Lower Bounds and Accelerated Algorithms in Distributed Stochastic Optimization with Communication Compression
This work addresses the communication bottleneck in large-scale distributed optimization, providing theoretical insights and a nearly optimal algorithm, though it is incremental as it builds on existing compressor types.
The paper tackles the problem of determining the optimal performance limits for distributed stochastic optimization with communication compression, establishing lower bounds for convergence rates across six settings and proposing NEOLITHIC, an algorithm that achieves these bounds up to logarithmic factors.
Communication compression is an essential strategy for alleviating communication overhead by reducing the volume of information exchanged between computing nodes in large-scale distributed stochastic optimization. Although numerous algorithms with convergence guarantees have been obtained, the optimal performance limit under communication compression remains unclear. In this paper, we investigate the performance limit of distributed stochastic optimization algorithms employing communication compression. We focus on two main types of compressors, unbiased and contractive, and address the best-possible convergence rates one can obtain with these compressors. We establish the lower bounds for the convergence rates of distributed stochastic optimization in six different settings, combining strongly-convex, generally-convex, or non-convex functions with unbiased or contractive compressor types. To bridge the gap between lower bounds and existing algorithms' rates, we propose NEOLITHIC, a nearly optimal algorithm with compression that achieves the established lower bounds up to logarithmic factors under mild conditions. Extensive experimental results support our theoretical findings. This work provides insights into the theoretical limitations of existing compressors and motivates further research into fundamentally new compressor properties.