Adaptive Top-K in SGD for Communication-Efficient Distributed Learning in Multi-Robot Collaboration

Distributed stochastic gradient descent (D-SGD) with gradient compression has become a popular communication-efficient solution for accelerating optimization procedures in distributed learning systems like multi-robot systems. One commonly used method for gradient compression is Top-K sparsification, which sparsifies the gradients by a fixed degree during model training. However, there has been a lack of an adaptive approach with a systematic treatment and analysis to adjust the sparsification degree to maximize the potential of the model's performance or training speed. This paper proposes a novel adaptive Top-K in Stochastic Gradient Descent framework that enables an adaptive degree of sparsification for each gradient descent step to optimize the convergence performance by balancing the trade-off between communication cost and convergence error with respect to the norm of gradients and the communication budget. Firstly, an upper bound of convergence error is derived for the adaptive sparsification scheme and the loss function. Secondly, we consider communication budget constraints and propose an optimization formulation for minimizing the deep model's convergence error under such constraints. We obtain an enhanced compression algorithm that significantly improves model accuracy under given communication budget constraints. Finally, we conduct numerical experiments on general image classification tasks using the MNIST, CIFAR-10 datasets. For the multi-robot collaboration tasks, we choose the object detection task on the PASCAL VOC dataset. The results demonstrate that the proposed adaptive Top-K algorithm in SGD achieves a significantly better convergence rate compared to state-of-the-art methods, even after considering error compensation.