Stochastic Optimization From Distributed Streaming Data in Rate-Limited Networks

Abstract

Motivated by machine learning applications in networks of sensors, Internet-of-Things devices, and autonomous agents, we propose techniques for distributed stochastic convex learning from high-rate data streams. The setup involves a network of nodes - each one of which has a stream of data arriving at a constant rate - that solve a stochastic convex optimization problem by collaborating with each other over rate-limited communication links. To this end, we present and analyze two algorithms - termed distributed stochastic approximation mirror descent (D-SAMD) and accelerated distributed stochastic approximation mirror descent (AD-SAMD) - that are based on two stochastic variants of mirror descent and in which nodes collaborate via approximate averaging of the local noisy subgradients using distributed consensus. Our main contributions are:1) bounds on the convergence rates of D-SAMD and AD-SAMD in terms of the number of nodes, network topology, and ratio of the data streaming and communication rates; and 2) sufficient conditions for order-optimum convergence of these algorithms. In particular, we show that for sufficiently well-connected networks, distributed learning schemes can obtain order-optimum convergence even if the communications rate is small. Furthermore, we find that the use of accelerated methods significantly enlarges the regime, in which order-optimum convergence is achieved; this is in contrast to the centralized setting, where accelerated methods usually offer only a modest improvement. Finally, we demonstrate the effectiveness of the proposed algorithms using numerical experiments.