Robust Multi-agent Optimization: Coping with Byzantine Agents with Input Redundancy

Abstract

This paper addresses the multi-agent optimization problem in which the agents try to collaboratively minimize $\frac{1}{k}\sum _{i=1}^k h_i$ for a given choice of k input functions $h_1, \ldots , h_k$. This problem finds its application in distributed machine learning, where the data set is too large to be processed and stored by a single machine. It has been shown that when the networked agents may suffer Byzantine faults, it is impossible to minimize $\frac{1}{k}\sum _{i=1}^k h_i$ with no redundancy in the local cost functions.

We are interested in the impact of the local cost functions redundancy on the solvability of $\frac{1}{k}\sum _{i=1}^k h_i$. In particular, we assume that the local cost function of each agent is formed as a convex combination of the k input functions $h_1, \ldots , h_k$. Depending on the availability of side information at each agent, two slightly different variants are considered. We show that for a given graph, the problem can indeed be solved despite the presence of faulty agents. In particular, even in the absence of side information at each agent, when adequate redundancy is available in the optima of input functions, a distributed algorithm is proposed in which each agent carries minimal state across iterations.

This research is supported in part by National Science Foundation awards NSF 1329681 and 1421918. Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the funding agencies or the U.S. government.