Log-Scale Quantization in Distributed First-Order Methods: Gradient-based Learning from Distributed Data

Abstract: Decentralized strategies are of interest for learning from large-scale data over networks. This paper studies learning over a network of geographically distributed nodes/agents subject to quantization. Each node possesses a private local cost function, collectively contributing to a global cost function, which the considered methodology aims to minimize. In contrast to many existing papers, the information exchange among nodes is log-quantized to address limited network-bandwidth in practical situations. We consider a first-order computationally efficient distributed optimization algorithm (with no extra inner consensus loop) that leverages node-level gradient correction based on local data and network-level gradient aggregation only over nearby nodes. This method only requires balanced networks with no need for stochastic weight design. It can handle log-scale quantized data exchange over possibly time-varying and switching network setups. We study convergence over both structured networks (for example, training over data-centers) and ad-hoc multi-agent networks (for example, training over dynamic robotic networks). Through experimental validation, we show that (i) structured networks generally result in a smaller optimality gap, and (ii) log-scale quantization leads to a smaller optimality gap compared to uniform quantization.