding of these limitations.
2. Algorithmic Correction via Error Feedback: By incorporating error feedback, ef-SGD retains critical information lost during gradient compression. This augmentation allows the recovery of convergence characteristics akin to those of full SGD, independently of the compression schema utilized.
3. Rigorous Theoretical Analyses: The authors deliver comprehensive proofs that establish the equivalence in convergence rates between ef-SGD and SGD, supporting these with elaborate theoretical foundations within smooth and non-smooth optimization contexts.
4. Empirical Validation: Extensive experiments on benchmark datasets such as CIFAR-10 and CIFAR-100 underscore the efficacy of ef-SGD. These results demonstrate superior convergence and generalization, highlighting a substantial decrease in communication costs in comparison to standard methods.

Implications and Future Directions

The implications of this research in distributed deep learning are significant. By transforming a compression challenge into a manageable error feedback process, the authors contribute a viable route to enhance scalability without losing out on convergence speed or generalization ability.

Furthermore, the paper invites future exploration into the multi-worker scenario and more adaptive error management mechanisms. Investigating the interaction of ef-SGD with other adaptive methods, such as Adam, could also yield interesting insights, enriching our understanding of optimizing large-scale neural networks.

In summary, the introduction of error feedback into gradient compression schemes provides a robust correction mechanism for the challenges associated with biased compression algorithms such as signSGD. This paper is a vital piece of work for researchers and practitioners aiming to optimize distributed learning processes, especially in scenarios with communication constraints.