Coded Stochastic ADMM for Decentralized Consensus Optimization With Edge Computing

Abstract

Big data, including applications with high security requirements, are often collected and stored on multiple heterogeneous devices, such as mobile devices, drones, and vehicles. Due to the limitations of communication costs and security requirements, it is of paramount importance to analyze information in a decentralized manner instead of aggregating data to a fusion center. To train large-scale machine learning models, edge/fog computing is often leveraged as an alternative to centralized learning. We consider the problem of learning model parameters in a multiagent system with data locally processed via distributed edge nodes. A class of minibatch stochastic alternating direction method of multipliers (ADMMs) algorithms is explored to develop the distributed learning model. To address two main critical challenges in distributed learning systems, i.e., communication bottleneck and straggler nodes (nodes with slow responses), error-control-coding-based stochastic incremental ADMM is investigated. Given an appropriate minibatch size, we show that the minibatch stochastic ADMM-based method converges in a rate of O(1/ √ k), where k denotes the number of iterations. Through numerical experiments, it is revealed that the proposed algorithm is communication efficient, rapidly responding, and robust in the presence of straggler nodes compared with state-of-the-art algorithms.

Coding for Large-Scale Distributed Machine Learning

“…Meanwhile, it is inefficient (sometimes even infeasible) to transmit all data to a central node for analysis. For the reason, distributed machine learning (DML), which stores and processes all or parts of data in different nodes, has attracted significant research interests and applications [ 1 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 ]. There are different methods of implementing DML, i.e., primal method (e.g., distributed gradient descend [ 4 , 7 ], federated learning [ 5 , 6 ]) and primal–dual method (e.g., alternating direction method of multipliers (ADMM)) [ 16 ].…”

“…For the global consensus, network coding can be used to reduce the communication loads and increase reliability. In [ 15 ], we preliminarily investigated how coding (MDS codes) can be used in local optimization (step (a)). A more detailed introduction is given as follows.…”

Adaptive Stochastic ADMM for Decentralized Reinforcement Learning in Edge Industrial IoT

“…The global variable 𝑧 𝑘+1 and gradient estimation 𝜇 𝑘+1 get updated at agent 𝑖 𝑘 and passed as tokens to its neighbour 𝑖 𝑘+1 through Hamiltonian cycle. When {𝜂 𝑘 = 0|𝑘 = 1, 2, ...}, the algorithm reduces to the vanilla stochastic incremental ADMM (sI-ADMM) as in [45]. Comparing with sI-ADMM, asI-ADMM constructs stochastic gradient 𝜇 𝑘+1 based on the information 𝐺 𝑖 𝑘 (𝜽 𝑘 𝑖 𝑘 ; 𝜻 𝑘 𝑖 𝑘 ) and 𝜇 𝑘 , while sI-ADMM only considers the current mini-batch gradient.…”

Performance Optimization of Distributed Primal-Dual Algorithms over Wireless Networks

“…Distributed optimization algorithms have two main classes: distributed primal algorithm [4]- [7] and distributed primaldual algorithm [8]- [12]. In [4], the authors proposed fast distributed gradient algorithms to minimize the sum of individual cost function.…”

“…A variant ADMM algorithm was proposed in [11], which has less communication overhead but with the same convergence rate of standard ADMM. To further reduce the communication overhead, the authors in [12] investigated coding for stochastic incremental distributed primal-dual algorithm. However, the above distributed primal-dual works [8]- [12] all ignored the affect of wireless factors (such as transmission error) when implementing distributed primal-dual algorithm over wireless communications.…”