In recent years, communication compression techniques have become increasingly important in overcoming the communication bottleneck in distributed learning. These techniques help to reduce the amount of data that needs to be transmitted between nodes, improving the efficiency of distributed training. While unbiased compressors have been extensively studied in the literature, biased compressors have received much less attention.
In this work, the authors investigate three classes of biased compression operators, two of which are novel, and examine their performance in the context of stochastic gradient descent and distributed stochastic gradient descent. The key finding of this study is that biased compressors can achieve linear convergence rates in both single node and distributed settings.
The authors provide a theoretical analysis of a distributed compressed SGD method with an error feedback mechanism. They establish that this method has an ergodic convergence rate that can be bounded by a term involving the compression parameter $delta$, the smoothness constant $L$, the strong convexity constant $mu$, as well as the stochastic gradient noise $C$ and the gradient variance $D$. This result provides a theoretical justification for the effectiveness of biased compressors in distributed learning scenarios.
In addition to the theoretical analysis, the authors also conduct experiments using synthetic and empirical distributions of communicated gradients. These experiments shed light on why and to what extent biased compressors outperform their unbiased counterparts. The results highlight the potential benefits of using biased compressors in practical applications.
Finally, the authors propose several new biased compressors that offer both theoretical guarantees and promising practical performance. These new compressors could potentially be adopted in distributed learning systems to further improve convergence rates and reduce communication overhead.
In summary, this work contributes to the understanding of biased compression operators in distributed learning. The findings suggest that biased compressors can lead to improved convergence rates, making them an attractive option for reducing communication overhead in distributed training. The proposed theoretical analysis and new compressors provide valuable insights and practical solutions for optimizing distributed learning systems.