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Decentralized optimization has found a significant utility in recent years,as a promising technique to overcome the curse of dimensionality when dealingwith large-scale inference and decision problems in big data. While thesealgorithms are resilient to node and link failures, they however, are notinherently Byzantine fault-tolerant towards insider data injection attacks.This paper proposes a decentralized robust subgradient push (RSGP) algorithmfor detection and isolation of malicious nodes in the network for optimizationnon-strongly convex objectives. In the attack considered in this work, themalicious nodes follow the algorithmic protocols, but can alter their localfunctions arbitrarily. However, we show that in sufficiently structuredproblems, the method proposed is effective in revealing their presence. Thealgorithm isolates detected nodes from the regular nodes, thereby mitigatingthe ill-effects of malicious nodes. We also provide performance measures forthe proposed method.

Detection and Isolation of Adversaries in Decentralized Optimization for Non-Strongly Convex Objectives