Communication-Efficient Distributed Optimization with Adaptability to System Heterogeneity

We consider the setting of agents cooperatively minimizing the sum of local objectives plus a regularizer on a graph. This paper proposes a primal-dual method in consideration of three distinctive attributes of real-life multi-agent systems, namely: (i) expensive communication, (ii) lack of synchronization, and (iii) system heterogeneity. In specific, we propose a distributed asynchronous algorithm with minimal communication cost, in which users commit variable amounts of local work on their respective subproblems. We illustrate this both theoretically and experimentally in the machine learning setting, where the agents hold private data and use a stochastic Newton method as the local solver. Under standard assumptions on Lipschitz continuous gradients and strong convexity, our analysis establishes linear convergence in expectation and characterizes the dependency of the rate on the number of local iterations. We proceed a step further to propose a simple means for tuning agents' hyperparameters locally, so as to adjust to heterogeneity and accelerate the overall convergence. Last, we validate our proposed method on a benchmark machine learning dataset to illustrate the merits in terms of computation, communication, and run-time saving as well as adaptability to heterogeneity.